Quantitative Image Restoration Irina Gladkova, Michael Grossberg, Fazlul Shahriar ABSTRACT Even with the most extensive precautions and careful planning, space based imagers will inevitably experience problems resulting in partial data corruption and possible loss. Such a loss occurs, for example, when individual image detectors are damaged. For a scanning imager this results in missing lines in the image. Images with missing lines can wreak havoc since algorithms not typically designed to handle missing pixels. Currently the metadata stores the locations of missing data, and naive spatial interpolation is used to fill it in. Naive interpolation methods can create image artifacts and even statistically or physically im- plausible image values. We present a general method, which uses non-linear statistical regression to estimate the values of the missing data in a principled manner. A statistically based estimate is desirable because it will preserve the statistical structure of the uncorrupted data and avoid the artifacts of naive interpolation. It also means that the restored images are suitable as input for higher-level statistical products. Previous methods replaced the missing values with those of a single closely related band, by applying a function or lookup table. We propose to use the redundant information in multiple bands to restore the lost information. The estimator we present in this paper uses values in a neighborhood of the pixel to be estimated, and propose a value based on training data from the uncorrupted pixels. Since we use the spatial variations in other channels, we avoid the blurring inherent spatial interpolation, which have implicit smoothness priors. 1. INTRODUCTION A common problem in satellite imagery is striping and scan line dropout. While transmission errors are sometimes the cause of this problem, a more frequent source is damage to individual detectors, or to the electronics that records the response of the detectors. Detectors are highly sensitive and precise elements, and despite extraordinary precautions and planning, damage is an unavoidable risk. Launch, deployment into the harsh environment of space, particle bombardment, radiation, and space dust can result in detector damage at any point of an imager’s life cycle. When a damaged detector produces noisy or distorted data, this results in periodic stripes. The periodic nature comes from the fact that each detector is responsible for several scan lines within an image. When the data from the detector is absent or so corrupted as to be unusable, the result is periodic dropped lines. There are many examples of imagers which suffer from periodic line drop. Classical examples include Landsat 4 and 5. More recent examples include the MODerate Resolution Imaging Spec- trometer (MODIS) on Aqua. The 1.6 micron band (Channel 6) of the instrument has 15 broken or noisy detectors, out of 20. Figure 1 shows a portion of an Aqua image with the malfunctioning detectors shown as dark stripes. As can be seen, many of the malfunctioning detectors are adjacent so there are large spatial gaps in the data making spatial interpolation inappropriate. This limits its use in many potential applications such as cloud detection over bright surfaces such as snow and ice. When faced with dropped scan lines, dummy values may be inserted to indicate lost data and the problem pixels are indicated in the metadata. While it is essential for end users to know which pixels represent reliable measurements, the presence of dummy values passes the burden of mitigating the data loss onto the end-user. Fundamental image processing operations such as 2D-convolution filters, or 2D Fourier transforms typically produce corrupt results if an image contains dummy values. To use standard image processing operations and off the shelf software, the missing data must be first estimated in some principled way. End users may have little or no knowledge of how to do that. It is important to note that many end users will often work with partial data, selected bands or regions of Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within the margin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission. 7695 - 45 V. 1 (p.1 of 12) / Color: No / Format: Letter / Date: 2010-03-08 02:07:37 PM SPIE USE: ____ DB Check, ____ Prod Check, Notes: