Related papers: Insights into analysis operator learning: From pat…

The success of many computer vision tasks lies in the ability to exploit the interdependency between different image modalities such as intensity and depth. Fusing corresponding information can be achieved on several levels, and one…

We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…

It is now well known that Markov random fields (MRFs) are particularly effective for modeling image priors in low-level vision. Recent years have seen the emergence of two main approaches for learning the parameters in MRFs: (1)…

The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained…

In the co-sparse analysis model a set of filters is applied to a signal out of the signal class of interest yielding sparse filter responses. As such, it may serve as a prior in inverse problems, or for structural analysis of signals that…

A trainable filter-based higher-order Markov Random Fields (MRFs) model - the so called Fields of Experts (FoE), has proved a highly effective image prior model for many classic image restoration problems. Generally, two options are…

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…

We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample…

Exploiting a priori known structural information lies at the core of many image reconstruction methods that can be stated as inverse problems. The synthesis model, which assumes that images can be decomposed into a linear combination of…

Sparse matrix ordering is a vital optimization technique often employed for solving large-scale sparse matrices. Its goal is to minimize the matrix bandwidth by reorganizing its rows and columns, thus enhancing efficiency. Conventional…

The concept of sparsity has been extensively applied for regularization in image reconstruction. Typically, sparsifying transforms are either pre-trained on ground-truth images or adaptively trained during the reconstruction. Thereby,…

We consider the analysis operator and synthesis dictionary learning problems based on the the $\ell_1$ regularized sparse representation model. We reveal the internal relations between the $\ell_1$-based analysis model and synthesis model.…

(This paper was written in November 2011 and never published. It is posted on arXiv.org in its original form in June 2016). Many recent object recognition systems have proposed using a two phase training procedure to learn sparse…

Sparse regularization techniques are well-established in machine learning, yet their application in neural networks remains challenging due to the non-differentiability of penalties like the $L_1$ norm, which is incompatible with stochastic…

In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…

This paper introduces a new method for learning and inferring sparse representations of depth (disparity) maps. The proposed algorithm relaxes the usual assumption of the stationary noise model in sparse coding. This enables learning from…

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an…

Learning solution operators for partial differential equations (PDEs) has become a foundational task in scientific machine learning. However, existing neural operator methods require abundant training data for each specific PDE and lack the…

Active learning enables efficient model training by leveraging interactions between machine learning agents and human annotators. We study and propose a novel framework that formulates batch active learning from the sparse approximation's…