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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.09815 |
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| _version_ | 1866911776429309952 |
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| author | Ozsar, Ege Kilmer, Misha Miller, Eric de Sturler, Eric Saibaba, Arvind |
| author_facet | Ozsar, Ege Kilmer, Misha Miller, Eric de Sturler, Eric Saibaba, Arvind |
| contents | We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution involves a unique PaLS formulation utilizing a single level-set function to restore scenes containing multi-contrast piecewise-constant objects without requiring knowledge of the number of objects or their contrasts. Unlike standard PaLS methods employing radial basis functions (RBFs), our model integrates anisotropic basis functions (ABFs), thereby expanding its capacity to represent a wider class of shapes. Furthermore, PaLEnTIR improves the conditioning of the Jacobian matrix, required as part of the parameter identification process, and consequently accelerates optimization methods. We validate PaLEnTIR's efficacy through diverse experiments encompassing sparse and limited angle of view X-ray computed tomography (2D and 3D), nonlinear diffuse optical tomography (DOT), denoising, and deconvolution tasks using both real and simulated data sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_09815 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR) Ozsar, Ege Kilmer, Misha Miller, Eric de Sturler, Eric Saibaba, Arvind Numerical Analysis Computer Vision and Pattern Recognition Image and Video Processing 65F22, 65F99, 65N21 We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution involves a unique PaLS formulation utilizing a single level-set function to restore scenes containing multi-contrast piecewise-constant objects without requiring knowledge of the number of objects or their contrasts. Unlike standard PaLS methods employing radial basis functions (RBFs), our model integrates anisotropic basis functions (ABFs), thereby expanding its capacity to represent a wider class of shapes. Furthermore, PaLEnTIR improves the conditioning of the Jacobian matrix, required as part of the parameter identification process, and consequently accelerates optimization methods. We validate PaLEnTIR's efficacy through diverse experiments encompassing sparse and limited angle of view X-ray computed tomography (2D and 3D), nonlinear diffuse optical tomography (DOT), denoising, and deconvolution tasks using both real and simulated data sets. |
| title | Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR) |
| topic | Numerical Analysis Computer Vision and Pattern Recognition Image and Video Processing 65F22, 65F99, 65N21 |
| url | https://arxiv.org/abs/2204.09815 |