Inertial gradient method for fluorescence molecular tomography
Image reconstruction in fluorescence molecular tomography involves seeking stable and meaningful solutions via the inversion of a highly under-determined and severely ill-posed linear mapping. An attractive scheme consists of minimizing a convex objective function that includes a quadratic error ter...
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doaj-ea9469ded8094872b1865c3dbe96db352021-03-22T02:17:57ZengWorld Scientific PublishingJournal of Innovative Optical Health Sciences1793-54581793-72052021-03-011422150002-12150002-1710.1142/S179354582150002410.1142/S1793545821500024Inertial gradient method for fluorescence molecular tomographyLei Wang0Hui Huang1College of Physics and Optoelectronic Engineering, Harbin Engineering University, 145 Nantong Avenue, Harbin, 150001, P. R. ChinaSchool of Basic Medical Sciences, Harbin Medical University, 157 Baojian Road, Harbin, 150081, P. R. ChinaImage reconstruction in fluorescence molecular tomography involves seeking stable and meaningful solutions via the inversion of a highly under-determined and severely ill-posed linear mapping. An attractive scheme consists of minimizing a convex objective function that includes a quadratic error term added to a convex and nonsmooth sparsity-promoting regularizer. Choosing ℓ1-norm as a particular case of a vast class of nonsmooth convex regularizers, our paper proposes a low per-iteration complexity gradient-based first-order optimization algorithm for the ℓ1-regularized least squares inverse problem of image reconstruction. Our algorithm relies on a combination of two ideas applied to the nonsmooth convex objective function: Moreau–Yosida regularization and inertial dynamics-based acceleration. We also incorporate into our algorithm a gradient-based adaptive restart strategy to further enhance the practical performance. Extensive numerical experiments illustrate that in several representative test cases (covering different depths of small fluorescent inclusions, different noise levels and different separation distances between small fluorescent inclusions), our algorithm can significantly outperform three state-of-the-art algorithms in terms of CPU time taken by reconstruction, despite almost the same reconstructed images produced by each of the four algorithms.http://www.worldscientific.com/doi/epdf/10.1142/S1793545821500024biomedical imagingimage reconstructioninverse problemstomography |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lei Wang Hui Huang |
spellingShingle |
Lei Wang Hui Huang Inertial gradient method for fluorescence molecular tomography Journal of Innovative Optical Health Sciences biomedical imaging image reconstruction inverse problems tomography |
author_facet |
Lei Wang Hui Huang |
author_sort |
Lei Wang |
title |
Inertial gradient method for fluorescence molecular tomography |
title_short |
Inertial gradient method for fluorescence molecular tomography |
title_full |
Inertial gradient method for fluorescence molecular tomography |
title_fullStr |
Inertial gradient method for fluorescence molecular tomography |
title_full_unstemmed |
Inertial gradient method for fluorescence molecular tomography |
title_sort |
inertial gradient method for fluorescence molecular tomography |
publisher |
World Scientific Publishing |
series |
Journal of Innovative Optical Health Sciences |
issn |
1793-5458 1793-7205 |
publishDate |
2021-03-01 |
description |
Image reconstruction in fluorescence molecular tomography involves seeking stable and meaningful solutions via the inversion of a highly under-determined and severely ill-posed linear mapping. An attractive scheme consists of minimizing a convex objective function that includes a quadratic error term added to a convex and nonsmooth sparsity-promoting regularizer. Choosing ℓ1-norm as a particular case of a vast class of nonsmooth convex regularizers, our paper proposes a low per-iteration complexity gradient-based first-order optimization algorithm for the ℓ1-regularized least squares inverse problem of image reconstruction. Our algorithm relies on a combination of two ideas applied to the nonsmooth convex objective function: Moreau–Yosida regularization and inertial dynamics-based acceleration. We also incorporate into our algorithm a gradient-based adaptive restart strategy to further enhance the practical performance. Extensive numerical experiments illustrate that in several representative test cases (covering different depths of small fluorescent inclusions, different noise levels and different separation distances between small fluorescent inclusions), our algorithm can significantly outperform three state-of-the-art algorithms in terms of CPU time taken by reconstruction, despite almost the same reconstructed images produced by each of the four algorithms. |
topic |
biomedical imaging image reconstruction inverse problems tomography |
url |
http://www.worldscientific.com/doi/epdf/10.1142/S1793545821500024 |
work_keys_str_mv |
AT leiwang inertialgradientmethodforfluorescencemoleculartomography AT huihuang inertialgradientmethodforfluorescencemoleculartomography |
_version_ |
1724209669781585920 |