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Restoration Methods

For j=1,2,...,p we denote by gj 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
  • f is the unknown target;
  • Kj is the PSF of the interferometer corresponding to the j-th orientation of the baseline;
  • bj is the average background due to sky emission;
  • wj is the noise term (Poisson and read-out noise);
  • the * denotes convolution product.

  • 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 Aj the matrix associated with the PSF Kj

    (3)

    and by the transposed matrix

    We also introduce the subtracted images gs,j

    (4)

    The restoration problem is the following: Given the images gj , the PSFs Kjand (estimates of) the backgrounds bj, to evalute a restored image fres such that Ajfres reproduce the subtracted images gs,j within the errors due to the noise.

    Given the restored image fres, the relative RSM restoration error is defined by

    (5)

    while the relative discrepancy is defined by

    (6)

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