The notation used in this paper is the following:

DNumber of detectors in the arrayBNumber of elements (pixels) in the reconstruction projection (measured) data emission density in the image (parameters to be estimated)f_{ji}Point Spread Function (PSF) or probability that an emission in pixeliin the source be detected at detectorjbackground in the data readout noise in the data detector gain corrections (flatfield) corrected PSF total detection probability for an emission from pixeliforward projection or blurring operationQ_{i}prior distribution density or default image (if any)

let be the corresponding arrays.

We shall work with the following imaging model: an object emits light with an intensity given by a spatial distribution . The light is focused by the optical system over a detector array consisting of individual, discrete, independent detectors. Each detector has a different quantum efficiency characterized by a gain correction distribution . A certain background radiation ,coming mainly from the sky but also from sources inside the detector system, is detected along with the spatial distribution . We assume that the detection process is Poisson distributed. Finally, the detector is read by an electronic process which adds a Gaussian readout noise with zero mean and known standard deviation . The imaging equation corresponding to this model is:

(1) |

Most imaging systems are described by Eq. (1), particularly those based on Charge Coupled Device (CCD) cameras, and Image Pulse Counting Systems (IPCS).

The background in Eq. (1) is an input in our algorithm. Some
authors (Bontekoe et al. 1994; Narayan & Nityananda 1986)
have raised
questions about the introduction of the background in Eq. (1).
Bontekoe et al. demonstrated that the solution depends on the background
in standard Maximum Entropy Method (MEM) algorithm. However, in our
approach, the background term includes not only light from the sky but
also light from sources inside the camera. In the case of a CCD camera,
the background term **b** can be considered as: (Snyder et al. 1993).
The term is the external background radiation. The term
is the internal background radiation from luminiscent
radiation on the CCD chip itself. The term is the number
of thermoelectrons that are generated by heat in the CCD and is the number of electrons that are due to bias or "fat
zeros". Those terms are all Poisson distributed random variables and
their sum can be represented by a single background term. We have not
observed in our algorithm the background dependence effect reported by
Bontekoe et al. (1994). In our opinion, if the background is large and
acurately known, it is better to include it in the equation and in the
reconstruction algorithm. Otherwise, it is always possible to set it to
zero in the algorithm and reconstruct the background as part of the
image.

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