The Implementation of Conjugate Gradient into Prior Discrete Fourier Transform

• Main Authors: Jin-Gui Li, 李進貴
• Other Authors: Hsin M. Shieh
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/19481267002707245662

碩士 === 逢甲大學 === 電機工程所 === 97 === For imaging problem from limited number of Fourier transform values, there will exist infinitely many mathematically allowable solutions. The determination of a good image from these results is formidable. To resolve this non-uniqueness, the traditional discrete Fourier transform (DFT) is a simple and efficient method, but usually obtain an unfavorable image. The prior discrete Fourier transform (PDFT) can improve this degradation problem by solving a minimum weighted norm solution in a suitably-designed Hilbert space as an image estimate. But the PDFT will have a computational problem when the data set is large. In particular, the conjugate gradient (CG) method is used to resolve the computational problem, for which the superiority of the CG to the Gauss Jordan (GJ) and the direct matrix inversion is discussed and analyzed.