Adaptive wavelet packets for image and video compression

In this dissertation, we investigate the design of image and video compression algorithms by using adaptive wavelet packet decomposition. For image compression, we present a spatial and frequency decomposition algorithm that extends and improves the existing double tree algorithm (2) by using a more flexible merging scheme, a more efficient quantizer, and an improved initial slope estimator. The new spatial merging scheme allows for mergers and for regions to form which are not possible with a quad-tree structure; this generalization yields a noticeable improvement in the overall R-D performance. The proposed Scalar/Pyramidal Lattice Vector quantizer improves the coding efficiency of the coefficients of wavelet packets. The initial slope estimator drastically reduces the computations needed to obtain the optimum decomposition. For video compression, we first develop an efficient temporal, spatial and frequency decomposition method for video coding. In this method, the given video sequence is decomposed into small volumes which adapt to the nonstationarity and the motion of the video signals. A three dimensional best wavelet packet is generated for each volume based on a rate and distortion criterion, such that the subbands of this 3D wavelet packet can be more efficiently coded than the original signals. This method does not require motion estimation/compensation; the motion information is contained in the high temporal subbands. It allows us to implicitly represent and code the motion information based on the given bit rate constraint. To alleviate the computational complexity of the 3D wavelet packet decomposition, in our second video compression algorithm, a large amount of temporal redundancy is removed through the use of low-high temporal subbanding and the DPCM (Differential Pulse Code Modulation) procedure. The coefficients of high temporal subbands and the original lowpass subbands or the difference of the low subbands from the DPCM loop, are decomposed by adaptive wavelet packets based on the rate and distortion criterion. Since the adaptive wavelet packet representation is capable of achieving a better R-D performance than subband coding or wavelet decompositions, it can be expected that the video coding algorithm proposed in this dissertation will yield an improvenent over the traditional 3D subband coding techniques. For possible use in various applications, a rate constrained coding and a quality (distortion) constrained coding versions of this video coding algorithm are developed and analyzed