Image Sampling And Reconstruction Based On Compressed Sensing Theory

The current signal processing field has the following two key difficulties:(1) the Nyquist sampling frequency is too high, resulting in sampled data is amount too large; (2) data acquisition mode was not advanced enough, which is sampling first and then compressing, resulting in it is not only a waste of sensing element, but also a waste of time and storage space. This appearance restricts, to some extent, the development of signal and information processing.Presently, the generation of a new compressed sensing theory is founded, for sparse signal or compressible signal. This method can obtain the signal and compress the data properly at the same time, in hence the sampling frequency can be lower than The Nyquist frequency. The prominent advantages are reducing the sampling data, saving storage space and so on, however, containing enough information. When necessary, the appropriate reconstruction algorithms can be used to obtain enough recovered data points from compressed sensing data and reconstruct to the primitive signal. Compressed sensing combining traditional data collection to data compression, is very suited for some conditions required a miniature device to achieve, however, does not need complex data encoding algorithm. Compressed sensing and sparse reconstruction have become a new research direction in the field of applied mathematics and signal processing.This paper does research on the theory of compressed sensing, especially, understands the principles and specific applications of the compressed sensing theory and discusses the current mainstream algorithms and uses the ways of the experiment to achieve several of the current and classical algorithms. This paper also does research on the methods as the feedback neural network for solving sparse representation problems along with its some improved researches by quantities of experiments. Numerical experiments are conducted to investigate the influence of dimensional parameters and the sparsity level. Additionally, the author uses three distinct indicators which can reflect the performance of the reconstruction more objective to compare performance of the feedback neural network with that of several present main reconstruction methods and gets very perfect result. The compressed sensing theory will be applied to image reconstruction by the framework which links the compressed sensing theory to the image reconstruction. For the current ways'slow pace and low quality of reconstruction shortcomings, applying the neural network in the image reconstruction algorithm can improve the image compression ratio and recovery performance. In the end the author combines the neural network reconstruction algorithms with the ranks equilibrium and blocking idea which is in the image processing to further enhance the recovery effect, meanwhile innovatively raises a kind of scheme for increasing the compression ratio and reconstruction efficiency through reconstructing the signal by different blocks based on singular and multiply image DWT. Numerical experiments are conducted to confirm the availability of the scheme which can virtually increase the compression ratio and performance to image.