Abstract

Bajkova's generalized maximum entropy method for reconstruction of complex signals is further generalized through the use of Kullback–Leibler cross entropy. This permits a priori information in the form of bias functions to be inserted into the algorithm, with resulting benefits to reconstruction quality. Also, the cross-entropy term is imbedded within an overall maximum a posteriori probability approach that includes a noise-rejection term. A further modification is transformation of the large two-dimensional problem arising from modest-sized two-dimensional images into a sequence of one-dimensional problems. Finally the added operation of three-point median window filtration of each intermediary one-dimensional output is shown to suppress edge-top overshoots while augmenting edge gradients. Applications to simulated complex images are shown.

© 1994 Optical Society of America

Reconstruction of complex signals using minimum Rényi information

B. Roy Frieden and Anisa T. Bajkova
Appl. Opt. 34(20) 4086-4093 (1995)

Reconstruction of a complex-valued object in coherent imaging through a random-phase screen

Nobuharu Nakajima and Bahaa E. A. Saleh
Appl. Opt. 33(5) 821-828 (1994)

Reconstruction of tomographic images from sparse data sets by a new finite element maximum entropy approach

Robert T. Smith, Csaba K. Zoltani, George J. Klem, and Monte W. Coleman
Appl. Opt. 30(5) 573-582 (1991)

Minimum entropy–neural network approach to turbulent-image reconstruction

Yuanmei Wang and B. Roy Frieden
Appl. Opt. 34(26) 5938-5944 (1995)

Reconstruction of three-dimensional chemiluminescence images with a maximum entropy deconvolution algorithm

Kathryn R. Gosselin and Michael W. Renfro
Appl. Opt. 51(11) 1671-1680 (2012)