Efficient Convolutional Forward Modeling and Sparse Coding in Multichannel Imaging
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929425607557120 |
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| author | Wang, Han Kvich, Yhonatan Pérez, Eduardo Römer, Florian Eldar, Yonina C. |
| author_facet | Wang, Han Kvich, Yhonatan Pérez, Eduardo Römer, Florian Eldar, Yonina C. |
| contents | This study considers the Block-Toeplitz structural properties inherent in traditional multichannel forward model matrices, using Full Matrix Capture (FMC) in ultrasonic testing as a case study. We propose an analytical convolutional forward model that transforms reflectivity maps into FMC data. Our findings demonstrate that the convolutional model excels over its matrix-based counterpart in terms of computational efficiency and storage requirements. This accelerated forward modeling approach holds significant potential for various inverse problems, notably enhancing Sparse Signal Recovery (SSR) within the context LASSO regression, which facilitates efficient Convolutional Sparse Coding (CSC) algorithms. Additionally, we explore the integration of Convolutional Neural Networks (CNNs) for the forward model, employing deep unfolding to implement the Learned Block Convolutional ISTA (BC-LISTA). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient Convolutional Forward Modeling and Sparse Coding in Multichannel Imaging Wang, Han Kvich, Yhonatan Pérez, Eduardo Römer, Florian Eldar, Yonina C. Signal Processing This study considers the Block-Toeplitz structural properties inherent in traditional multichannel forward model matrices, using Full Matrix Capture (FMC) in ultrasonic testing as a case study. We propose an analytical convolutional forward model that transforms reflectivity maps into FMC data. Our findings demonstrate that the convolutional model excels over its matrix-based counterpart in terms of computational efficiency and storage requirements. This accelerated forward modeling approach holds significant potential for various inverse problems, notably enhancing Sparse Signal Recovery (SSR) within the context LASSO regression, which facilitates efficient Convolutional Sparse Coding (CSC) algorithms. Additionally, we explore the integration of Convolutional Neural Networks (CNNs) for the forward model, employing deep unfolding to implement the Learned Block Convolutional ISTA (BC-LISTA). |
| title | Efficient Convolutional Forward Modeling and Sparse Coding in Multichannel Imaging |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2403.09505 |