Dictionary Learning Based Regularization in Quantitative MRI: A Nested Alternating Optimization Framework
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909648624287744 |
|---|---|
| author | Dong, Guozhi Hintermüller, Michael Sirotenko, Clemens |
| author_facet | Dong, Guozhi Hintermüller, Michael Sirotenko, Clemens |
| contents | In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general dynamical image reconstruction technique, wherein a radio-frequency pulse sequence gives rise to a time-discrete physics-based mathematical model which acts as a side constraint in our inverse problem. To enhance reconstruction quality, we employ dictionary learning as a data-adaptive regularizer, capturing complex tissue structures beyond handcrafted priors. For computing a solution of the resulting non-convex and non-smooth optimization problem, we alternate between updating the physical parameters of interest via a Levenberg-Marquardt approach and performing several iterations of a dictionary learning algorithm. This process falls under the category of nested alternating optimization schemes. We develop a general overall algorithmic framework whose convergence theory is not directly available in the literature. Global sub-linear and local strong linear convergence in infinite dimensions under certain regularity conditions for the sub-differentials are investigated based on the Kurdyka-Lojasiewicz inequality. Eventually, numerical experiments demonstrate the practical potential and unresolved challenges of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11977 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dictionary Learning Based Regularization in Quantitative MRI: A Nested Alternating Optimization Framework Dong, Guozhi Hintermüller, Michael Sirotenko, Clemens Optimization and Control 35R30, 49J52, 49J53, 92C55, 68T05 In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general dynamical image reconstruction technique, wherein a radio-frequency pulse sequence gives rise to a time-discrete physics-based mathematical model which acts as a side constraint in our inverse problem. To enhance reconstruction quality, we employ dictionary learning as a data-adaptive regularizer, capturing complex tissue structures beyond handcrafted priors. For computing a solution of the resulting non-convex and non-smooth optimization problem, we alternate between updating the physical parameters of interest via a Levenberg-Marquardt approach and performing several iterations of a dictionary learning algorithm. This process falls under the category of nested alternating optimization schemes. We develop a general overall algorithmic framework whose convergence theory is not directly available in the literature. Global sub-linear and local strong linear convergence in infinite dimensions under certain regularity conditions for the sub-differentials are investigated based on the Kurdyka-Lojasiewicz inequality. Eventually, numerical experiments demonstrate the practical potential and unresolved challenges of the method. |
| title | Dictionary Learning Based Regularization in Quantitative MRI: A Nested Alternating Optimization Framework |
| topic | Optimization and Control 35R30, 49J52, 49J53, 92C55, 68T05 |
| url | https://arxiv.org/abs/2506.11977 |