Nonlinear Locally Adaptive Techniques for Image Filtering and Restoration in Mixed Noise Environments

In this thesis, nonlinear locally adaptive techniques of noise removal and restoration are considered for image processing applications in mixed noise environments. These techniques are designed and tested for radar, ultrasound, and gray-level test images. The image observation models take into account the influence of fluctuating (additive and multiplicative) and impulsive noise as well as blurring effects. Hard-switching robust adaptive algorithms are proposed and analyzed for radar image processing. In these algorithms, a proper filter for each pixel is selected from a set of filters using a local activity indicator (LAI). The problems of design and optimization of L-filters, including their application in hard-switching algorithms, are considered for speckle imagery. The analysis of the algorithms for LAI calculation is performed for different noise models. Considerable attention is given to the selection of thresholds in hard-switching schemes. Several locally adaptive techniques of image restoration are considered in the context of mixed noise models. A simple locally adaptive algorithm is described based on switching of the regularization parameter depending upon the LAI value. In the other algorithms, nonlinear locally adaptive filters are used for preprocessing of blurred images. We also propose iterative restoration techniques, where a nonlinear filtering operation is used in place of the constraint operator. The effectiveness of the proposed methods is demonstrated by means of numerical simulations. Nonlinear spatially adaptive multiscale methods are proposed for noise removal (denoising) based on the so-called block-median pyramidal transform (BMPT). The BMPT is based on non-overlapping block decompositions using the median operation and polynomial interpolation. In addition to the softand hard-thresholding schemes, a locally adaptive thresholding technique that uses a scale dependent local variance is employed. The probability distribution of the BMPT coefficients is analytically derived under the assumption of independent and identically distributed (i.i.d.) input samples. The results of this statistical derivation are used for selecting the thresholds for denoising. Numerical simulations demonstrate that the proposed multiscale methods are effective for noise removal in images. The results of the thesis are presented in the publications in the appendix.