Study On Compressed Sensing Algrithom And Its Application In Vector Quantization

Compressed sensing is currently a novel signal processing method,which comprises of sampling, compressing and coding. It has broken the Nyquist sampling theorem, and can reconstruct the original signal in a high probability using the method to solve a convex optimal problem in case of a small amount of measurement results.Due to its characteristics, compressed sensing has been extensively used in voice, images and so on. In this thesis, we compare the difference of reconstruction algorithms of compressed sensing and apply them in vector quantization.We firstly introduce the basic theory of compressed sensing, and then discuss several reconstruction algorithms of compressed sensing ,including greedy algorithm, such as OMP,ROMP,SP, convex optimization algorithm (GPSR,IHT,SL0), and non-convex algorithm (IRLS). The numerical simulations show that SL0 and IRLS algorithm have more accurate than other algorithms in the reconstruction quality. SP algorithm is slightly worse and ROMP and OMP are more slight. GPSR and IHT algorithm have the worst reconstruction quality. For example for Lena image, Peak signal-to-noise rate (PSNR) of the reconstructed image is greater than 45 dB with SL0 and IRLS algorithm, and is equal to 40 dB with SP algorithm. In terms of reconstructed using time, IHT algorithm is the optimal one since it only needs a few seconds to reconstrunct the image, which is less than other reconstructed algorithms.We then consider the application of compressed sensing in neural network vector quantization. Vector quantization is an effective lossy compression method, but the quality of reconstructed signal is bad with a big compression ratio. We apply the different compressed sensing reconstruction algorithms, such as OMP, GP, SP, IRLS, SL0 and GPSR, to the neural network-based vector quantization. By numerical simulations, we find that the quality of image in neural network vector quantization has been improved several dB using compressed sensing. For lena, girl and couple image, the PSNR of the recosntruced image in neural network vector quantization have been enhanced to 6-7dB,3-4dB and 1dB using compressed sensing. For the same condition, GPSR algorithm has a good quality with higher 0.1-1dB to other algorithms and needs shorter time in the reconstruction.