1. Introduction

The most common cause of striping in satellite imagery is from calibration or performance differences among the detectors of a sensor [1]. This leads to observable striping artifacts aligned with scan direction, which are usually of low variance (Fig. 1(b)). The pattern of striping noise exhibits periodicity in the along-track direction with the period equal to the number of detectors in a sensor. The variance of striping noise is relatively small compared to the features in the image. This is the most common type of striping noise in the thermal 11–12 μm bands of the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (SNPP) satellite, and the Moderate Resolution Imaging Spectroradiometer (MODIS) onboard the Terra and Aqua satellites [1].

 

Fig. 1 Destriping of ocean color products nL_w(671) (upper panels: (a)–(c)) and chlorophyll-a concentration (lower panels: (d)–(f)) obtained by VIIRS-SNPP on July 16, 2013 around 17:38 UTC near (36°S, 55°W). The original data are shown in panels (b) and (e), while the destriped data are shown in panels (c) and (f). The values along the black line in panel (b) are plotted in panels (a) and (d) with black lines from original images (panels (b) and (e)) and red lines from destriped images (panels (c) and (f)).

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Another type of striping artifact is from differences in the reflectance of the opposite sides of the rotating mirror used to redirect the incoming light into the optical path of the sensor [2]. Such differences usually amount to an almost constant offset for data within one scan from the same side of the mirror and alternating between neighboring scans from the different sides of the mirror (Fig. 2(b)). In addition, there may be some angle dependence, resulting in a larger variance in this artifact for larger scan angles. This kind of artifact affects some visible bands of MODIS Terra and Aqua satellite data [2].

 

Fig. 2 Destriping of ocean color products nL_w(412) (upper panels: (a)–(c)) and Chl-a concentration (lower panels: (d)–(f)) obtained by MODIS-Aqua on December 3, 2013 at around 05:05 UTC near (26°N, 123°E). The original data are shown in panels (b) and (e), while the destriped data are shown in panels (c) and (f). The values along the black line in panel (b) are plotted in panels (a) and (d) with black lines from original images (panels (b) and (e)) and red lines from destriped images (panels (c) and (f)).

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The third source of striping in solar reflective bands comes from changes in solar-sensor geometry from different detectors, which are arranged in an array and scan slightly offset of the target area. This is because the amount of light reflected from the ocean-atmosphere system has a very strong solar-sensor geometry dependence, especially in high glint regions. The change in solar and sensor-viewing angles is roughly proportional to detector number, giving rise to a linear modulation of data within one scan, and a discontinuity in data between the adjacent scans (Fig. 3(b)). A typical observation of fixed pixels along the track direction produces a saw-tooth pattern with a period equal to the number of detectors [3]. However, these are real features (signals) measured by satellite sensors, not noise.

 

Fig. 3 Destriping of ocean color products nL_w(412) (upper panels: (a)–(c)) and diffuse attenuation coefficient K_d(490) (lower panels: (d)–(f)) obtained from VIIRS-SNPP on April 19, 2014 at around 21:20 UTC near (13°S, 114°W). The original data are shown in panels (b) and (e), while the destriped data are shown in panels (c) and (f). The values along the black line in panel (b) are plotted in panels (a) and (d) with black lines from original images (panels (b) and (e)) and red lines from destriped images (panels (c) and (f)).

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When the striping is related to the characteristics of detectors in a sensor, it is natural to remove these artifacts from sensor data records before any further processing to get the satellite-derived data products because the processing algorithms may be adversely affected by the striping artifacts. However, as discussed previously, the source of striping in solar reflective bands is largely from changes in sensor-zenith angle, and the saw-tooth structure of striping in reflectance data correlates with variations of sensor-zenith angle for different detectors. Thus, the top-of-atmosphere (TOA) radiance changes that correspond to the sensor-zenith angle variation are the true satellite sensor-measured TOA radiances. It makes no sense and is incorrect to destripe the TOA radiances in the sensor data records (or Level-1B data) directly.

For ocean color remote sensing, however, normalized water-leaving radiance spectra nL_w(λ) data are derived by carrying out atmospheric correction for removing atmosphere and ocean surface effects [4–6]. In particular, satellite-derived nL_w(λ) data should have no dependence on solar-sensor geometry [5, 7–9], i.e., there should be no detector-dependent features in nL_w(λ) images. Consequently, all ocean biological and biogeochemical products, e.g., chlorophyll-a (Chl-a) concentration [10, 11], water diffuse attenuation coefficient at 490 nm K_d(490) [12–14], etc., which are derived from nL_w(λ) spectra, should have no detector-dependent features. Therefore, detector-related striping noise will appear in nL_w(λ) spectra images and these artifacts should be removed by the destriping algorithm. The destriped nL_w(λ) spectra are then used to calculate all ocean biological and biogeochemical products such as Chl-a and K_d(490) rather than performing direct destriping of those products. For various satellite ocean color applications, e.g., chlorophyll-a frontal product [15], it is critical to have non-striped Chl-a images.

In this paper, we describe our effort to remove striping effects for improved satellite-derived ocean color products. The paper is organized as follows. In Section 2, we briefly review the main steps of the destriping method by Bouali and Ignatov (2014) [1] and present the details on how to modify and adapt this method to remove striping artifacts from satellite-derived nL_w(λ) data. In Section 3, we show some examples of how the adapted destriping algorithm performs in various conditions, and finally summarize our conclusions in Section 4.

2. Methodology

Bouali and Ignatov (2014) [1] recently introduced a new approach to remove detector produced striping noise in thermal infrared bands used to derive sea surface temperature (SST). This approach entails an iterative procedure that splits the image into a striped component with otherwise few features and a stripe-free component with most of the actual image features. The striped component is then passed through a filter to eliminate the stripes, and the resultant slowly varying the smooth component is added back to the stripe-free component to produce the final destriped image. The advantage of this method is that the procedure to separate the image into striped and stripe-free components is very efficient, so that any subsequent filtering of a striped component does not blur any genuine features of the image. To minimize any artifacts that may be introduced by the destriping procedure, this method assumes that striping noise has a relatively small variance, and any gradients above an appropriate threshold level should be preserved [1].

In fact, the algorithm may be thought of as a two-step procedure. The first step of the destriping algorithm splits the original image into the striped (but otherwise featureless) and the destriped components. The second step involves using a nonlinear filter to remove striping artifacts from the striped component of the image.

Before splitting the image into striped and stripe-free components, the domain of points that are subject to destriping is defined. This is done to preserve any sharp image features, as well as to exclude parts of the image (such as land, ice, and clouds) that do not need to be destriped. In the context of destriping the solar reflective band data, the assumption that striping artifacts are small in magnitude compared to image features is not always valid, as shown in Fig. 2 and Fig. 3. This makes it significantly more challenging to define the appropriate destriping domain. Fortunately, because destriping takes place after atmospheric correction [4–6] (i.e., for nL_w(λ) data), additional information is readily available. First, land, ice, and clouds are masked with a fill value in the image data, and can be easily excluded from any further analysis. The remaining pixels are used to calculate the absolute values of gradients used to define the destriping domain.

Following the original formulation of the destriping method [1], we use the thresholds of the absolute value of gradients to define the destriping domain. The destriping domain includes all pixels where gradients (both along and across the scan) are below the pre-determined threshold values. However, instead of using static values for these thresholds, we recalculate and adjust them for each data granule, based on the information in the gradient data itself. Since the amplitude of striping is extremely large in the high sun glint areas, pixels in these areas are disregarded when deriving the values of thresholds of derivatives. However, once the threshold values are obtained, some parts of the high glint areas may still pass the condition on gradients to fall into the destriping domain, and in many cases these data can be successfully destriped. The remaining pixels are used to calculate gradients both along-scan and across-scan directions, which are accumulated in histograms (see Fig. 4). The threshold values (for gradients both along- and across-scan directions) are computed from these histograms as follows:

 

Fig. 4 A typical histogram of the absolute values of gradients of the normalized water-leaving radiance derived from VIIRS band M1 (center wavelength 410 nm), along and across the scan direction.

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Once the destriping domain is determined, an iterative procedure to split the image into striped and stripe-free components takes place. We introduce a mask M(x, y) to denote the destriping domain, and define it as:

In general, solving the discrete Poisson equation (Eq. (4)) implies solving a system of linear equations for u(x, y). However, it is simplified by transforming to the Fourier space (denoted by indices (k_x, k_y)) where the linear equations decouple into simple algebraic equations for different Fourier components, i.e.,

The image obtained from reconstruction is smooth and does not contain striping artifacts. However, disposing some of the original image information using the restricted gradients means that some of the genuine features are missing in the restored image. Therefore, the image splitting procedure is repeated again on the residual image, which is the difference of the original image and the smoothed image obtained from Poisson reconstruction (see Fig. 5). After several repeated iterations, the residual contains striping artifacts with little to no genuine features from the original image. While Bouali and Ignatov (2014) [1] describe a more rigorous way to find the optimal number of iterations in the destriping algorithm, in practice, with our implementation about eight iterations produces very good results for the vast majority of cases observed, and any subsequent iterations do not yield a noticeable improvement in image quality.

 

Fig. 5 A flowchart of the destriping algorithm.

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After the image is split into striped and stripe-free components, most of the useful information is contained in the latter. However, the striped component may still contain slowly varying changes in the average value. This information is recovered after filtering the striped component of the image, which is the second part of the destriping algorithm.

Due to the unidirectional nature of striping, the filtering domain is chosen that consists of a single line of the nearest pixels with the same position along the scan. The extent of filtering domain in pixels along the track (or cross scan) direction can vary and is determined by one of the filter parameters. Striping artifacts due to changes in detector calibration and due to changes in viewing angle show a repeating pattern with the size of a scan line (Figs. 1 and 3). Therefore, for the bands affected by these kinds of striping artifacts, the size of the filter is chosen to be equal to number of detectors in a sensor. However, striping due to differences in rotating mirror sides introduces an artifact with a pattern that repeats only after two scans (see Fig. 2). Thus, for bands where striping due to differences in mirror reflectance is significant, the size of the filter needs to be doubled. In our analysis, this only applies to MODIS bands that correspond to wavelengths of 412, 443, and 645 nm.

To remove the artifacts from the striped image component, a nonlinear Gaussian type filter is used, whereby the value of the filtered result is obtained by a following formula:

Table 1. Parameters Used to Destripe nL_w(λ) Data Obtained from VIIRS-SNPP for 7 Moderate-resolution Visible and Near-infrared Bands

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Table 2. Parameters Used to Destripe nL_w(λ) Data Obtained from MODIS-Aqua for 13 Visible and Near-infrared Bands

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Lastly, after the nonlinear filter has removed striping artifacts from the striped image component, it is combined with the striping-free component to produce the final destriped image. A flowchart of the destriping algorithm is shown in Fig. 5.

3. Results

We show comparisons of original (striped) and destriped ocean color product images for several cases with various ocean optics conditions, striping artifacts, and different spectral bands of VIIRS and MODIS-Aqua sensors. Ocean color products derived from MODIS-Aqua and VIIRS have been discussed in various studies [17–20].

Figure 1 shows the effect of destriping on VIIRS data for nL_w(671) and Chl-a. The original red band data nL_w(671) (Fig. 1(b)) show a large variation in the high sediment waters of La Plata dispersing in the ocean. However, some detector striping is evident. In Fig. 1(c), these striping artifacts are removed from nL_w(671) data, while the genuine features are retained (along with some non-directional noise). Figure 1(e) shows the original data for Chl-a, calculated from the original data of nL_w(λ) with λ = 443, 486, and 551 nm, and also shows large variations mixed with striping artifacts. Figure 1(f) shows Chl-a obtained from the destriped nL_w(λ) data where the striping artifacts are removed retaining the genuine features of the original image. It is emphasized here that the destriping algorithm was not applied to Chl-a imagery directly. The improved Chl-a image (Fig. 1(f)) was re-derived from destriped nL_w(λ) spectra data. The line plots (Fig. 1(a)) show a comparison between the original and the destriped data along the black line in Fig. 1(b). From this comparison, it is clear that the average value of data is unaffected by the destriping procedure. In Figs. 1–3, gray areas represent land, and white areas denote clouds. The black area in Figs. 1(e)–1(f) denotes pixels where slightly negative values of nL_w(λ) in the blue bands do not allow Chl-a values to be derived [10].

Figure 2 shows quality improvement of the data products derived from MODIS-Aqua imagery. The original nL_w(412) image (Fig. 2(b)) shows a considerable variation of radiance in coastal turbid waters of the East China Sea, but it also contains significant striping artifacts, which are most prominently due to sensor mirror-side differences as indicated by the alternating pattern of offsets in adjacent scans. In the destriped image (Fig. 2(c)), these artifacts are removed, while the genuine details of the original image are retained. The original data for Chl-a for the same area are shown in Fig. 2(e), and are derived from nL_w(λ) with λ = 443, 488, and 551 nm (or 555 nm). It shows a similar pattern in striping artifacts propagated from nL_w(443) whose corresponding MODIS-Aqua band also suffers from differences in sensor mirror sides. Using destriped nL_w(λ) to derive Chl-a (Fig. 2(f)) significantly improves image quality by removing the striping artifacts while retaining the intricate detailed features characteristic to the region with sharp and dynamic changes in Chl-a concentration. The line plots across the scan direction (Figs. 2(a) and 2(d)) show that the average values of nL_w(412) or Chl-a are not affected by the destriping procedure.

In Fig. 3, we show the performance of destriping in very different conditions, corresponding to VIIRS imagery from rather homogenous waters of the South Pacific. The nL_w(412) data (Fig. 3(b)) show relatively fine features that are almost overwhelmed by a strong striping pattern due to changing solar-sensor geometry from scan to scan. The adaptive nature of destriping method allows recovering of the fine features in the destriped image (Fig. 3(c)) even in these conditions. The lower panels (Figs. 3(e) and 3(f)) show the corresponding improvement in diffuse attenuation coefficient K_d(490), derived from nL_w(λ) with λ = 486, 551, and 671 nm [14]. Again, the destriping algorithm was not applied directly to the K_d(490) image for the improved K_d(490) imagery in Fig. 3(f). The line plots (Figs. 3(a) and 3(d)) indicate that the average values are unaffected. It should be pointed out that the destriping algorithm may be less effective under certain conditions. A sparse cloud mask characteristic to open ocean conditions creates many sharp gradients, which are retained by the destriping algorithm. Consequently, in such areas with scattered clouds, the striping artifacts may not be completely removed (and can be seen in parts of Figs. 3(c) and 3(f)).

Improvements in image quality due to destriping are also reflected in the data statistics. To demonstrate that, we assess how much the value of nL_w(λ) for each pixel deviates from an average calculated over a square box centered over the particular pixel, and measure the statistical properties of the distribution of such deviations from the box average. In this analysis, we only include valid open ocean data pixels outside of the high glint regions and with sensor-zenith angles less than 60°. Each box average has to have at least 25% valid pixels to be included in statistics, and the data for each pixel are weighted proportionally to the number of valid pixels included in the box average.

Figure 6 shows the comparison of the distributions of deviations from the average calculated over a box of 9 × 9 pixels, obtained from nL_w(443) data before and after the destriping procedure. The statistical sample includes 62 in 85-second long VIIRS data granules taken over the South Pacific during January 2014. Both distributions have a mean value of zero, as expected for the deviations from the average values. However, the distribution of data before destriping is skewed (not symmetric), with the mode shifted from the mean value. This is because the striping noise may not be symmetrically distributed about the box average. For example, if one detector has a systematic high bias, it will skew the distribution of deviations from the box average. For data with no artifacts, we expect that the deviations from the average over a small box would be randomly distributed, and that the distribution over many samples would be symmetric. Thus, skewed distribution of deviations from the box average can be seen as an indicator of the presence of artifacts in the data. Destriped data show a much more symmetric distribution—a sign that the artifacts are removed—and a decreased STD from the mean value. The improvements in statistics are consistent for data from all bands and for a variable box size used to calculate the average values. These results are summarized in Table 3. In all cases, the mean values of distributions are zero, both before and after the destriping procedure. The data before destriping tend to show slightly non-symmetric distributions of deviations from the average values, as indicated by the nonzero values of the distribution mode. This asymmetry is reduced in destriped data, with the mode closer to the mean (zero). In addition, removing striping artifacts from nL_w(λ) data results in consistently narrower distributions of deviations from the average, and a decrease of STD values seen for all cases.

 

Fig. 6 Comparison of histograms of deviations from 9 × 9 box average for nL_w(443), calculated over a set of 62 in 85-second VIIRS data granules, taken over the South Pacific during January 2014.

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Table 3. Statistics Obtained before and after Destriping Is Applied, All Units in mW·cm⁻²·μm⁻¹·sr⁻¹

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As a routine quantitative measure of data quality improvement from the destriping procedure, we have implemented into the ocean color data processing system the calculation of the normalized improvement factor (NIF) and normalized distortion factor (NDF), which were introduced by Bouali and Ignatov (2014) [1], after destriping ocean color data. The NDF quantifies the relative change with destriping in the gradients along the scan direction, which are mostly not affected by striping artifacts and should be preserved by the destriping procedure. On the other hand, the NIF quantifies relative change in gradients across the scan. Performing 8 iterations in the destriping algorithm (see Fig. 5), produces a NDF around 92–95%, indicating that the majority of the horizontal gradients have been retained in the destriped data, and a consistently positive NIF ranging from 12% to 25%, depending on the band. These results are consistent with the optimal range of the values of NIF and NDF reported by Bouali and Ignatov (2014) [1].

The destriping algorithm relies on striped parts of an image being reasonably well connected. This condition is not fulfilled in VIIRS bow-tie areas where deletions of first and last lines in a scan separate adjacent scans, and essentially results in requiring each scan to be destriped independently. While this causes almost no issue in the case of detector striping, the saw-like striping due to changing the viewing angle cannot be removed in these areas. As a result, a mapped image shows prominent striping artifacts specifically in bow-tie areas. This problem can be mitigated by temporarily filling the gaps in VIIRS bow-tie areas with interpolated data using the adjacent scans. This improves connectivity of the destriping domain, so that the destriping algorithm can use the information from adjacent scans to remove the saw-like striping artifacts from the bow-tie areas. This drastically decreases observed striping in the mapped data in regions corresponding to VIIRS bow-tie areas (Fig. 7).

 

Fig. 7 Mapped images of Chl-a derived from VIIRS-SNPP, obtained on May 23, 2014 at 19:12 UTC near (26°N, 84°W): (a) the original image; (b) destriped image without filling bow-tie areas before destriping; (c) fully destriped image obtained by filling the trimmed scans in bow-tie area before destriping.

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Additional improvement to the derived mapped data can be obtained with a proper treatment of boundaries between adjacent data granules. Without information from the adjacent granules, striping artifacts may not be completely removed from the data in the first and the last scans in the granule. The solution is to extend the data by adding the data from the previous and the following data granules before the destriping procedure. Typically, a layer of a couple of scans is enough to ensure that the transition of destriped data between adjacent granules is seamless.

Finally, in this work, all the adaptive adjustments of parameters involve statistics over a whole granule of data, often spanning areas with different conditions. Conceivably, further improvements may be possible with a more local adjustment of parameters.

4. Conclusions

We have shown that strong striping artifacts encountered in satellite-derived Level-2 nL_w(λ) spectra from solar reflective bands can be effectively removed by a relatively straightforward application of a recently introduced destriping method [1] with an adaptive choice of the parameters. While this method was previously applied to remove much smaller amplitude striping in thermal emissive bands due to detector performance differences, it nevertheless performs surprisingly well to remove much larger amplitude striping artifacts in nL_w(λ) spectra, as long as the necessary parameters are adjusted adaptively based on image statistics. Removal of striping artifacts from nL_w(λ) spectra also translates into much improved image quality for derived ocean biological and biogeochemical quantities, such as Chl-a and K_d(490). Our computational implementation of this method into the global operational ocean color data processing stream is very efficient, adding only a small fraction (~5–10%) of time to the processing stream, while significantly improving the quality of data products. We anticipate that this very flexible and efficient destriping method may be used (perhaps with some minor modifications) to remove striping artifacts from other multi-detector satellite data, as well as prove useful in other remote sensing areas beyond the demonstrated applications in the ocean color and SST fields.