M.Sc Student | Giryes Raja |
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Subject | Automatic Parameter Tuning for Inverse Problems |

Department | Department of Computer Science |

Supervisors | Professor Michael Elad |

Professor Yonina Eldar | |

Full Thesis text |

Linear inverse problems are very
common in signal and image processing. In these problems, an original image **x**
is deteriorated by a (known) linear operator **H**, followed by additive
white Gaussian noise **w**. Given the measurement **y**=**Hx**+**w**,
the goal is to reconstruct **x**. When the image **x** is known to have a
sparse representation over a dictionary** D**, an effective way to recover **x**
is to use an iterative shrinkage algorithm. This algorithm provides an
iterative estimator for **x** denoted by *h _{lambda}*

In our work we use this estimator to
drive an automatic tuning of the estimator *h _{lambda}*

Our work differs from this
contribution in several important ways. First, our proposed algorithms for
parameter selection handle any matrix **H**, including ill-posed and even rectangular
operators. Second, we put forward two additional parameter setting schemes,
both based on a greedy approach that tunes the *lambda* per iteration with
and without a look-ahead option. This way, each iteration leads to a different value
of *lambda*, and this gives a natural way to set the number of iterations
simultaneously - the iterations can be stopped when the estimated MSE
improvement is below a certain threshold. Third, we offer a way to adopt the
parameter *lambda* to the scale of the atoms in the representation, thus
enabling different shrinkage per scale. Fourth and last, we provide extensive
comparisons to conventional methods for parameter selection showing the
superiority of the use of GUSRE.