Research On Signal Reconstruction Algorithm Of Compressed Sensing Based On Gradient Projection Method

With the rapid development of science and technology, the signals in actual become more and more complex, the classical signal processing techniques are incompetent for that, and the Nyquist sampling theorem is also be challenged. Compressed sensing theory came into being, which can apply to all compressible signals. Compressed sensing is a technique that enables us to fully reconstruct particular classes of signals with the appropriate if the original is sampled at a rate below the Nyquist rate. It includes three aspects:sparse representation, measurement matrix and reconstruction algorithm. Of the three, the reconstruction algorithm is more important and also be a hot topic.At present, there have a variety of reconstruction algorithms in compressed sensing, but their speed is not fast. This paper focuses on the gradient projection algorithm, which has a lot of advantages, such as better reconstruction, low computational complexity, simple structure and be easy to implement. But it has general speed compared to other algorithms, and not resolves the reconstruction of image signal. To those problems, we proposed improve methods in this paper. First of all, we propose an improved gradient projection algorithm, we chose a variable step instead of the optimal step in iterative process, and the results show that the improved algorithm is faster than the original algorithm under the same conditions. Second, because that it is next to impossible to reconstruct an image with random measurement matrix for the matrix need large memory, we proposed a based-block gradient projection algorithm, which can improve the quality of the reconstruction compare to the method in a column-wise manner. At the same time, we improved the partial Fourier measurement matrix, and used this matrix instead of random measurement matrix in the compressed sampling, which reduced the size of measurement matrix, and the experimental results show that the improved method is effective.