Role of positivity for error reduction in images
Charles L. Matson · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
In this paper, the role positivity plays in error reduction in images is analyzed both theoretically and with computer simulations for the case of wide-sense-stationary Fourier- domain noise. It is shown that positivity behaves as a signal-dependent support constraint. As a result, the mechanism by which positivity results in noise reduction in images is by correlating measured Fourier spectra. An iterative linear algorithm is employed to enforce the positivity constraint in order to facilitate an image domain variance analysis as a function of the number of iterations of the algorithm. Noise reduction can occur only in the asymmetric part of the positivity-enforced support constraint when positivity is applied just as noise reduction only occurs in the asymmetric part of the true support constraint when support is applied. Unlike for support, noise decreases in the image domain in a mean square sense as the signal-to-noise ratio of the image decreases. However, it is shown that this image-domain noise decrease does not noticeably improve identification of image features.