Title :
Image representation by spectral amplitude: conditions for uniqueness and optimal reconstruction
Author :
Shapiro, Yossi ; Porat, Moshe
Author_Institution :
Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa, Israel
Abstract :
New results in image representation and reconstruction from partial Fourier information are introduced. In particular, necessary and sufficient conditions for unique representation of two-dimensional signals (images) by spectral amplitude are introduced. It is shown that under mild conditions only half of the spatial information is required compared to the one-dimensional case. An algorithm far image reconstruction from spectral amplitude is described and examples of reconstructed image are presented. Based on the analysis of the reconstruction algorithm, a theorem on optimal reconstruction from Fourier amplitude is introduced, and it is proven that images of geometric form are best reconstructed by the algorithm. The results are compared to the dual case of image representation by spectral phase and conclusions are presented and discussed
Keywords :
Fourier analysis; image reconstruction; image representation; optimisation; spectral analysis; Fourier amplitude; geometric images; image reconstruction; image representation; necessary conditions; optimal reconstruction; partial Fourier information; reconstruction algorithm; spatial information; spectral amplitude; spectral phase; sufficient conditions; theorem; two-dimensional signals; unique representation; Algorithm design and analysis; Apertures; Convergence; Electron optics; Image analysis; Image reconstruction; Image representation; Iterative algorithms; Optical diffraction; Optical signal processing; Reconstruction algorithms; Signal processing algorithms; Sufficient conditions;
Conference_Titel :
Image Processing, 1998. ICIP 98. Proceedings. 1998 International Conference on
Conference_Location :
Chicago, IL
Print_ISBN :
0-8186-8821-1
DOI :
10.1109/ICIP.1998.727357
