Dilated POCS: Minimax Convex Optimization
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866915802652868608 |
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| author | Yu, Albert R. Marks II, Robert J. Schubert, Keith E. Baylis, Charles Egbert, Austin Goad, Adam Haug, Sam |
| author_facet | Yu, Albert R. Marks II, Robert J. Schubert, Keith E. Baylis, Charles Egbert, Austin Goad, Adam Haug, Sam |
| contents | Alternating projection onto convex sets (POCS) provides an iterative procedure to find a signal that satisfies two or more convex constraints when the sets intersect. For nonintersecting constraints, the method of simultaneous projections produces a minimum mean square error (MMSE) solution. In certain cases, a minimax solution is more desirable. Generating a minimax solution is possible using dilated POCS. The minimax solution uses morphological dilation of nonintersecting signal convex constraints. The sets are progressively dilated to the point where there is intersection at a minimax solution. Examples are given contrasting the MMSE and minimax solutions in problems of tomographic reconstruction of images. Dilated POCS adds a new imaging modality for image synthesis. Lastly, morphological erosion of signal sets is suggested as a method to shrink the overlap when sets intersect at more than one point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_04759 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dilated POCS: Minimax Convex Optimization Yu, Albert R. Marks II, Robert J. Schubert, Keith E. Baylis, Charles Egbert, Austin Goad, Adam Haug, Sam Image and Video Processing Signal Processing Alternating projection onto convex sets (POCS) provides an iterative procedure to find a signal that satisfies two or more convex constraints when the sets intersect. For nonintersecting constraints, the method of simultaneous projections produces a minimum mean square error (MMSE) solution. In certain cases, a minimax solution is more desirable. Generating a minimax solution is possible using dilated POCS. The minimax solution uses morphological dilation of nonintersecting signal convex constraints. The sets are progressively dilated to the point where there is intersection at a minimax solution. Examples are given contrasting the MMSE and minimax solutions in problems of tomographic reconstruction of images. Dilated POCS adds a new imaging modality for image synthesis. Lastly, morphological erosion of signal sets is suggested as a method to shrink the overlap when sets intersect at more than one point. |
| title | Dilated POCS: Minimax Convex Optimization |
| topic | Image and Video Processing Signal Processing |
| url | https://arxiv.org/abs/2206.04759 |