The Study Of Compressed Signal Reconstruction Algorithm And Its Applications

Traditional signal sampling is the Nyquist criterion for theoretical guidance, and it claims more than twice the sample rate to bandwidth. With the development of technology and science, bandwidth tends bigger in the practical application of signal sampling, traditional theory sampling can not meet our needs. A new sampling theory emerged, namely compressive sensing theory. It implements sampling and compression simultaneously in the signal sampling process, and need not to get massive sampling data, thus saving time and storage space. Currently, compressed sensing theory is a research hotspot in the international, it has a high practical value in many areas, so it will have a very broad application prospects.This paper introduces the theory of compressed sensing system, it is one of the core aspects: the sparse representation of the signal, the designing of the measurement matrix and the reconstruction algorithms are described in detail, and we mainly introduce several typical algorithms of the reconstruction algorithms and compare their performance through experiments. Reconstruction algorithms based on smoothed L0 norm minimization are 2-3 times faster than other algorithms in the same or better accuracy, this paper made the following study on smooth L0 norm minimization algorithm:SL0 algorithm selects the smoothed Gaussian function as the function of the approximate estimate of L0 norm, In this paper we choose the complex trigonometric functions, the functional image shows complex trigonometric function is steeper than the existing Gaussian function, so it has a better approximation performance. For reasons that steepest descent method is jagged in searching path and Newton’s method is slow when iterative point is far from optimal solution, this paper combines the above two methods, and use the steepest-descent approach in the first several step and then followed by Damped Newton method in the iterative process of optimization. Numerical simulations illustrates the effectiveness of the improved algorithm, and compared with other algorithms, this algorithm is significantly improved in image reconstruction accuracy.NSL0 algorithm is also a reconstruction algorithm based on smoothed L0 norm, For the shortcomings of slowing convergence using a damped-Newton algorithm when vector isaway from the optimal solution, this paper uses the steepest-descent method in the first several iterations and then uses a damped-Newton method. We designed an effective iterative step in the iterative process of damped-Newton method. The iterative step obtained by one-dimensional exact search for the first iteration. By designing updating scheme of iterative step, the calculation of each iteration step is more effective, so it is able to enhance the convergence rate in ensuring the accuracy of the reconstruction at the same time. We joined the Support, which estimated by the sparse vector obtained by previous iteration. Then established an approximate L0 norm minimization problem based on the Support. Artificial data and machine image experiments illustrates the effectiveness of the improved algorithm.