Research On Image Reconstruction Technique Based On Compressed Sensing Theory

In recent years, the compressed sensing(CS) theory, which appeared from the signal processing field, break the conventional Nyquist sampling theory which requires the sampling frequency must at least twice the highest frequency of signal to reconstruct the original signal accurately. And the cost of the information storage、processing and transmission are significantly reduced. This paper realizes the reconstruction of the signal and image by the CS theory, and mainly research on the following aspects in this paper:(1)Based on the discrete fourier transform (DFT) and wavelet transform, this paper realizes the accurate reconstruction of one-dimension signal and two-dimension image by applying the OMP algorithm.(2)This paper completes the reconstruction of the images base on the block CS which used the discrete cosine transform (DCT). The quality of subjective vision and PSNR of the algorithm are better than the original algorithm, and the storage space for the Gaussian matrix is smaller after the image blocking. The reconstruct of the image block is also easier to achieve.(3)A novel enhancement scheme based on the above algorithm was proposed in this paper. In this scheme, a weighting matrix will be multiplied on the Gaussian matrix to put different emphasis on different frequency components according to the characteristics of human perception system. The experimental results show that the proposed algorithm can get better reconstruction performances than the above algorithm, and it can get better PSNR performance at different sampling rates.(4)This paper adds the wavelet thresholding method to the OMP algorithm, and set appropriate threshold to choose the coefficients by the wavelet transform in the iterative process of the OMP algorithm. At last, we complete the signal and image denoising by this method. It also has a better performance in the denoising for signal or image than the traditional wavelet soft thresholding method.