Local Approximations in Demosaicing and Deblurring of Digital Sensor Data

This thesis is dedicated to demosaicing and deblurring problems in digital image processing and their solution exploiting signal adaptive filtering. In particular, we use filtering based on the local polynomial approximation (LPA) and the paradigm of the intersection of confidence intervals (ICI) for the adaptive selection of the scales of LPA. This filtering is nonlinear and spatially-adaptive with respect to the smoothness and irregularities of the image. In the first part of the thesis, demosaicing is studied. It refers to the problem of interpolation of complete red, green, and blue values for each pixel, to make a color RGB image, from downsampled gray-scale mosaic-like raw data recorded by a single-chip digital camera. We propose a novel technique for demosaicing that shows results that, to the best of our knowledge, are a significant improvement over the state of the art. Traditionally, in demosaicing the input signal is assumed to be noise-free. However, the raw data is always noisy and thus prefiltering has commonly been used prior to demosaicing. We show that the demosaicing and denoising designed as a single procedure can be significantly more efficient than analogous independent procedures. In this thesis, we do not restrict ourselves to the conventional stationary Gaussian noise model. In the developed technique, we also take into account the signal-dependant Poisson noise which is much more relevant for digital imaging sensors. As a result, we achieve higher quality of image restoration as demonstrated by extensive experiments for both artificial and real data taken directly from the sensor of a camera phone. The second part of the thesis is dedicated to image deblurring. We develop several techniques as an evolution from conventional deconvolution with a known blur to blind deconvolution with an unknown blur. We propose techniques for digital optical sectioning, multi-channel and single-channel blind deconvolution, and techniques for automatic selection of the regularization parameter