Compressed sensing for image processing

Data compression technology is one of the effective measures to improve the wireless data transmission speed. The traditional data compression technology is based on Nyquist sampling law, and reduces its redundancy according to the characteristics of the data itself, so as to achieve the purpose of compression. The compressed sensing theory (CS) that has emerged in recent years is not subject to Nyquist sampling law. It uses non adaptive linear projection to maintain the original structure of the signal, and extracts as much information from as little data as possible by directly collecting compressed data. This dissertation expounds the basic principle of compressed sensing method, analyzes the CS theoretical framework and key technical problems, introduces the advantages of compressed sensing technology in wireless sensing, focuses on the latest progress in signal sparse transformation, observation matrix design and signal reconstruction algorithm, and discusses the existing difficult problems in the research. Using MATLAB software, based on the different Dictionary matrix selection, such as random matrix and discrete cosine transform (DCT) matrix, the high probability reconstruction of one-dimensional signal and twodimensional image is realized by diverse algorithms, like iteration soft threshold algorithm (IST), iteration hard threshold algorithm (IHT), and orthogonal matching pursuit algorithm (OMP). Comparing the reconstructed results with the original signal, the results show that as long as the sampling number m (much less than the sampling rate required by Nyquist theorem) can contain the useful information required by the image, CS algorithm can accurately reconstruct the image, and the reconstruction effect is also better. Moreover, some further discussion is also included, regarding the CS algorithm used in image inpainting and image denoising.Master of Science (Signal Processing