Image Sparse Representation Method Based On Compression Perception

In this thesis we systematically introduce the related basic concepts about compressedsensing, a newly-developing field in signal processing techniques. Compressive Sensingtheory (abbreviated as CS) is just based on sparse representation, and which is a novel signalsampling and processing theory under the condition that the signal is compressible or sparse.However, there are still some problems to solve in CS theory and sparse representation theoryand the signal reconstruction, so all of them need further research.This dissertation focuses on Compressive Sensing theory. It mainly studies the methodsof signal sparse representation and the methods of the signal reconstruction and obtainscertain research results.The main contributions and research results of the thesis are as follows:1. Detailed introduction the three contents of Compressive Sensing theory, that is signalsparse representation, random measurement and the signal reconstruction.2. A new dual-tree sparse decomposition algorithm is proposed. In this algorithm, theredundant atom dictionary is firstly divided into several subsets according to itscharacteristics, then each subset is further subdivided into smaller sets, after severallayer-by-lay r partition, a tree structure of the atom dictionary is formed. Then in thefollowing iterative decomposition, this tree structure can guide the signal to bedecomposed in correct direction. Once the tree structure is finished, it will increase thedecomposing speed once and for all.3. In this paper, an new Modified Sparsity Adaptive Matching Pursuit Algorithm isproposed for signal reconstruction without prior information of the sparsity. Firstly, anew sparsity estimation method based on atom matching test is used to get an initialestimation of sparsity. Then it realized the close approach of signal sparse step by stepunder the frame of sparsity Adaptive Matching Pursuit (SAMP). But the step size in thenew algorithm is variable rather than the fixed one in SAMP algorithm. At the beginning of step iterations, high value of step size, causing fast convergence of the algorithm isused initially to realize the coarse approach of signal sparse, and in the later stepiterations smaller value of step size, advancing the performance of the algorithm is usedto achieve the precise approach of signal sparse. Finally, it realized the precisereconstruction of sparse signal.