Research On Band-limited Signal Reconstruction From Nonuniform Sampling Based On Landweber Iteration Schemes

Fast Fourier Transform (FFT) is a fast and efficient algorithm for computing the discrete Fourier transform (DFT) and its inverse transform.It is widely used in many fields. In FFT algorithm, the sampling intervals must be equal. However, in practical applications, we can not guarantee the sample data distributing in uniform grids. So research on Non-uniform sampling has theoretical and practical meanings. Some scholars proposed the Non-uniform Fast Fourier Transform algorithm(NUFFT). In this thesis, I analyzed the NUFFT algorithm as well as its application in the CT, and based on the Landweber Scheme, propose the Band-Limited signal image reconstruction algorithm from Non-uniform sampling. According to band-limited signal non-uniform sampling theory, we studied the sampling methods and sampling formats, attributing the reconstruction of band-limited signal to integral equation in the frequency domain. After discretion, the reconstruction problem is changed into the problem of solving linear equations. Using the effective method, Landweber iteration, according to the the convergence condition of Landweber iteration, I study the iterative parameter choice to accelerate the convergence of the algorithm. After that, I give a numerical example to simulate the results and demonstrate the effectiveness of the proposed method.