Image Compressed Sensing Based On Bandelet Transform

In2005, Candes and Donoho proposed Compressive Sensing theory,which is amilestone in the history. The theory breakthrough the limit of Nyquist Theory.It solve thesignal processing bottleneck: sampling frequency is at least twice as many as the originalsignal,if it can be complete without loss of precise original signal from the sampling.Compressive Sensing theory is a new theory, which compress datas while sampling. It doesnot need compress after sampling. Principle of prior knowledge is used in CompressiveSensing that signal is sparse or compressibility.It is different from Nyquist Theory which onlyuses bandwidth of signal as its prior knowledge.It provides the possibility.to reduce the cost ofsignal measurement.Sparse is a very important part in the image Compressive Sensing theory.The Thetraditional sparse representation use wavelet transform generally. But the wavelet transformcan’t use the geometry characteristic of signal,so it can not achieve the optimal sparse.Compression sensing reconstruction also can’t get the best results with wavelet transform.In order to solve the problem above, Image Compressed sensing based on Bandelettransform domain is proposed after researching variety of sparse representation. Bandelettransform is a mage representation method unfolds in recent years. It can make full use of thegeometry of the image achieve the optimal sparse representation. Image Compressed sensingbased on Bandelet transform domain solve the problem in image Compressive Sensing thatthe reconstruction is week because of sparse representation.The algorithm is proposed forward the process is as follows:First of all, Image compressed sensing theory and the foundations of mathematics areresearched.It is divided into three parts:sparse representation,measurement and reconstruction.Then,characteristics of wavelet transform and Bandelet transform in the image sparserepresentation are analyzed.It provide theoretical basis for Bandelet transform into imageCompression Sensing.Finally, Compressed sensing based on Bandelet transform domain are proposed. thesimulation experiment after the analysis of experimental results, and and and based onwavelet transform and DCT transform Contourlet transform domain mentioned the imagecompression sensor in the visual and PSNR data contrast, confirmed the superiority of the proposed method is put forward in this paper, especially for the gray distribution is more rulesof the image compression in the sensor. Verify the correctness of the above theory analysis.