Modeling the distribution of patches with shift-invariance: Application to SAR image restoration

Abstract

Patches have proven to be very effective features to model natural images and to design image restoration methods. Given the huge diversity of patches found in images, modeling the distribution of patches is a difficult task. Rather than attempting to accurately model all patches of the image, we advocate that it is sufficient that all pixels of the image belong to at least one well-explained patch. An image is thus described as a tiling of patches that have large prior probability. In contrast to most patch-based approaches, we do not process the image in patch space, and consider instead that patches should match well everywhere where they overlap. In-order to apply this modeling to the restoration of SAR images, we define a suitable data-fitting term to account for the statistical distribution of speckle. Restoration results are competitive with state-of-the art SAR despeckling methods.

Patch-based SAR image classification: The potential of modeling the statistical distribution of patches with Gaussian mixtures

“…EPLL has been adapted to SAR image restoration in [10] where its performance for despeckling has been shown to be similar to the state of the art. As a by product, the algorithm provides a map of the best atom selected to represent each patchx of the denoised image 1 as expressed below…”

“…GMM are known to well model the distribution of patches extracted from natural images. The Expected Patch Log-Likelihood (EPLL) algorithm introduced in [9] and extended to SAR imaging in [10] achieves state-of-the-art denoising performance. Its GMM is learned with an Expectation-Maximization algorithm applied to 10 6 patches of size 8 × 8 extracted from natural images.…”

“…As the model learned in [9] has proven being powerful enough to encode a large variability of structures within a patch (as shown by its efficiency at despeckling SAR images in [10]), it may provide useful features to represent local structures in SAR images see figure 1. We propose in the following to assess the ability of this GMM based feature through a simple classification task.…”

“…1. The denoised version of a 1-look SAR image using [10] and the corresponding Gaussian models map. Each color of the colormap respresents one of the Gaussian models.…”

“…To achieve the training procedure, we first denoise a set of eight amplitude-calibrated TerraSAR-X SAR images of one meter resolution using the procedure described in [10]. The sizes of the images are between 1000×1000 and 2000×2000 pixels, and they are manually labeled into N L = 3 classes: urban area, high vegetation, homogeneous area (low vegetation and water).…”