Learning Spatially Adaptive $\ell_1$-Norms Weights for Convolutional Synthesis Regularization
This work addresses image reconstruction for low-field MRI, offering an interpretable method that is incremental in improving regularization techniques.
The paper tackled image reconstruction in low-field MRI by proposing an unrolled algorithm to learn spatially adaptive weights for convolutional synthesis regularization, achieving visually and quantitatively comparable results to established methods while maintaining interpretability.
We propose an unrolled algorithm approach for learning spatially adaptive parameter maps in the framework of convolutional synthesis-based $\ell_1$ regularization. More precisely, we consider a family of pre-trained convolutional filters and estimate deeply parametrized spatially varying parameters applied to the sparse feature maps by means of unrolling a FISTA algorithm to solve the underlying sparse estimation problem. The proposed approach is evaluated for image reconstruction of low-field MRI and compared to spatially adaptive and non-adaptive analysis-type procedures relying on Total Variation regularization and to a well-established model-based deep learning approach. We show that the proposed approach produces visually and quantitatively comparable results with the latter approaches and at the same time remains highly interpretable. In particular, the inferred parameter maps quantify the local contribution of each filter in the reconstruction, which provides valuable insight into the algorithm mechanism and could potentially be used to discard unsuited filters.