Wavelet domain partition-based signal processing with applications to image denoising and compression

This dissertation addresses the problems of image denoising and compression. Image denoising and compression are the fundamental problems in image processing, and often use transform techniques. In this dissertation, the wavelet transform is used and new signal processing techniques are applied in the wavelet domain. The sparsity of the wavelet transform, i.e., a signal energy is concentrated on few large magnitude coefficients, is a main property exploited by wavelet based image processing applications. The new methods for image denoising problem introduced in this dissertation exploits the directional structure of the two-dimensional wavelet transform. For image compression, correlations between adjacent scales (levels) and coefficient pixels, i.e., inter and intra-correlation, are adaptively exploited in the proposed algorithm.; The most frequently used technique in image denoising problems is a thresholding operation. Thresholding the wavelet coefficients exploits the sparse property of the wavelet transform. Applying thresholding to all coefficients uniformly, however, produces oversmoothing of edges and undersmoothing in uniform regions. Recently, adaptive wavelet thresholding utilizing spatial and adjacent scale correlations has been shown to yield good results. This dissertation introduces a related, but more direct, technique for adaptively processing wavelet coefficients based on partitioning of the coefficient space. In the wavelet domain, the coefficient space is partitioned through vector quantization and mask functions are used to obtain the denoised wavelet coefficients. This approach is better able to exploit structure in the coefficient domain and presented simulations show that the proposed technique yields superior performance compared with current wavelet denoising methods.; A new embedded wavelet image compression method, using quad-partition-based wavelet domain image compression, is also proposed. The introduced method uses a quad-partition-based embedded image compression scheme on the highest bit plane and structure and combined encoding scheme to exploit the inter and intra correlation in the lower bit planes. The proposed algorithm has lower complexity than the recently reported PCAS algorithm yet produces better performance. The algorithm exploits the sparsity and clustering properties in the wavelet domains for exploiting the intra-correlation and multiresolutional tree structure for exploiting the inter-correlation. On the highest bit planes in the wavelet transform domains, iteratively partitioning the coefficients in the intra-wavelet domains and representing the significance of the partitions with one bit significantly reduces the complexity of arithmetic coding by reducing the number of wavelet coefficient pixels to encode. Further bit plane encoding uses intra-correlation and inter-correlation of the wavelet coefficients. Experimental compressions of the test images show superior compression performance compared with state-of-the-art compression algorithms.; In conclusion, a generalized thresholding method using a partition based mask operation for image denoising and new embedded bit plane coding algorithm for image compression are proposed. The both techniques can be also applied to structured signals such as ECG and medical related signals for denoising and compression.