id: 03996976 dt: j an: 03996976 au: Liang, Z.; Hart, H. ti: Bayesian image processing of data from constrained source distributions. I: Non-valued, uncorrelated and correlated constraints. so: Bull. Math. Biol. 49, 51-74 (1987). py: 1987 pu: Springer, New York la: EN cc: ut: constrained source distributions; correlated constraints; EM algorithm; a priori unvalued source distribution information; quadratic optimization; Bayesian image processing algorithms; Poisson; Gaussian statistics; maximum entropy; maximum likelihood equations; a priori source information ci: Zbl 0615.62150 li: ab: A series of Bayesian image processing algorithms which incorporate various classes of a priori source information in treating data which obeys Poisson and Gaussian statistics is derived using maximum entropy considerations. The standard maximum likelihood equations are shown to be a special case of Bayesian image processing when the a priori information about a source distribution $\{ϕ\sb j\}$ is solely that a non- vanishing probability for each element value $ϕ\sb j$ exists only in some finite interval, $a\sb j\le ϕ\sb j\le b\sb j.$ Bayesian image processing equations of the a priori source information that all $ϕ\sb j$ are finite $-\infty <ϕ\sb j<\infty$ and each $ϕ\sb j$ distribution has a defined mean ${\bar ϕ}\sb j$ and a defined variance $σ\sb j$ are derived. The Bayesian image processing equations are also derived when the a priori source information is that all $ϕ\sb j\ge 0$ and that each $ϕ\sb j$ distribution has a defined mean ${\bar ϕ}\sb j$ and a defined variance $σ\sb j$. The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods. rv: