Bi‐dictionary learning model for medical image reconstruction from undersampled data

In recent years, dictionary learning has shown to be an efficient tool in recovering images from their degraded, damaged or incomplete version. Especially, for medical images that contain significant details and characteristics. In this work, the authors are interested in this unsupervised learning technique for discovering and visualising the underlying structure of a medical image. Therefore, an adaptive bi‐dictionary learning model for recovering magnetic resonance (MR) image from undersampled measurements is introduced. The proposed model learns two dictionaries, one over the underlying image and the other over its sparse gradient. Hence, the algorithm minimises a linear combination of three terms corresponding to the least‐squares data fitting, dictionary learning over the pixel domain, and gradient‐based dictionary. Numerically, experimental results on several MR images demonstrate that the proposed bi‐dictionary framework can improve reconstruction accuracy over other methods.