Compressed Sensing Based On Adaptive Contourlet Transform And Its Application In Image Compression

Compressed sensing theory breaks the shackle of the sample rate asked by the Nyquist sampling theorem,which can grab image at a rate far below the Nyquist sample rate and compress image simultaneously.By corresponding reconstruction algorithm,the original image could be recovered in an accurate way with high probability.Notice that sparsity is the precondition for applying compressed sensing theory.Most often,image won't be sparse naturally,then we need put image in an appropriate transform domain to obtain sparse representation.Compressed sensing theory states that the sparser representation can develop into better reconstruction quality,which means that the selected transform domain is crucial to reconstruction effect.Contourlet transform can use few large coefficients to effectively approximate smooth contours that are key features in visual information of natural images,which offers a set of concise,flexible and efficient sparse transform bases.This paper studies compressed sensing based on contourlet transform and its application in image compression,and the main innovations are shown as:1.On the basis of nonuniform directional filter bank,we improve its practicability and reduce its redundancy ratio,finally propose adaptive directional filter bank with nonuniform partitioning and no redundancy.By replacing traditional directional filter bank in contourlet transform with adaptive directional filter bank,we obtain a new contourlet transform——adaptive contourlet transform.According to the orientation distribution of bandpass image from each Laplacian Pyramid stage,adaptive contourlet transform can adaptively generate the matched nonuniform partitioning with arbitrary number of subbands,which means the sparser representation.Theoretical analysis and simulation results show that,at the same compression ratio,new contourlet transform achieves better reconstruction quality in compressed sensing system.2.The role Laplacian Pyramid filter bank plays in new contourlet transform is scale decomposition,and the resulting bandpass image without sampling contains some data redundancy,which is undesirable in image compression.To solve this problem,we replace Laplacian Pyramid filter bank with wavelet transform.Wavelet transform generates one low-frequency and three high-frequency parts at each stage,and the four parts will be critically sampled to remove redundancy they contain.After applying adaptive directional filter bank to each high-frequency part,the input image can achieve adaptive directional decomposition in multiscale without redundancy.Compard to wavelet transform with the same redundancy ratio,theoretical analysis and simulation results show that this scheme gets better compression performance.