1. Introduction

Sea surface temperature (SST) is a geophysical variable that plays a major role in weather forecasting, hurricane prediction, oceanography, climate studies, and fisheries management. SST measurements derived from satellite instruments include uncertainties that degrade its usefulness for studies dependent on highly accurate SST retrievals and for downstream processing of SST imagery. This degradation affects detection of thermal fronts and understanding of their seasonal and decadal variability (Belkin and Cornillon 2005; Kahru et al. 2012). One major source of uncertainty is the sensor radiometric calibration performance and more specifically the existence of stripe noise in clear-sky top-of-the-atmosphere (TOA) calibrated radiances or brightness temperatures (BTs) used for the production of SST maps. Stripe noise, also referred to as striping or scan line noise, is an artifact that generally appears in images as a high-frequency unidirectional pattern. It is an inevitable consequence of the acquisition principle used in pushbroom and whiskbroom scanners, where one dimension of the image is obtained using multiple detectors, while the other is continuously generated by the satellite orbital motion. Regardless of its nature (i.e., radiometric, spectral, or electronic), the nonuniformity of the detectors’ response induces artificial spatial variations either in the entire image or in a restricted subdomain, that is, a particular range of BTs.

In whiskbroom scanners such as the Moderate Resolution Imaging Spectroradiometer (MODIS) or the Visible Infrared Imaging Radiometer Suite (VIIRS), some degree of striping is expected despite extensive prelaunch characterization and postlaunch onboard calibration (Cao et al. 2013). In MODIS and VIIRS, the radiometric response of individual detectors is adjusted with a two-point calibration strategy. Using the blackbody and space view as uniform stable radiation targets, calibration coefficients derived on a scan-by-scan basis should compensate for detectors’ nonuniformity and account for potential temporal degradations. Although this approach may reduce scan line errors, it does not guarantee full mitigation of the striping effect. At best, level 1B data [termed the sensor data records (SDRs) for VIIRS] may visually appear as stripe free. Even when compliant with sensor prelaunch uniformity requirements, as is the case for VIIRS (Cao et al. 2013), these hardly discernible residual stripes can be amplified by level 2 algorithms and propagate into SST products. In fact, the correction of atmospheric effects (mostly water vapor) for SST retrieval typically uses split-window techniques that reduce signal-to-stripe noise ratios (SSNR) in BT differences. Moreover, SST formulations such as the nonlinear SST (NLSST) algorithm multiply the differential term (customarily the BT difference: 11–12 and 3.7–12 μm) by a first-guess SST, which in turn acts as a noise amplifier. Consequently, it is necessary to reduce striping at level 1 to generate full-sensor-resolution SST products with both improved radiometric accuracy and image quality.

Destriping is similar to so-called nonuniformity correction (NUC) algorithms, better known in the context of ground-based infrared imaging cameras. NUC techniques are dedicated to the correction of pronounced fixed pattern noise (which is not necessarily unidirectional) and share conceptual similarities with destriping methods that will not be discussed in this paper. Readers are referred to Tendero and Gilles (2012) for an up-to-date approach and an overview on the NUC literature.

Research in satellite imagery destriping has been an ongoing effort since the Multispectral Scanner (MSS) launched onboard Landsat-1 in 1972. Algorithms developed for the reduction of stripe noise in satellite imagery can be divided into two major categories, equalization and scene-based methods.

Equalization techniques take into account the acquisition principle of the instrument and attempt to adjust the radiometric response of individual detectors. When an absolute reference is not available or when it is not accurate enough (as it is the case for scan-by-scan-based calibration), destriping can be done using statistical models. For whiskbroom scanners, images derived from separate detectors are assumed to have similar statistics. This leads to estimating linear correction factors—that is, gains and offsets using the moment-matching method (Horn and Woodham 1979) or normalization lookup tables (NLUT) with the histogram-matching approach (Horn and Woodham 1979; Weinreb et al. 1989). The validity of the “detectors viewing the same scene” assumption is improved by restricting the computation of statistical parameters only to homogeneous areas (Gadallah and Csillag 2000; Wegener 1990). Other equalization techniques include the algorithms developed in Corsini et al. (2000) and Franz (1998) for the destriping of model output statistics B (MOS-B) data, in Lyon (2009) for the Ocean Color Monitor (OCM), and the bowtie-based equalization approach described in Antonelli et al. (2004) and Bisceglie et al. (2009) for MODIS data.

Scene-based methods represent a substantial fraction of the destriping literature. The periodic aspect of striping observed in instruments such as the Landsat MSS, the Landsat Thematic Mapper (TM), and the Geostationary Operational Environmental Satellite (GOES) has triggered a strong interest in the design of destriping algorithms based on standard image filtering. Low-pass and finite-impulse-response filters implemented in the spatial or frequency domain were explored in Srinivasan et al. (1988), Crippen (1989), Pan and Chang (1992), Simpson et al. (1995, 1998), Chen et al. (2003). Unfortunately, these methods are known to result in a large amount of blur and ringing artifacts that confine their use to simple cosmetic applications. Alternative filtering techniques have also been devised from multiresolution analysis using wavelets (Torres and Infante 2001; Yang et al. 2003). The multidirectional aspect of bidimensional wavelet decomposition enables the thresholding of only horizontal wavelet coefficients prior to reconstruction, thus limiting distortion in restored signals. More recent variational methods are well suited for ill-posed inverse problems such as destriping. Gradient field integration (Frankot and Chellappa 1988) and gradient domain manipulation (Bhat et al. 2008) techniques, although mainly oriented toward computer vision and graphics, were the starting point of the destriping algorithm described in Bouali (2010). The resulting variational destriping model cannot be used for images with different classes of geophysical objects, because the standard L² norm introduces blurring artifacts along sharp discontinuities. Exploiting further the unique geometrical characteristics of stripe noise, Bouali and Ladjal (2010, 2011) introduced an edge-preserving model based on unidirectional variations. The algorithm is able to provide optimal performance in MODIS spectral bands severely affected with striping. It was recently used for the intersensor uniformity performance comparisons of MODIS and VIIRS SST bands (Bouali and Ignatov 2012a) and the estimation of detector biases in MODIS thermal emissive bands (Bouali and Ignatov 2012b). We note that the benefit of the L¹ norm used in the model comes at the price of extensive computational time compared to standard quadratic models. This major drawback for near-real-time processing of large image datasets has prompted the design of the algorithm described in this paper.

The Advanced Clear-Sky Processor for Ocean (ACSPO) is the current operational retrieval system developed at the National Oceanic and Atmospheric Administration (NOAA)’s National Environmental Satellite, Data, and Information Service (NESDIS) by the Center for Satellite Applications and Research (STAR) and the Office of Satellite and Product Operations (OSPO). It generates clear-sky radiances and SSTs from BTs observed with the Advanced Very High Resolution Radiometer (AVHRR) on board NOAA and Meteorological Operational (MetOp) satellites, MODIS on board Terra and Aqua, and more recently VIIRS on board the Suomi National Polar-Orbiting Partnership (S-NPP) platform. Currently, no preprocessing is applied to level 1 BTs, which leads to SST products affected with stripe noise. To improve the quality of full-sensor-resolution SST maps, an automatic adaptive destriping algorithm was developed at NESDIS for future operational use within the ACSPO system. The algorithm was applied to level 1 BTs and was shown to 1) reduce substantially the degree of striping in derived SST products; 2) keep signal distortion at a minimal level—that is, the geometrical features of SST images remain intact after the destriping; and 3) perform in near–real time, a major requirement for its operational use. This paper is organized as follows: In section 2, we provide a detailed technical description of the destriping methodology. We also discuss the evaluation of image quality improvement and define two quantitative metrics to assess the performance of the stripe reduction algorithm. Section 3 provides information on the data used for this study and reports all the necessary results that demonstrate the benefits of destriping BTs on level 1B/SDR data prior to SST production. Section 4 concludes this paper.

2. Algorithm

a. Noise model

In the following, we will consider images as bidimensional functions defined in Ω, a bounded domain of ℝ². The image degradation model can be expressed as follows:

View Expanded

where

• (x, y) are the Cartesian coordinates of a pixel in ,

• f(x, y) is the observed signal at pixel (x, y),

• η(x, y) is the stripe noise, and

• u(x, y) is the true signal to be estimated.

In many image perturbation models, the term η in (1) is modeled as a white Gaussian noise with zero mean. In the case of stripe noise, however, geometrical considerations are more valuable than statistical assumptions. For instance, striping is a highly anisotropic noise and affects only one component of the image gradient field. This simple observation can be highly useful if incorporated properly in a variational-based denoising scheme. We also note that unlike fixed pattern noise in IR cameras, striping in a whiskbroom scanner is not fully unidirectional, in that it does not represent a constant offset for a given scan line. For example, a VIIRS scan is obtained with a double-sided, continuously rotating mirror that covers ±56° rotational sector in 0.55 s. This time interval is large enough for electronic–optical components or mechanical vibrations to interfere with detectors’ response and to modify the amplitude of stripe noise within a single scan.

b. Directional hierarchical decomposition

In Tadmor et al. (2004), the authors introduced a novel approach [Tadmor–Nezzar–Vese (TNV)] to decompose an image lying in BV space (space of functions of bounded variation) into a sum of images defined in the intermediate (BV, L²) space. The resulting decomposition scheme leads to a set of images with scale-dependent texture. The multiscale stratification is achieved by successively solving the well-known Rudin–Osher–Fatemi (ROF) model (Rudin et al. 1992) using dyadic Lagrange multipliers. The TNV approach can be generalized to functionals other than the original ROF model. In the following, we propose a decomposition strategy similar to the TNV methodology but restricted to the L² space and exploiting image gradient fields. Given that stripe noise mainly affects the gradient of the observed image in the along-track direction, we suggest using a data fidelity term associated with the gradient in the cross-track direction, while the regularization is applied to the along-track direction. We consider the following variational decomposition:

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where ∂_x and ∂_y denote the partial derivatives in the cross-track and along-track directions, respectively; λ₀ is a positive coefficient, and the “⋅” symbol in the second term of the energy functional represents an element-by-element multiplication. The matrix alleviates the problem of using the L² norm over the L¹ norm. It limits the introduction of blur artifacts by retaining the values of the gradient field along sharp discontinuities. To distinguish homogeneous regions from sharp edges, is defined using a threshold on the image gradient norm as

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For SST applications, a threshold of ε = 0.8 K km⁻¹ was determined empirically for signals corresponding to VIIRS BTs at the resolution of 0.75 km. In addition to highly uniform cloud, desert, and homogeneous ice regions, this threshold is able to preserve all ocean pixels including sharp thermal fronts associated with ocean upwelling events and eddies. The minimization of (2) decomposes the noisy observation f into an initial estimate u₀ and a term υ₀ composed of striping and additional scale-dependent information we wish to retrieve. To do so, the variational decomposition is further extended by replacing the initial observation f with the initial noisy estimate υ₀ and by refining the Lagrange multiplier λ₀. This can be achieved by solving

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which leads to another formulation of the noisy observation as f = u₀ + u₁ + υ₁. Iterating this decomposition framework results in a directional hierarchical decomposition (DHD) that boils down, at iteration k, to the minimization of

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It follows that the hierarchical expansion of f takes a multilayered form as

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The DHD offers a major advantage for the reduction of striping. In fact, it acts as a directional filter in the spatial domain that progressively retrieves cross-track variations in the term υ_k while isolating the stripe noise in its high-frequency domain. Smoothing of the noisy signal υ_k instead of the image f then leads to an estimate of the true scene with minimum distortion. One point to be addressed is the number of iterations required in the decomposition scheme. As the number of iterations tends to infinity, the Lagrange multiplier λ₀.2^−k converges to 0 and [u_k, υ_k] converge to one solution of the ill-conditioned problem:

View Expanded

which is given by u_k = υ_k + , where the matrix represents one constant per line—that is,

View Expanded

Given that striping is generally not constant over a scan line, the decomposition scheme should be stopped before the horizontal variations of the stripe noise are retrieved in the term u₀ + … + u_N. To determine a stopping criterion, we simply rely on the amount of useful information remaining in the term υ_N. This is achieved by continuously monitoring a given metric throughout the hierarchical decomposition and stopping at the iteration where a satisfactory percentage of information has been retrieved in the term u₀ + … + u_N.

c. Nonlocal filtering

The iterative minimization of the energy functional (2) leads to a practical separation of anisotropic noise from other high-frequency structures of f (Bouali 2010). The term υ_N, in addition to striping, also contains a low-frequency component that has to be retrieved for the estimation of the true scene. Although the use of a simple low-pass filter may be appealing given the homogeneity of the term υ_N (imposed by the iterative process as well as the binary matrix ), it can also lead to errors if multiple classes of uniform geophysical objects coexist in the same image. This is typically the case when smooth cirrus clouds spatially blend with surrounding clear-sky pixels without creating sharp gradients. A simplistic filtering of υ_N in the spatial domain could then erroneously propagate cold BT values of cirrus clouds into clear-sky pixels. To overcome this limitation, the smoothing of υ_N should take into account large differences between pixel values. Furthermore, additional a priori knowledge of the striping characteristics could be highly beneficial if incorporated in the smoothing of υ_N. This a priori information includes 1) an estimate of expected stripe noise magnitude [e.g., derived from prelaunch radiometric calibration or on-orbit characterization of noise equivalent difference temperature (NEΔT), the minimal temperature variation resolved by the sensor detectors]; and 2) the geometrical signature of striping in the imagery, which depends on the number of detectors in the focal plane assembly (FPA). These two points motivate the use of nonlocal filtering. Nonlocal techniques, also known as neighborhood filters, are increasingly popular and their application to image denoising problems have demonstrated good performance compared to traditional methods. This class of methods does not use the common assumption of locally smooth signals but relies instead on the high degree of nonlocal self-similarity observed in natural images. The concept of neighborhood is extended beyond the spatial domain, and the value of a noisy pixel is computed as a weighted average of pixels that are similar in a certain sense. Similarity is measured by a weighting function that may include spatial distances (Lee 1983), radiometric distances (Yaroslavsky 1987)—both as in the bilateral filter (Smith and Brady 1995); the L² norm of surrounding fixed-size patches used in the nonlocal means (Buades et al. 1995); and many other possible metrics. We restrict the filtering of the term υ_N to those pixels with radiometric differences below a certain threshold to keep reconstruction errors within a bounded range. If stripe noise remains within expected levels as it was demonstrated for VIIRS SST bands (Bouali and Ignatov 2012a), then this threshold can be conveniently selected with respect to band-dependent specified NEΔT (see Table 1) and may be further increased if detectors’ temporal degradation leads to stronger striping during the instrument life mission. We denote by w(x, y, x′, y′) the weighting function that measures the radiometric similarity between pixels (x, y) and (x′, y′). We define w(x, y, x′, y′) as follows:

View Expanded

This formulation ensures that two pixels with large radiometric differences are given small weights. The parameter σ controls the decay of the weighting coefficients with respect to the radiometric distance between pixels and depends on the NEΔT. Typically, we select a value of σ² = NEΔT/2. The true value of a noisy pixel υ_N(x, y) is then estimated with

View Expanded

where C(x, y) is a normalization term given by

View Expanded

and (x, y) is a spatial neighborhood of pixel (x, y). To account for the number of detectors D in the FPA and the unidirectionality of striping, (x, y) can be defined as

View Expanded

Note that Ω′ is a subdomain of Ω defined with respect to the binary matrix as

View Expanded

For an even number of detectors, the value of Δ_y can be fixed to D/2. We recall that D = 16 for VIIRS “M” bands. For Δ_y = D/2, a pixel acquired with—for example, detector 8—will have a neighborhood (x, y) composed of pixels acquired with detectors 1–16, that is, all other detectors. To account for possible mirror side differences, one would select Δ_y = D. We note, however, that the analysis conducted in Bouali and Ignatov (2012a) did not indicate the existence of mirror banding in VIIRS SST imagery. The nonlocal filtering Yaroslavsky neighborhood filter (YNF) of the term υ_N can then be expressed as

View Expanded

with

View Expanded

For N iterations used in the DHD, an estimate of the true signal is given with

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Table 1.

VIIRS SST band characteristics. Ttyp represents the typical temperature.

View Table

d. Optimization

We describe the optimization method here that derives a minimizer of the variational model described in section 2b. We denote the energy functional used in (2):

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The solution u₀ from (2) satisfies the Euler–Lagrange equation given by

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which simplifies to

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We denote by (ξ_x, ξ_y) the spatial frequency variables in the Fourier domain, i is the imaginary unity, and recall a mathematical property of the Fourier transform of a derivative function—namely,

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To simplify notations in the following, we will denote as the Fourier transform of a and is the element-by-element multiplication of a with the matrix —that is, = .a. The Fourier transform of (19) leads to

View Expanded

An estimate of the solution [u₀, υ₀] to the minimization of (2) can be computed in the Fourier space as

View Expanded

An inverse Fourier transform will provide an estimate of [u₀, υ₀] in the spatial domain. At the Nth iteration, we are minimizing the energy functional E_N(υ_N−1, λ_N), defined as

View Expanded

After simplification, its Euler–Lagrange equation leads to

View Expanded

Shifting to Fourier space, the previous equation can be formulated as

View Expanded

leading to the following solutions at the Nth iteration:

View Expanded

In practice, both and need not be computed because the simple relationship existing between solutions of successive iterations—that is, —allows us to compute one of the terms, and , from the other.

e. Image quality

Many image-based metrics have been defined in the destriping literature to evaluate the improvement in image quality. However, most of these indexes were devised for highly pronounced stripe noise and are not suitable when striping has a low or moderate amplitude—that is, close to prelaunch sensor NEΔT specifications. The noise reduction (NR) ratio (Simpson et al. 1995), for example, is defined in the frequency domain and quantifies the reduction of periodic patterns resulting from detectors’ systematic biases. Therefore, it does not apply for random stripes. The radiometric improvement factors IF1 and IF2 (Corsini et al. 2000) are computed in the spatial domain and measure the degree of smoothing of cross-track profiles (mean value of each scan line) after image destriping. When these indices are used, it is implicitly assumed that the high-frequency component of the image cross-track profile is due to striping. This assumption does not hold when the magnitude of scan line noise is significantly weaker than the signal true variations or when striping is not uniform across the range of observed BTs. Finally, we note that quantifying the reduction of noise is necessary but not sufficient to demonstrate the effectiveness of a destriping algorithm. In fact, an additional metric is required to evaluate the amount of information preserved in the destriped image. This is customarily done by evaluating the image distortion (ID) index, (Simpson et al. 1995; Bouali and Ladjal 2011), which cannot be used in our case because only specific regions of the images (determined by the binary matrix ) are considered for the reduction of striping. To overcome the limitations of existing metrics for image quality analysis, we define two new indices. Denoting u as an estimate of the true signal derived from a noisy observation f, we define the normalized improvement factor (NIF) and the normalized distortion factor (NDF) as

View Expanded

View Expanded

respectively. The NIF and NDF indexes quantify in the subdomain Ω′ the reduction of spatial variations with respect to the original image in the along-track and cross-track directions, respectively. The NDF plays a role comparable to full-reference metrics because the variations of the degraded and restored images should be similar in the scan direction. A value of NDF equal to 1 indicates no loss of information after denoising. We defined the NIF such that it is negative if the along-track variation of the restored image is higher than the original one which, would be a clear indication of poor destriping or collateral degradation. Note that the analytical expressions of NIF and NDF are not symmetric. The NDF could be defined analogously to the NIF if the cross-track variation of the destriped image was expected to systematically decrease. However, this is not always the case because of the edge-preserving role played by the binary matrix . Finally, we point out that NDF values are mainly used as a stopping criterion in the DHD described in section 2b. Through qualitative analysis, we have selected a threshold of 0.95 for NDF, which was determined based on the perceptual criteria that images with a NDF above this value are visually indistinguishable. Unlike the NIF, the NDF index is not reported here because it does not explicitly portray an improvement of the imagery. It is only used to check the radiometric fidelity to the original data for every processed granule. We show in Fig. 1 how the NDF converges to 1 with respect to the number of iterations used in the DHD.

Typical example of NDF with respect to the number of iterations used in the DHD.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Typical example of NDF with respect to the number of iterations used in the DHD.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Typical example of NDF with respect to the number of iterations used in the DHD.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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The destriping algorithm can be summarized as follows:

• Input: Striped image f

• 1: Initialize λ₀ = 1 and binary matrix

• 2: Solve

• 3: While [NDF (f, u_k≥1) < 0.95]

  • Update λ_k = λ₀/2^k−1

  • Solve

• 4: End

• 5: Apply nonlocal filter YNF to υ_k

• Ouput:.

3. Results

The algorithm described in this paper aims toward improved full-sensor-resolution SST imagery by reducing the amount of stripe noise in level 1 data. We applied it to those VIIRS thermal emissive bands currently used in the ACSPO system, including M12 (3.7 μm), M15 (11 μm), and M16 (12 μm). The VIIRS SDRs correspond to BTs derived from TOA-calibrated radiances. In NESDIS’s ACSPO system, standard 86-s VIIRS granules are aggregated into 10-min granules that represent images of 3200 × 5394 pixels. To demonstrate the potential of the destriping approach for operational use, 3 days of global VIIRS data acquired from 20 to 22 January 2013 were processed. For each of the 432 granules (144 granules, each 10 min long, per day per spectral band), bands M12, M15, and M16 were destriped separately and used as input into the ACSPO version 2.12 to generate SST fields. ACSPO SST output was then compared to SST maps generated from original SDRs to evaluate the improvement resulting from the stripe reduction algorithm. The NIF index defined in section 2e was computed for each SST granule over the 3-day period and is shown in Fig. 2. Overall, the destriping performance is stable over the 3-day period, as expected from an adaptive correction. Note that the temporal variations of the NIF within a single day result from different degrees of striping in the SST imagery and depend on many factors, such as a first-guess SST or analytical formulation of the SST retrieval equation (which is different for daytime and nighttime). Small values of the NIF index are associated with granules acquired over cold regions and/or nighttime granules derived from a conventional multichannel SST (MCSST) that does not include a first-guess SST. Evaluation of the NIF was not performed for granules with an extremely small percentage of clear-sky pixels because the NIF index (as any image quality metric) is not representative of the destriping performance if the number of clear-sky pixels is too small or if clear-sky pixels are highly scattered over the image domain. As can be seen in Fig. 2, the destriping of SDRs can lead to NIF values in SST imagery of up to +25%. In addition, the NIF remains constantly positive throughout the testing period. In fact, the NIF index is defined so that any degradation to the image, such as an increase of stripe noise, would result in negative values of the NIF. However, this was never observed for the entire 3-day period and constitutes an important consistency check for the operational use of the destriping algorithm.

NIF computed over 3 days of VIIRS ACSPO SST data. Note that the NIF was multiplied by 100 in these graphs to show percentage of improvement.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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NIF computed over 3 days of VIIRS ACSPO SST data. Note that the NIF was multiplied by 100 in these graphs to show percentage of improvement.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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NIF computed over 3 days of VIIRS ACSPO SST data. Note that the NIF was multiplied by 100 in these graphs to show percentage of improvement.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Conventional metrics used in previous studies, such as NR and ID, were not evaluated given the weak magnitude of stripe noise in the VIIRS SST bands, well within specifications (Cao et al. 2013). Nonetheless, we explain the impact of destriping in the frequency domain. Periodic striping introduces a clear signature in the column-averaged power spectrum, and appears as peaks centered at specific frequencies. However, the striping patterns observed in VIIRS SST bands are not periodic. Stripe noise translates in the column-averaged power spectrum as rapid fluctuations in the high-frequency range that should be attenuated after destriping. The line-averaged power spectrums of the degraded and restored images should remain similar because of the unidirectionality of stripe noise. As shown in Fig. 3, the proposed algorithm performs as expected. High-frequency variations observed in the column-averaged power spectrums are smoothed without any modification to the line-averaged power spectrums.

(top) Column- and (bottom) line-averaged power spectrum of (left) original and (right) destriped images.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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(top) Column- and (bottom) line-averaged power spectrum of (left) original and (right) destriped images.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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(top) Column- and (bottom) line-averaged power spectrum of (left) original and (right) destriped images.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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The visual improvement of SST maps at the pixel level is illustrated in Fig. 4. Note that entire 10-min VIIRS SST granules or significantly large images are not displayed because this would not genuinely represent the perceptual impact of the striping effect. Instead, smaller images with 256 × 256 pixels dominated by clear-sky areas and representative of the overall performance of the algorithm were selected.

(left) VIIRS SST images of 256 × 256 pixels size generated with ACSPO without preprocessing of BTs. (right) Same images generated with ACSPO from destriped BTs. The images were acquired at (top) 1130 UTC 20 Jan 2013 over the Mediterranean Sea, (middle) 0740 UTC 21 Jan 2013 in the Bay of Bengal, (bottom) 1910 UTC 22 Jan 2012 in the Gulf of Mexico.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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(left) VIIRS SST images of 256 × 256 pixels size generated with ACSPO without preprocessing of BTs. (right) Same images generated with ACSPO from destriped BTs. The images were acquired at (top) 1130 UTC 20 Jan 2013 over the Mediterranean Sea, (middle) 0740 UTC 21 Jan 2013 in the Bay of Bengal, (bottom) 1910 UTC 22 Jan 2012 in the Gulf of Mexico.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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(left) VIIRS SST images of 256 × 256 pixels size generated with ACSPO without preprocessing of BTs. (right) Same images generated with ACSPO from destriped BTs. The images were acquired at (top) 1130 UTC 20 Jan 2013 over the Mediterranean Sea, (middle) 0740 UTC 21 Jan 2013 in the Bay of Bengal, (bottom) 1910 UTC 22 Jan 2012 in the Gulf of Mexico.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Visual inspection of Fig. 4 suggests that the quality of ACSPO SST images generated from preprocessed BTs is superior to the original data. They do not reveal any pronounced residual stripes or blur. SST geometrical features possibly obstructed by stripe noise are significantly enhanced without loss of gradient sharpness. Such improvement opens a new perspective for improved detection of thermal fronts in full-sensor-resolution SST maps.

We plotted in Fig. 5, the cross-track profile of stripe noise affecting the SST images displayed in Fig. 4 to demonstrate the importance of reducing sensor-dependent uncertainties. Cross-track profiles are one-dimensional signals representing the mean value of each scan line and provide a good indication of the degree of stripe noise affecting a given signal. Figure 5 shows that residual scan-by-scan errors in level 1 BTs, although well within specifications (Cao et al. 2013), can lead to uncertainties in full-resolution SST data of up to ±0.2 K. It is important to point out that the downsampling used to produce lower-resolution SST products (typically 2, 4, or 9 km) does not remove these uncertainties but only reduces their visual effect in the lower-resolution imagery.

Cross-track profiles of estimated stripe noise in kelvins (K) derived from SST images in Fig.4 with (top left) corresponding to the (top), (top right) to the (middle), and (bottom) to the (bottom) of Fig. 4.

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Cross-track profiles of estimated stripe noise in kelvins (K) derived from SST images in Fig.4 with (top left) corresponding to the (top), (top right) to the (middle), and (bottom) to the (bottom) of Fig. 4.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Cross-track profiles of estimated stripe noise in kelvins (K) derived from SST images in Fig.4 with (top left) corresponding to the (top), (top right) to the (middle), and (bottom) to the (bottom) of Fig. 4.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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The core principle of the described adaptive destriping lies on the DHD scheme and is illustrated in Fig. 6. It can be seen that the initial term u₀ represents an approximation of the true signal, while the term υ₀ contains stripe noise as well as high-frequency structures that belong to the original data. As the number of iterations in the DHD increases, geometrical structures in υ_k are gradually retrieved in the term u₀ + … + u_k, leaving a highly anisotropic image υ_k. Monitoring of the NDF index at each iteration as shown in Fig. 1 provides a reliable stopping criteria for the number of iterations required in the DHD. In fact, the NDF quickly converges to 1, and the DHD can be stopped as soon as the threshold of 0.95 is reached. Note that the convergence of NDF to 1 depends on the updating strategy of the Lagrange multiplier λ_k and the initial value of λ₀, which was selected here as 1. We adopted a dyadic update as was done in the TNV multiscale decomposition. Although it may lead to residual striping in the restored image, faster convergence of the NDF can be obtained by updating the regularizing coefficient with λ_k = λ₀.α^−k, where α > 2.

Illustration of the DHD throughout multiple iterations (top) term u₀ + … + u_N and (bottom) term υ_N. Note how the useful information is progressively extracted from the noisy term υ_N without retrieving the striping.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Illustration of the DHD throughout multiple iterations (top) term u₀ + … + u_N and (bottom) term υ_N. Note how the useful information is progressively extracted from the noisy term υ_N without retrieving the striping.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Illustration of the DHD throughout multiple iterations (top) term u₀ + … + u_N and (bottom) term υ_N. Note how the useful information is progressively extracted from the noisy term υ_N without retrieving the striping.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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In Fig. 7, we show how the stripe noise affects the ACSPO cloud mask. The series of cloud tests introduces spatial inconsistencies because of the low SSNR in images derived from the difference of spectral band or from SST fields. This compromises scene identification and may affect the accuracy of SST retrievals. The preprocessing of BTs for stripe noise reduces horizontally distributed false alarms in the cloud mask.

(left) Original ACSPO SST cloud mask. (right) ACSPO SST cloud mask with preliminary destriping of BTs. Notice how the destriping improves the spatial consistency of the clouds mask.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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(left) Original ACSPO SST cloud mask. (right) ACSPO SST cloud mask with preliminary destriping of BTs. Notice how the destriping improves the spatial consistency of the clouds mask.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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(left) Original ACSPO SST cloud mask. (right) ACSPO SST cloud mask with preliminary destriping of BTs. Notice how the destriping improves the spatial consistency of the clouds mask.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Figure 8 shows that in both full-sensor-resolution and downsampled SST maps, the distinction between true and artificial features may not be straightforward for spatial discontinuities with low to moderate magnitude. As a consequence, accurate detection of thermal fronts may become a challenging task for automatic algorithms or experienced oceanographers. This is a serious concern for studies based on long-term analysis of SST data and aimed to estimate the probability of thermal fronts and subsequently identify seasonal and decadal trends in ocean dynamics. If stripe noise is not accounted for, then high thermal gradients will cumulate with time and affect the reliability of SST frontal probability products.

Impact of stripe noise on the detection of SST fronts. The Sobel filter was applied on a subset of ACSPO VIIRS SST maps. The VIIRS image was acquired on 31 Jan 2013 on the west coast of Australia. (top) Full sensor resolution of 0.75 km and (bottom) downsampled resolution of 4-km ACSPO (left) with destriping of BTs and (right) without preprocessing of BTs.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Impact of stripe noise on the detection of SST fronts. The Sobel filter was applied on a subset of ACSPO VIIRS SST maps. The VIIRS image was acquired on 31 Jan 2013 on the west coast of Australia. (top) Full sensor resolution of 0.75 km and (bottom) downsampled resolution of 4-km ACSPO (left) with destriping of BTs and (right) without preprocessing of BTs.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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Impact of stripe noise on the detection of SST fronts. The Sobel filter was applied on a subset of ACSPO VIIRS SST maps. The VIIRS image was acquired on 31 Jan 2013 on the west coast of Australia. (top) Full sensor resolution of 0.75 km and (bottom) downsampled resolution of 4-km ACSPO (left) with destriping of BTs and (right) without preprocessing of BTs.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00035.1

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4. Conclusions

In this paper, we proposed a novel approach that compensates for stripe noise [which we emphasize is well within specifications for the VIIRS instrument (Cao et al. 2013)] and reduces its propagation from level 1B clear-sky BTs into level 2 SST. The resulting algorithm was tested on a 3-day global dataset derived from the Suomi-NPP VIIRS instrument. BTs from VIIRS bands M12, M15, and M16 were destriped prior to the generation of SST with the NESDIS’s ACSPO system. Through quantitative analysis and visual investigation, we demonstrated that the proposed approach provides excellent image quality enhancement; stripe noise is substantially reduced without interfering with SST geometrical features.

It must be noted that many SST providers rely on an alternative approach to reduce stripe noise (Zavody et al. 1995; Brisson et al. 2002; Merchant et al. 2013). Since the striping in SST data is partly due to the multiplication of the “water vapor” proxy (difference between two spectral bands) with a first-guess SST, spatially smoothing the differential term with a n × n averaging window can simultaneously reduce the effect of striping and Gaussian noise in the SST maps. Nonetheless, this strategy provides only a cosmetic enhancement because of the spatial filter being restricted only to the differential terms and not being applied to individual bands. Unlike the algorithm described in this paper, it cannot be considered as a destriping method.

Finally, we point out the future benefits of this work in the context of level 4 ultra-high-resolution (UHR) SST. Level 4 SST products represent gap-free spatiotemporally interpolated maps and are customarily used as input in radiative transfer models (RTMs) and numerical weather prediction (NWP) models. A recent study (LaCasse et al. 2008) showed that the initialization of the Weather Research and Forecasting Model (WRF) with a highly resolved level 4 SST (e.g., 1-km-resolution SST from MODIS) instead of a lower-resolution input [i.e., National Centers for Environmental Prediction (NCEP)’s real-time global (RTG) 6-km-resolution SST analysis] provides improved weather prediction in coastal areas. The use of level 4 UHR SST will grow more popular in the near future because of the increasing need for accurate weather forecast and hurricane landfall prediction, and will require additional processing efforts to improve the quality of whiskbroom polar-orbiting sensor SST imagery.

Work to demonstrate the applicability of the proposed algorithm for both Terra and Aqua MODIS is underway and will be documented in a future paper.