Image relighting has emerged as a problem of significant research interest inspired by augmented reality applications. Physics-based traditional methods, as well as black box deep learning models, have been developed. The existing deep networks have exploited training to achieve a new state of the art; however, they may perform poorly when training is limited or does not represent problem phenomenology, such as the addition or removal of dense shadows. We propose a model which enriches neural networks with physical insight. More precisely, our method generates the relighted image with new illumination settings via two different strategies and subsequently fuses them using a weight map (w). In the first strategy, our model predicts the material reflectance parameters (albedo) and illumination/geometry parameters of the scene (shading) for the relit image (we refer to this strategy as intrinsic image decomposition (IID)). The second strategy is solely based on the black box approach, where the model optimizes its weights based on the ground-truth images and the loss terms in the training stage and generates the relit output directly (we refer to this strategy as direct). While our proposed method applies to both one-to-one and any-to-any relighting problems, for each case we introduce problem-specific components that enrich the model performance: 1) For one-to-one relighting we incorporate normal vectors of the surfaces in the scene to adjust gloss and shadows accordingly in the image. 2) For any-to-any relighting, we propose an additional multiscale block to the architecture to enhance feature extraction. Experimental results on the VIDIT 2020 and the VIDIT 2021 dataset (used in the NTIRE 2021 relighting challenge) reveals that our proposal can outperform many state-of-the-art methods in terms of well-known fidelity metrics and perceptual loss.

High resolution Magnetic Resonance (MR) images are desired for accurate diagnostics. In practice, image resolution is restricted by factors like hardware and processing constraints. Recently, deep learning methods have been shown to produce compelling state-of-the-art results for image enhancement/super-resolution. Paying particular attention to desired hi-resolution MR image structure, we propose a new regularized network that exploits image priors, namely a low-rank structure and a sharpness prior to enhance deep MR image super-resolution (SR). Our contributions are then incorporating these priors in an analytically tractable fashion \color{black} as well as towards a novel prior guided network architecture that accomplishes the super-resolution task. This is particularly challenging for the low rank prior since the rank is not a differentiable function of the image matrix(and hence the network parameters), an issue we address by pursuing differentiable approximations of the rank. Sharpness is emphasized by the variance of the Laplacian which we show can be implemented by a fixed feedback layer at the output of the network. As a key extension, we modify the fixed feedback (Laplacian) layer by learning a new set of training data driven filters that are optimized for enhanced sharpness. Experiments performed on publicly available MR brain image databases and comparisons against existing state-of-the-art methods show that the proposed prior guided network offers significant practical gains in terms of improved SNR/image quality measures. Because our priors are on output images, the proposed method is versatile and can be combined with a wide variety of existing network architectures to further enhance their performance.

While neural networks have achieved vastly enhanced performance over traditional iterative methods in many cases, they are generally empirically designed and the underlying structures are difficult to interpret. The algorithm unrolling approach has helped connect iterative algorithms to neural network architectures. However, such connections have not been made yet for blind image deblurring. In this paper, we propose a neural network architecture that advances this idea. We first present an iterative algorithm that may be considered a generalization of the traditional total-variation regularization method on the gradient domain, and subsequently unroll the half-quadratic splitting algorithm to construct a neural network. Our proposed deep network achieves significant practical performance gains while enjoying interpretability at the same time. Experimental results show that our approach outperforms many state-of-the-art methods.

Blind image deblurring remains a topic of enduring interest. Learning based approaches, especially those that employ neural networks have emerged to complement traditional model based methods and in many cases achieve vastly enhanced performance. That said, neural network approaches are generally empirically designed and the underlying structures are difficult to interpret. In recent years, a promising technique called algorithm unrolling has been developed that has helped connect iterative algorithms such as those for sparse coding to neural network architectures. However, such connections have not been made yet for blind image deblurring. In this paper, we propose a neural network architecture based on this idea. We first present an iterative algorithm that may be considered as a generalization of the traditional total-variation regularization method in the gradient domain. We then unroll the algorithm to construct a neural network for image deblurring which we refer to as Deep Unrolling for Blind Deblurring (DUBLID). Key algorithm parameters are learned with the help of training images. Our proposed deep network DUBLID achieves significant practical performance gains while enjoying interpretability at the same time. Extensive experimental results show that DUBLID outperforms many state-of-the-art methods and in addition is computationally faster.

Cell nuclei detection is a challenging research topic because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell nuclei. This has been a topic of enduring interest with promising recent success shown by deep learning methods. These methods train Convolutional Neural Networks (CNNs) with a training set of input images and known, labeled nuclei locations. Many such methods are supplemented by spatial or morphological processing. Using a set of canonical cell nuclei shapes, prepared with the help of a domain expert, we develop a new approach that we call Shape Priors with Convolutional Neural Networks (SP-CNN). We further extend the network to introduce a shape prior (SP) layer and then allowing it to become trainable (i.e. optimizable). We call this network tunable SP-CNN (TSP-CNN). In summary, we present new network structures that can incorporate 'expected behavior' of nucleus shapes via two components: learnable layers that perform the nucleus detection and a fixed processing part that guides the learning with prior information. Analytically, we formulate two new regularization terms that are targeted at: 1) learning the shapes, 2) reducing false positives while simultaneously encouraging detection inside the cell nucleus boundary. Experimental results on two challenging datasets reveal that the proposed SP-CNN and TSP-CNN can outperform state-of-the-art alternatives.

High resolution magnetic resonance (MR) images are desired for accurate diagnostics. In practice, image resolution is restricted by factors like hardware, cost and processing constraints. Recently, deep learning methods have been shown to produce compelling state of the art results for image super-resolution. Paying particular attention to desired hi-resolution MR image structure, we propose a new regularized network that exploits image priors, namely a low-rank structure and a sharpness prior to enhance deep MR image superresolution. Our contributions are then incorporating these priors in an analytically tractable fashion in the learning of a convolutional neural network (CNN) that accomplishes the super-resolution task. This is particularly challenging for the low rank prior, since the rank is not a differentiable function of the image matrix (and hence the network parameters), an issue we address by pursuing differentiable approximations of the rank. Sharpness is emphasized by the variance of the Laplacian which we show can be implemented by a fixed {\em feedback} layer at the output of the network. Experiments performed on two publicly available MR brain image databases exhibit promising results particularly when training imagery is limited.

Detection of cell nuclei in microscopic images is a challenging research topic, because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell nuclei. This has been a topic of enduring interest with promising recent success shown by deep learning methods. These methods train for example convolutional neural networks (CNNs) with a training set of input images and known, labeled nuclei locations. Many of these methods are supplemented by spatial or morphological processing. We develop a new approach that we call Shape Priors with Convolutional Neural Networks (SP-CNN) to perform significantly enhanced nuclei detection. A set of canonical shapes is prepared with the help of a domain expert. Subsequently, we present a new network structure that can incorporate `expected behavior' of nucleus shapes via two components: {\em learnable} layers that perform the nucleus detection and a {\em fixed} processing part that guides the learning with prior information. Analytically, we formulate a new regularization term that is targeted at penalizing false positives while simultaneously encouraging detection inside cell nucleus boundary. Experimental results on a challenging dataset reveal that SP-CNN is competitive with or outperforms several state-of-the-art methods.

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and classification. It is well-known that solving for the sparse coefficient vector to maximize these priors results in a hard non-convex and mixed integer programming problem. Most existing solutions to this optimization problem either involve simplifying assumptions/relaxations or are computationally expensive. We propose a new greedy and adaptive matching pursuit (AMP) algorithm to directly solve this hard problem. Essentially, in each step of the algorithm, the set of active elements would be updated by either adding or removing one index, whichever results in better improvement. In addition, the intermediate steps of the algorithm are calculated via an inexpensive Cholesky decomposition which makes the algorithm much faster. Results on simulated data sets as well as real-world image recovery challenges confirm the benefits of the proposed AMP, particularly in providing a superior cost-quality trade-off over existing alternatives.

In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting from spike and slab prior maximization is known to be a hard non-convex problem, and existing solutions involve simplifying assumptions and/or relaxations. We propose an approach called Iterative Convex Refinement (ICR) that aims to solve the aforementioned optimization problem directly allowing for greater generality in the sparse structure. Essentially, ICR solves a sequence of convex optimization problems such that sequence of solutions converges to a sub-optimal solution of the original hard optimization problem. We propose two versions of our algorithm: a.) an unconstrained version, and b.) with a non-negativity constraint on sparse coefficients, which may be required in some real-world problems. Experimental validation is performed on both synthetic data and for a real-world image recovery problem, which illustrates merits of ICR over state of the art alternatives.