TY - JOUR
AU - Kunze, Herb
AU - La Torre, Davide
AU - Vrscay, Edward
PY - 2013/11/01
Y2 - 2023/12/01
TI - COLLAGE-BASED INVERSE PROBLEMS FOR IFSM WITH ENTROPY MAXIMIZATION AND SPARSITY CONSTRAINTS
JF - Image Analysis and Stereology
JA - Image Anal Stereol
VL - 32
IS - 3
SE - Short Research Communication
DO - 10.5566/ias.v32.p183-188
UR - https://www.ias-iss.org/ojs/IAS/article/view/1030
SP - 183-188
AB - We consider the inverse problem associated with IFSM: Given a target function <em>f</em>, find an IFSM, such that its invariant fixed point <span style="text-decoration: overline;"><em>f</em></span> is sufficiently close to <em>f</em> in the <em>L<sup>p</sup></em> distance. In this paper, we extend the collage-based method developed by Forte and Vrscay (1995) along two different directions. We first search for a set of mappings that not only minimizes the collage error but also maximizes the entropy of the dynamical system. We then include an extra term in the minimization process which takes into account the sparsity of the set of mappings. In this new formulation, the minimization of collage error is treated as multi-criteria problem: we consider three different and conflicting criteria <em>i.e.</em>, collage error, entropy and sparsity. To solve this multi-criteria program we proceed by scalarization and we reduce the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented. Numerical studies indicate that a maximum entropy principle exists for this approximation problem, <em>i.e.</em>, that the suboptimal solutions produced by collage coding can be improved at least slightly by adding a maximum entropy criterion.
ER -