Learning joint demosaicing and denoising based on sequential energy minimization

Learning a variational network for reconstruction of accelerated MRI data

“…We formulate image reconstruction as a variational model and embed this model in a gradient descent scheme, which forms the specific VN structure. The VN was first introduced as a trainable reaction-diffusion model (6) with application to classic image processing tasks (6,29,30). All these tasks are similar in the sense that the data are corrupted by unstructured noise in the image domain.…”

“…All parameters of the approach are learned from data. This approach has been successfully applied to a number of image processing tasks including image denoising (6), JPEG deblocking (6), demosaicing (29) and image inpainting (30). For MRI reconstruction, we rewrite the trainable gradient descent scheme with time-varying parameters ${\mathbf{K}}_i^t$, ${\mathbf{\Phi }}_i^{tʹ}$ , λ t as $${\mathbf{u}}^{t+1}={\mathbf{u}}^t-true\sum _{i=1}^{N_k}{false({\mathbf{K}}_i^{t}false)}^{\top }{\mathbf{\Phi }}_i^{tʹ}false({\mathbf{K}}_i^t{\mathbf{u}}^{t}false)-{\lambda }^t{\mathbf{A}}^{\ast }false(\mathrm{boldA}{\mathbf{u}}^t-\mathrm{boldf}false),0\le t\le T-1.$$Additionally, we omit the step size α t in Eq.…”

“…Chen et al (6) introduce a trainable reaction-diffusion approach that performs early stopping on the gradient scheme Equation [5] and allows the parameters, such as filters, activation functions and data term weights, to vary in every gradient descent step t. All parameters of the approach are learned from data. This approach has been successfully applied to a number of image processing tasks including image denoising (6), JPEG deblocking (6), demosaicing (29) and image inpainting (30). For MRI reconstruction, we rewrite the trainable gradient descent scheme with time-varying parameters K t i ; U t0 i ; k t as…”

Parametric Majorization for Data-Driven Energy Minimization Methods

“…Later works [27,23,43,44] allow the lower-level parameters to change in between the fixed number of iterations, leading to structures that model differential equations and stray further from underlying modelling. As pointed out in [53], these strategies are more aptly considered as a set of nested quadratic lower-level problems. Several techniques have been developed in the field of structured support vector machines (SSVMs) [92,28,1,95] that are very relevant to the task of learning energy models, as SSVMs can be understood as bi-level problems with a lower-level energy that is linear in θ and often a noncontinuous higher-level loss.…”

Discriminative Transfer Learning for General Image Restoration

“…Some representative examples of such methods include trainable random field models such as separable Markov random field (MRFSepa) [35] regression tree fields (RTF) [36], cascaded shrinkage fields (CSF) [8], trainable nonlinear reaction diffusion (TRD) models [9] and their extensions [37], [38], [39]. The state-ofthe-art CSF and TRD methods can be derived from the FoE model [30] by unrolling corresponding optimization iterations to be feed-forward networks, where the parameters of each network are trained by minimizing the error between its output images and ground truth for each specific task.…”