Research On Image Compressive Sensing Technology Based On Redundant Dictionary

Based on the sparsity and compressibility 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. Because of the lower sample rate and fewer sampling values, it is easier to design hardware of the signal acquisition system, the cost of the transmission and storage of sampling data reduces largely as well.Compressive sensing theory mainly contains three core problems: the design of measurement matrix which satisfies Restricted Isometry Property(RIP) or uncorrelated property; the design of sparse dictionary which can sparsely represent signals; the design of reconstruction algorithm which can reconstruct the original signals quickly and accurately. The sparsity of signal is the promise of the theory of compressive sensing, to ensure that the signals obtain sparsity, the signals are usually expanded based on the sparse dictionary. The design of measurement matrix is the key to compressive sensing theory, measurement matrix and sparse dictionary are required to be uncorrelated. Reconstruction algorithm is a means of reconstructing signal in compressive sensing theory. The design of fast, accurate and robust reconstruction algorithm has always been the focus of the study of compressive sensing theory.As to image compressive sensing, Gan proposed block compressive sensing. By dividing the large size image into blocks, the processing of each image block is processed separately, the speed of sampling and reconstruction is accelerated, and the storage space is saved. This paper mainly studies the random observation process and the design of sparse dictionary in image compressive sensing, the main work are as follows.1. Traditional block compressive sensing(BCS) of images uses the same measurement rate to measure each block, while different image blocks contains different structural features, the number of measurements varies as well. In this paper, an adaptive measurement rate setting method is proposed. According to the variance, the image blocks are classified into different classes, then, different measurement rates are assigned to each class of blocks according to their variance. Through the reasonable allocation of limited measurement resources, the effectiveness of measurement is improved greatly. The simulation results show that the quality of reconstruction image of proposed method outperforms the non-adaptive method.2. In the process of sparse dictionary training in image block compressive sensing, all the image blocks are sparsely represented under the same sparse dictionary. It sets a great demand on the richness of structural features of dictionary atoms. The features of the image blocks varies a lot, in order to improve the adaptability of dictionary to image blocks, a method of training dictionaries based on classified image blocks is proposed. The image blocks are classified according to the variance; parameters of learning algorithm are set to be different for training different sparse dictionaries. The features of dictionaries trained by proposed method are better consistent with the image blocks, and the sparse approximation of blocks based on the sparse dictionaries is more accurate.3. Combined with adaptive measurement rate setting method and the method of training dictionary based on classified blocks, the blocks are reconstructed by Orthogonal Mathing Pursuit(OMP)algorithm. Reasonable distribution of measurements brings more effective measurements; the sparse dictionaries trained on classified blocks are more accurate for sparse representation. Therefore, compared with the original method, the improved method obtains a better reconstruction result, and a higher PSNR value of reconstruction image.