Compressed Sensing And The Application In Digital Image Compression Coding

As a new research field in recent years, compressed sensing has aroused wide concern in the academic circles at home and abroad, which has been applied in the video processing, image processing and audio processing. In the field of image processing, the compressed sensing has made certain research results in pattern recognition, image denoising and deblurring.As the theoretical foundation of traditional image compression algorithm in the sampling step, Nyquist has pointed out that in order to reconstruct the original signal accurately, the sampling rate must be more than two times the original signal bandwidth, which makes the transmission of information received many limits. At the same time, the traditional orthogonal sparse basis can not reflect the essential characteristics of signals completely, and some signal cannot be sparsely represented sufficiently, which will decrease the quality of the reconstructed signal. The compressed sensing theory breaks through the limitations of the Nyquist sampling theorem, which uses a little signal sampling to totally or partly recover the original signal. As an important branch of sparse representation, the redundant dictionary can reconstruct the signal by its own characteristics. Therefore, using the redundant dictionary to replace the orthogonal sparse basis will bring a better quality of reconstructed signalIn this paper, we analyze the synchronicity of the sampling and compressing in the process of compressed sensing and the nonorthogonality of the atoms in the K-SVD dictionary. Based on the analysis, we further develop an adaptive digital image compression algorithm. The innovation of this algorithm is that:using K-SVD dictionary to replace DCT and DWT basis, which can represent the image according to its own characteristics, to improve the quality of the reconstructed image; only encoding the weights and position of the non-zero coefficients in the sparse matrix which can improve the compression ratio. Through a large number of experiments, we compare the reconstructed images under different parameters and analyze the effect on the ratio and the quality. We also compare with the JPEG and JPEG2000. By adjusting the parameters, the ratio and the quality will be better than that by using JPEG and JPEG2000, which shows the feasibility and the superiority of the algorithm. The disadvantage of the algorithm is that, because of the complexity of K-SVD algorithm itself, it makes the algorithm more expensive time in the operational phase, so optimizing the speed of the algorithm needs to be improved.