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Restoration Methods
For j=1,2,...,p we denote by g
_{j} the p images corresponding to p different orientations of
the baseline of LBT. They are arrays NxN and they are assumed to be given by: (1) where _{j} is the PSF of the interferometer corresponding to the j-th orientation of the baseline; _{j} is the average background due to sky emission; _{j} is the noise term (Poisson and read-out noise); The Discrete Fourier Trasforms (DFT) of are denoted by If the convolution product is defined as a cyclic convolution, then equation (1) becomes (2) The DFTs can be easily and efficiently computed by means of the FFT algorithm when N is a power of 2. In the following we denote by A _{j} the matrix associated with the PSF K_{j} (3) and by the transposed matrix We also introduce the subtracted images g _{s,j} (4) The restoration problem is the following: Given the images g _{j} , the PSFs K_{j}and (estimates of)
the backgrounds b_{j}, to evalute a restored image fres such that A_{j}f_{res}
reproduce the subtracted images g_{s,j} within the errors due to the noise. Given the restored image f _{res}, the relative RSM restoration error is defined by (5) while the relative discrepancy is defined by (6) |