Image Super-Resolution with Deep Dictionary

Since the first success of Dong et al., the deep-learning-based approach has become dominant in the field of single-image super-resolution. This replaces all the handcrafted image processing steps of traditional sparse-coding-based methods with a deep neural network. In contrast to sparse-coding-based methods, which explicitly create high/low-resolution dictionaries, the dictionaries in deep-learning-based methods are implicitly acquired as a nonlinear combination of multiple convolutions. One disadvantage of deep-learning-based methods is that their performance is degraded for images created differently from the training dataset (out-of-domain images). We propose an end-to-end super-resolution network with a deep dictionary (SRDD), where a high-resolution dictionary is explicitly learned without sacrificing the advantages of deep learning. Extensive experiments show that explicit learning of high-resolution dictionary makes the network more robust for out-of-domain test images while maintaining the performance of the in-domain test images.Comment: ECCV 202

Learning Linear Groups in Neural Networks

Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a priori specification of the desired symmetries. We present a neural network architecture, Linear Group Networks (LGNs), for learning linear groups acting on the weight space of neural networks. Linear groups are desirable due to their inherent interpretability, as they can be represented as finite matrices. LGNs learn groups without any supervision or knowledge of the hidden symmetries in the data and the groups can be mapped to well known operations in machine learning. We use LGNs to learn groups on multiple datasets while considering different downstream tasks; we demonstrate that the linear group structure depends on both the data distribution and the considered task

SC-VAE: Sparse Coding-based Variational Autoencoder

Learning rich data representations from unlabeled data is a key challenge towards applying deep learning algorithms in downstream supervised tasks. Several variants of variational autoencoders have been proposed to learn compact data representaitons by encoding high-dimensional data in a lower dimensional space. Two main classes of VAEs methods may be distinguished depending on the characteristics of the meta-priors that are enforced in the representation learning step. The first class of methods derives a continuous encoding by assuming a static prior distribution in the latent space. The second class of methods learns instead a discrete latent representation using vector quantization (VQ) along with a codebook. However, both classes of methods suffer from certain challenges, which may lead to suboptimal image reconstruction results. The first class of methods suffers from posterior collapse, whereas the second class of methods suffers from codebook collapse. To address these challenges, we introduce a new VAE variant, termed SC-VAE (sparse coding-based VAE), which integrates sparse coding within variational autoencoder framework. Instead of learning a continuous or discrete latent representation, the proposed method learns a sparse data representation that consists of a linear combination of a small number of learned atoms. The sparse coding problem is solved using a learnable version of the iterative shrinkage thresholding algorithm (ISTA). Experiments on two image datasets demonstrate that our model can achieve improved image reconstruction results compared to state-of-the-art methods. Moreover, the use of learned sparse code vectors allows us to perform downstream task like coarse image segmentation through clustering image patches.Comment: 15 pages, 11 figures, and 3 table

Fast and Interpretable Nonlocal Neural Networks for Image Denoising via Group-Sparse Convolutional Dictionary Learning

Nonlocal self-similarity within natural images has become an increasingly popular prior in deep-learning models. Despite their successful image restoration performance, such models remain largely uninterpretable due to their black-box construction. Our previous studies have shown that interpretable construction of a fully convolutional denoiser (CDLNet), with performance on par with state-of-the-art black-box counterparts, is achievable by unrolling a dictionary learning algorithm. In this manuscript, we seek an interpretable construction of a convolutional network with a nonlocal self-similarity prior that performs on par with black-box nonlocal models. We show that such an architecture can be effectively achieved by upgrading the $\ell 1$ sparsity prior of CDLNet to a weighted group-sparsity prior. From this formulation, we propose a novel sliding-window nonlocal operation, enabled by sparse array arithmetic. In addition to competitive performance with black-box nonlocal DNNs, we demonstrate the proposed sliding-window sparse attention enables inference speeds greater than an order of magnitude faster than its competitors.Comment: 11 pages, 8 figures, 6 table

Fully Trainable and Interpretable Non-Local Sparse Models for Image Restoration

Non-local self-similarity and sparsity principles have proven to be powerful priors for natural image modeling. We propose a novel differentiable relaxation of joint sparsity that exploits both principles and leads to a general framework for image restoration which is (1) trainable end to end, (2) fully interpretable, and (3) much more compact than competing deep learning architectures. We apply this approach to denoising, jpeg deblocking, and demosaicking, and show that, with as few as 100K parameters, its performance on several standard benchmarks is on par or better than state-of-the-art methods that may have an order of magnitude or more parameters.Comment: ECCV 202

A Flexible Framework for Designing Trainable Priors with Adaptive Smoothing and Game Encoding

We introduce a general framework for designing and training neural network layers whose forward passes can be interpreted as solving non-smooth convex optimization problems, and whose architectures are derived from an optimization algorithm. We focus on convex games, solved by local agents represented by the nodes of a graph and interacting through regularization functions. This approach is appealing for solving imaging problems, as it allows the use of classical image priors within deep models that are trainable end to end. The priors used in this presentation include variants of total variation, Laplacian regularization, bilateral filtering, sparse coding on learned dictionaries, and non-local self similarities. Our models are fully interpretable as well as parameter and data efficient. Our experiments demonstrate their effectiveness on a large diversity of tasks ranging from image denoising and compressed sensing for fMRI to dense stereo matching.Comment: NeurIPS 202