Data-Driven Learning of a Union of Sparsifying Transforms Model for Blind Compressed Sensing
This work addresses the challenge of reconstructing MRI images without prior knowledge of the sparse signal model, offering a domain-specific improvement for medical imaging applications.
The authors tackled the problem of blind compressed sensing (BCS) in MRI by proposing a framework to simultaneously reconstruct images and learn an unknown sparsifying model from undersampled measurements, resulting in better quality image reconstructions compared to recent methods, with the union of transforms model outperforming a single adaptive transform.
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements. Specifically, our model is that the patches of the underlying image(s) are approximately sparse in a transform domain. We also extend this model to a union of transforms model that better captures the diversity of features in natural images. The proposed block coordinate descent type algorithms for blind compressed sensing are highly efficient, and are guaranteed to converge to at least the partial global and partial local minimizers of the highly non-convex BCS problems. Our numerical experiments show that the proposed framework usually leads to better quality of image reconstructions in MRI compared to several recent image reconstruction methods. Importantly, the learning of a union of sparsifying transforms leads to better image reconstructions than a single adaptive transform.