Model-based inversion played a dominant role in biomedical imaging prior to deep learning gaining widespread popularity and broad recognition. Model-based techniques rely on a forward model derived by modeling the imaging process analytically on the basis of physical laws. Typically, the forward model is formulated as y= J (x)+ n, where y∈ Rm is the observation, x∈ Rn is the underlying image data to be recovered, J is the mapping from image domain to observations, and n∈ Rm is the corruptive noise process.

Under many circumstances, the problem of estimating x from y is ill-posed, because the imaging process is often compressive owing to practical constraints [1]. For instance, in magnetic resonance imaging (MRI) one may undersample the image in order to accelerate the acquisition process; in computed tomography (CT) a reduction of dose through sparse views in X-ray radiation is generally preferred for patients’ safety, which translates into an underdetermined forward model. Therefore, to reliably estimate x, a prior structure is often incorporated either by capturing physical principles or through manual handcrafting. The underlying image x can then be estimated by solving a regularized optimization problem: