Abstract
We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its fixed point f is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces 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.
| Original language | English |
|---|---|
| Title of host publication | ICNPAA 2016 World Congress |
| Subtitle of host publication | 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences |
| Publisher | American Institute of Physics Inc. |
| Volume | 1798 |
| ISBN (Electronic) | 9780735414648 |
| DOIs | |
| Publication status | Published - Jan 27 2017 |
| Event | 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016 - La Rochelle, France Duration: Jul 4 2016 → Jul 8 2016 |
Conference
| Conference | 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016 |
|---|---|
| Country | France |
| City | La Rochelle |
| Period | 7/4/16 → 7/8/16 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
IFSM fractal image compression with entropy and sparsity constraints : A sequential quadratic programming approach. / Kunze, Herb; La Torre, Davide; Lin, Jianyi.
ICNPAA 2016 World Congress: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Vol. 1798 American Institute of Physics Inc., 2017. 020090.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - IFSM fractal image compression with entropy and sparsity constraints
T2 - A sequential quadratic programming approach
AU - Kunze, Herb
AU - La Torre, Davide
AU - Lin, Jianyi
PY - 2017/1/27
Y1 - 2017/1/27
N2 - We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its fixed point f is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces 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.
AB - We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its fixed point f is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces 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.
UR - http://www.scopus.com/inward/record.url?scp=85013627084&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85013627084&partnerID=8YFLogxK
U2 - 10.1063/1.4972682
DO - 10.1063/1.4972682
M3 - Conference contribution
AN - SCOPUS:85013627084
VL - 1798
BT - ICNPAA 2016 World Congress
PB - American Institute of Physics Inc.
ER -