Application of compressed sensing

Abstract

Since the rise of the Internet, images, texts, audios and videos have become important methods for people to obtain information on the Internet. Images are the most intuitive way to obtain information among these methods. With the rapid increasing demand for image data, the traditional Nyquist sampling theory will generate a large amount of sampled data, which brings great difficulties to the transmission and storage of image data. Images can be damaged during acquiring from sensor or transmission in communication channel. Based on the sparsity of the signal, the compressive sensing theory can sample signal at the rate which is far below the Nyquist sampling frequency, and accurately reconstruct the original signal from sample data. And Traditional image restoration algorithms can't well remove the noise pollution in the image, and the compressed sensing theory can make up for these shortcomings. The main research content of this dissertation is as follows: (1) Introduce the sparse representation, measurement matrix, signal reconstruction ,dictionary design and dictionary learning. Generate a 2D-DCT dictionary. This 2D-DCT dictionary is used as initial dictionary. One training image is used to update the dictionary by KSVD. The sparse representation is calculated by OMP. After that, ten images are used to train the dictionary and judge the performance of this dictionary trained by ten images in comparison with trained by one. (2) An overlapped block reconstruction structure is used in denoising. The reconstruction block overlaps with each other every 4 pixel. Then every pixel will be shared by 4 blocks (excepts pixels near boundary). This denoising method is compared with the mean filter to judge which performs better.