The Image Compression Algorithm Based On Compressed Sensing Theory

Traditional image compression technique is limited by the Nyquist sampling theorem,so it requires huge memory space and fast data processing rate, and it is difficult toimplement its hardware system. The theory of compressed sensing breaks the limitation ofthe traditional sampling theorem and permits to sample and compress data simultaneously,makes up the drawbacks of the compression technique. Therefore, based on theachievements of previous researchers, this paper researches on the image compressionalgorithm based on compressed sensing theory.Firstly, in order to compare the image sparse representation ability between the MLDdictionary and KSVD dictionary, this paper uses the one hundred thousand image blocksof the Berkeley image library to train four kinds of different size of redundant dictionary,and computes the sparse representation error under different sparse level.Secondly, in order to improve the reconstruction precision of the image and the visualpresentation of the texture areas, this paper applies compressed sensing theory to imagecompression, and proposes a new kind of sampling methods: it samples the edge of thehigh frequency part of the image densely and the non-edge part randomly in the encoder,instead of using the measurement matrix to obtain the lower-dimensional observationdirectly in the traditional compressed sensing theory. In the decoder, this paper uses theposition of the sample-points to structure the block measurement matrix adaptively,realizing a overlap-block image reconstruction using smoothed l0reconstruction algorithm,combined the result with the interpolation amplification of the down-sampled points of thelow frequency part of the image realizing a high precision image reconstruction.Finally, in order to improve the compression ratio of the image, this paper proposes anew kind of classify methods, it uses the edge detector operator to classify the imageblocks, and uses different sampling rate to sample different image blocks. This papertrains classified dictionary with the help of the above-mentioned classify method, andstructures optimized measurement matrix that matching the dictionary and sampling rateto project different kinds of the image blocks to a lower-dimension. In the decoder, this paper uses smoothed l0reconstruction algorithm to obtain high-precision reconstructionimage.