Wavelets and filter Banks novel approaches for real and complex valued transform designs

Abstract

quotProcessing of natural images stored as 2-D discrete signals is an inevitable task in almost all areas of image processing. In order to have the desired processing results, directional image representation can be considered as an indispensable step which is similar to what the human visual system (HVS) does. Research in the HVS has confirmed the importance of directional selectivity as a constituent that forms a vital role in visual information processing and its perception. Since, the directional information is often present at various spatial resolutions of an newlineimage, one has to capture multiresolution property for its efficient representation. The problem of designing multiresolution transform based image representations having directional selectivity has been a topic of wide interest over many years. newline newlineIn this thesis, using the concepts of wavelets and filter banks, we propose several novel multiresolution transform designs that have finer directional selectivity. We have classified them accordingly, based on, whether the directional decomposition of an input image has real or complex-valued representation. newline newlineRegarding the real-valued transform representation, we present designs for newlinethree transforms with higher directionality by using additional filter bank stages in conjunction with the traditional decimated (subsampled) and undecimated (nonsubsampled) wavelet transforms. All three designs have better adaptability to the oriented features in the underlying image, since the filter bank construction enables us to design the filters with better frequency selectivity. In our next work, we propose two nonsubsampled transform designs belonging to a class of multiresolution directional filter banks. The proposed designs have simple structure newlinebut nonuniform frequency partitions which effectively model the irectional newlinefrequency distribution of natural images. Also, our designs need reduced computational requirements than the nonsubsampled counterparts obtained using their original subsampled approaches. All the proposed