| Presentation | 1998/12/11 Approximation of Convexly Constrained Pseudoinverse by Hybrid Steepest Descent Method Isao YAMADA, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Recently, Sabharwal and Potter considered convexly constrained linear inverse problem accompanied by prior knowledge that the solutions belong to a closed convex set. This formulation captures an important class of signal processing problems that includes (i) time-limited extrapolation with subspace constraints, (ii) image reconstruction with positivity constraint, and (iii) signal restoration accompanied by constrants on amplitude, support, or energy etc. Sabharwal and Potter proposed an algorithm by introducing Tikhonov's regularization technique to solve the convexly constrained linear inverse problem. Unfortunately since the convergence of Sabharwal and Potter's algorithm to the unique solution of the problem has not directly been discussed, this extremely important problem has not been resolved yet. In this note, we remark that the convexly constrained linear inverse problem can be solved directly by applying a corollary of the Hybrid Steepest Descent Method proposed by the authors. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Convexly Constrained Pseudoinverse / Constrained Linear Inverse Problem / Hybrid Steepest Descent Method / Generalized convex feasible set / Nonexpansive mapping / Fixed point theorem / Convex projection |
| Paper # | DSP98-136 |
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| Conference Information | |
| Committee | DSP |
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| Conference Date | 1998/12/11(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Digital Signal Processing (DSP) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Approximation of Convexly Constrained Pseudoinverse by Hybrid Steepest Descent Method |
| Sub Title (in English) | |
| Keyword(1) | Convexly Constrained Pseudoinverse |
| Keyword(2) | Constrained Linear Inverse Problem |
| Keyword(3) | Hybrid Steepest Descent Method |
| Keyword(4) | Generalized convex feasible set |
| Keyword(5) | Nonexpansive mapping |
| Keyword(6) | Fixed point theorem |
| Keyword(7) | Convex projection |
| 1st Author's Name | Isao YAMADA |
| 1st Author's Affiliation | Dept. of Electrical and Electronic Eng., Tokyo Institute of Technology() |
| Date | 1998/12/11 |
| Paper # | DSP98-136 |
| Volume (vol) | vol.98 |
| Number (no) | 451 |
| Page | pp.pp.- |
| #Pages | 4 |
| Date of Issue | |