Research On Reconstruction Algorithms Of Blind Band-limited Functions Based On Orthogonal Matching Pursuit

Blind band-limited signal extrapolation method is an important research direction of signal reconstruction, its application field included radar, geology, medicine, astronomy etc. Because of the band-limited signal in time domain is infinitely long, we research the signal obtained by time domain observation, only part of the observation signals, sometimes we don’t know in the practical application of the signal with limited range, so how to make use of time domain sampling to reconstruct blind band-limited signal is an important topic of the current research signal reconstruction.If we know the limited range of the band-limited signal, we can use the G-P algorithm or Landweber iteration algorithm to reconstruct signal. If the observation interval is small, the band-limited signal extrapolation is a severely ill-posed problem. At this time, using the G-P algorithm or Landweber iteration algorithm is hard to get effective reconstruction results.In compression perception, orthogonal matching pursuit algorithm (OMP) is a simple and easy to implement effective sparse signal reconstruction algorithm which under the condition of certain limited isometric. It can reconstruct signal a sets and its values. In this paper, using the orthogonal matching pursuit algorithm to research the reconstruction of blind band-limited signal. According to the expansion of long ball wave and the properties of band-limited signal eigenvalue, we get the approximate summation of finite entries of band-limited signal. When the limited interval get bigger, band-limited signal satisfy certain isometric properties. According to Sanz-Huang theorem, I structured discrete form of band-limited signal, and proved by the single and many band. I analysis the data of error in the numerical simulation, getting the more accurate band-limited interval. Band-limited signal reconstruction effect is better with T increasing, so the orthogonal matching pursuit algorithm is a good method in the reconstruction of blind band-limited signal.