Adaptive-Interpolative Subband Decomposition for Lossless and Lossy Image Compression

Abstract

In this dissertation, two decorrelation techniques are proposed for the application of lossless and lossy image compression. The basic concept of the proposed methods is based on interpolative subband decomposition. The interpolation filters used in the proposed schemes are adapted to satisfy the characteristic of image being decomposed. Furthermore, the interpolation filter parameters are optimally designed based on an l1 and l2 norm minimization to reduce statistical dependence between the detail subbands as much as possible. The first technique, the optimum scalar decomposition, simply decomposes image into subbands where one subband is retained and other subband is approximated by a scalar multiple of the retained subband. Contrarily, to improve the decorrelation performance, the other technique movivated by the linear decomposition transform employs a two-dimensional decorrelation structure to decorrelate the decomposed subbands. In this study, the decorrelation performance evaluations of the proposed decorrelation methods are examined and compared with those obtained from the linear decomposition transform and the S+P-transform. For lossless image compression, the comparative Huffman and SPIHT coding results (bits/pixel) obtained from the proposed schemes, the linear decomposition transform, and the S+P-transform are illustrated. In lossy image compression, however, not only the numerical results but also the perceptual image quality obtained with the proposed methods are compared to those employing the linear decomposition transform and the wavelet transform. For numerical results, the fidelity of reconstructed images are evaluated in terms of PSNR(dB), PNE1(%), and PNE2(%) criteria. The Fourier transform’s phase and magnitude components of the reconstructed images are compared to the original image in term of SNR(dB). Moreover, the Sobel edge operator is employed to investigate edge preservation in the reconstructed images obtained by different tested methods compared to the original image.