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Inversion of picture operators |
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| Affiliation: | 1. Electronics and Communication Engineering, Sathyabama Institute of Science and Technology, Jeppiaar Nagar, Rajiv Gandhi Salai, Chennai, Tamilnadu, India;2. Electronics and Communication Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh, India;3. Bayview Asset Management, LLC, Florida, United States of America;1. IRIT, Université de Toulouse, CNRS, Toulouse INP, UT3, Toulouse, France;2. Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, France;3. Université de Lyon, INSA‐Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1294, F‐69621, Villeurbanne, France |
| Abstract: | Inversion of operators on pictures is shown to be an important part of classical image restoration techniques. A method is presented for nonlinear inversion of operators that enables nonlinear restoration. The problem of out of range values is handled by introducing a new definition for operations on pictures such that the set of all pictures is a vector space. It is empirically shown that the Conjugate Gradients algorithm converges quickly in this vector space and enables inversion of operators on big pictures with relatively little computation. Examples are given for applications of this method to linear and nonlinear operators. |
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