Fourier Transform Compressed Sensing Reconstruction Of Real Discrete Sparse Signal

The signal reconstruction can be attributed to that the original signal is recovered from the sampling signal in the frequency domain. However the signal sampling is limited by the Shannon sampling theorem. The appearance of compressed sensing theory broke through the bottleneck of the Shannon sampling theorem. And high-resolution signal acquisition became possible. Compressed sensing is a sparse or compressible signal technology for signal reconstruction. Fourier transform plays an important role in the signal reconstruction and MRI. So the article will use the compressed sensing of the discrete Fourier transform to conduct the signal reconstruction.The theoretical basis of reconstruction algorithm includes the compressed sensing problem of discrete Fourier transform, the conditions to stable reconstruction, solution to convex optimization problem, including non constraints, equality constraints and inequality constraints and the method of transformation.The image reconstruction algorithm is based on compressed sensing. The problem can be transformed into solving the minimum L-1norm. The minimum L-1norm is a convex optimization problem. We are using the steepest descent method and the interior point method in linear programming method to solve convex optimization problem. And we present numerical experiments with internal point method in MATLAB and achieve good results.