Wavelet Packet Image Compressed Sensing

With the rapid developme nt of information technolo gy, peop le’s demands for theima ge informatio n are increasing as well. How to store, process and transmit the largeamount of ima ge data is an important s ubject which is worth to be stud ied.Compressed sens ing breaks through the bottle neck of Sha nno n samp ling theory and itprovides a new way for how to acquire information. Compressed sens ing has got agreat attention in the fie ld of ima ge process ing. Image compressed sensing has madecertain progress. However, there are two shortcomings in most methods of the waveletima ge compressed sensing. The first one is that the wave let trans form is used tosparse the images and it makes the high frequency parts aren’t decomposed further.The second one is that the samp ling number is genera lly set manually whic h makesthe samp ling number is fixed, so the samp ling number can’t be selected adaptive lywhich makes the effects of some reconstructed images are poor.The wave let packet ima ge compressed sensing is stud ied in this paper in whichthe wave let packet transform is used to imp rove the image sparse degree. At the sametime, in order to reduce the samp ling and reconstructio n time, the information entropyand mathe matica l expectation are adopted to classify the signa ls. What’s more, thesequentia l compressed sens ing is introduced in this paper and we also make someimprove ments to this method. By doing this, the compressed sens ing processingsigna l can samp le adaptive ly. The ma in work is as fo llows:(1)Review the traditiona l image compressio n and summarize its ins uffic ie nt.Then the advantages of image compressed sens ing are pointed out. Also, some typica lmethods of ima ge compressed sensing are described. The advanta ges of these methodsand some commo n proble ms of the m are summarized.(2)The adaptive wave let packet image co mpressed sensing is proposed, in whichthe wave let packet transform is used to decompose the image. After the ima ge isdecomposed, all the wa velet coeffic ients are thresho ld processed according to themathematica l expectation. The n wave let packet blocks are class ified to different typesof signa l adaptive ly with the introduction of mathematica l expectation andinformatio n entropy. The correspond ing samp ling methods are designed to deal withdifferent types of s igna ls, which can adapt to the different characteristics of ima ges.Experime nta l results show that, whe n the sa mpling number s are the same, ourproposed algorithm can not only greatly improves the reconstruction qua lity of ima ges, but also reduces the computatio nal co mple xity and required me mory.(3)The sequentia l wa ve let packet compressed sensing is put forward, in whichthe sequentia l compressed sensing is used to dea l with wave let packet blocks. Afterthe image is decomposed by wave let packet transform, the relatio nships betweenwavelet packet blocks’ mathe matical expectation and the ir samp ling number areanalyzed according to the relations hips between the ir mathe matica l expectation andthe ir sparse degree. Then the samp ling length of the initia l samp ling s igna l ispredicted through mathe matica l expectation. This not only overcomes the defic ienc iesof the sequential compressed sens ing, but a lso the sa mpling number can be selectedadaptively. Experimenta l results show that, there are really have a proportiona lrelations hip between the mathe matica l expectation and the eventua lly samp lingnumber, so the initial sa mp ling number is predicted by the mathe matica l expectationis reasonable.