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: