Research On Image Recovery Algorithms Based On Compressed Sensing

In the field of signal processing,how to obtain required information by retaining a small amount of valid data has become a new requirement.Compressed sensing theory shows that if the signal is compressible or sparse in an orthogonal transform domain,then projected dimensionality reduction can be achieved through the measurement matrix.Then the signal can be efficiently reconstructed with a small number of measured values using appropriate reconstruction algorithms.Compressed sensing theory breaks the limitations of the Nyquist theorem on the sampling frequency and completes data compression while sampling the signal.The paper mainly studies the design of measurement matrix and realization of image reconstruction in compressed sensing theory,and puts forward some improvements on the basis of previous research.The main research contents are as follows:1.The measurement matrix is Schmidt-orthogonalized,and the projection vector of the measurement matrix is projected on the orthogonal base using the projection principle.The difference between the vector and the projection is calculated to minimize the correlation of the vectors in the matrix.Experiments show that projection principle is applied to map the row vectors of the measurement matrix onto the orthogonal basis,and the smaller the number of orthogonalized M is,the greater the improvement of the compressed sensing measurements measurement matrix.2.A reconstruction algorithm based on sparse feature weights of structure groups is proposed.The weights decrease with the increase of sparse coefficients.Small weights are used for large sparse coefficients while large weights are used for small sparse coefficients so that they can be adaptive to the sparse coefficients of the image structure block group.This method can better preserve the effective information of the image and improve the reconstruction quality.The Gaussian random measurement matrix is adopted as the measurement matrix,and reconstruction is performed based on the soft threshold shrinking method.Experiments show that the quality of image reconstruction is higher than that of similar algorithms.3.Based on the superiority of the orthogonalization of the measurement matrix,theSchmidt orthogonalization processing of the Gaussian random measurement matrix in the sparse feature weighted reconstruction algorithm of the structure group is proposed.On the basis of the sparse feature weighting algorithm of the structural group,an improved reconstruction algorithm is implemented using the orthogonalized measurement matrix.Experimental results show that the improved reconstruction algorithm effectively improves the quality of image reconstruction.Compared with similar algorithms,the average gain of the peak signal-to-noise ratio is about 1 dB under the condition of similar time.