Research On Reconstruction Algorithm Based On Compressed Sensing

Compressed sensing is a new type of sparse sampling. There are two different aspects from the classical Shannon sampling. Firstly, it is random sampling instead of uniform sampling. Secondly, the interpolation is used in Shannon sampling while the algorithm of optimization in mathematic is used in the compressed sensing. It means the compressed sensing reconstructs the original signal by searching the least sparse sampling points. Hence it saves the process of compressing after sampling, that is to say, it integrates with the two processes. So it saves much more storage and will have potential application in the engineering.In this paper, we principally invest the algorithm of the compressed sensing, which includes two major parts, the sparse matrix and the measurement matrix respectively. We give some examples of the sparse matrix. Specially, we propose the fractional Fourier transform as the sparse representation of the original signal creatively and analyze its feasibility. Also we give the condition meeting the measurement matrix and exemplify some model of the measurement matrix.As a new theory, the reconstructed algorithm of compressed sensing emerges a lot recently. Some authors proposed the block compressed sensing in order to improve the real-time. However it used the same measurement matrix in every block of the image. It means the value of every block is not distinction except the amounts of the pixel. For an image, the edge is the important part, which is also the sensitive to mankind vision. The proportion of the edge in each block is different as so as the importance of each block. In this paper, we propose the weighted block compressed sensing based on mankind vision. Then we apply it to the orthogonal matching pursuit and minimization total variation. In order to verify the effectiveness of the algorithm, we perform a lot of numerical simulation. We show that the new method can improve the real-time comparing with the algorithm of compressed sensing without blocking and the PSNR nearly one decibel comparing with the algorithm of the block compressed sensing respectively.