As the highperformance data compression algorithms,lapped transform(LP) and wavelet has gained more and more concern,Now,wavelet transformer has become the core of JPEG2000 and LP is the core of JPEG XP,which is a nextgeneration image compression standard under constructing.The dissertation develops some work about image compression based on lapped transform and wavelet transform.The paper is organized as:Chapter 1 mainly discusses the signification of the subject and summarizes the current research on lapped transform.Chapter 2 gives a particular introduction of LP and DCT which is the basis of LP,and points out the shortage.In Chapter 3 an optimal LOT algorithm with integer lifting structure is proposed and Chapter 4 analyzes the performance of eight points DCT of this LOT algorithm.Following by a prescaling DCT algorithm using recursive method and calculates the optimal scaling factor corresponding to the N points DCT. Based on the conclusion of this,an optimal LOTâ…¡algorithm,in the floating number viewpoint,is proposed.Chapter 5 testifies the shortage of a sparse matrix decompose algorithm of DCT and gives amendatory expressions,and then analyzes the symmetrical,invertible,integer LBT.Chapter 6 proposes a new compression algorithm for far infrared medical image using wavelet transform.Chapter 7 designs an optimal color transfer for realtime video.The main contributions in this dissertation include as follows:1.We propose a new integer realization algorithm for the lapped transform from the whole system viewpoint.It has the following merits:uniform factor, inplace calculation,low complexity,accounting for the processing of border pixels.2.We propose a new algorithm for the typeâ…¡lapped transform(LTâ…¡),and the new algorithm makes full use of the relationship of DCT and DST.Its complexity is less than one third of the original LTâ…¡for the rotation matrix in the decomposition.Compared with the simply LTâ… ,it has similar complexity.3.DCT is the basis of lapped transform,and we analyze a decomposition method of DCT and find its inaccuracy.Different fast algorithms for DCT have different scaling factor,therefore,they have different complexity.We proposes a optimal scaling factor using a recursive method,based on this new result,we propose a new and optimal eight points DCT,which can reach the theoretical multiplications lower hound with smaller angles and suitable for integer implication using lifting structure.4.Lapped biorthogonal transform(LBT) is very difficult for invertible, symmetrical integer realization using lifting structure because of its special structure.We analyze an invertible,symmetrical integer LBT structure using filter viewpoint and point out the limitation.5.We present an image compression algorithm for farinfrared medical image from the aspect of engineering.The new algorithm can prove good result for the nearlossless medical compression compared with famous JPEGLS.6.We propose an optimal color transfer algorithm and applied it in realtime video successfully.
