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Diffusion magnetic resonance imaging (dMRI) is a crucial non-invasive technique for exploring the microstructure of the living human brain. Traditional hand-crafted and model-based tissue microstructure reconstruction methods often require…

The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…

Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in…

This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…

In a sparse representation based recognition scheme, it is critical to learn a desired dictionary, aiming both good representational power and discriminative performance. In this paper, we propose a new dictionary learning model for…

The concept of deep dictionary learning has been recently proposed. Unlike shallow dictionary learning which learns single level of dictionary to represent the data, it uses multiple layers of dictionaries. So far, the problem could only be…

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image…

Multiview representation learning is very popular for latent factor analysis. It naturally arises in many data analysis, machine learning, and information retrieval applications to model dependent structures among multiple data sources. For…

The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…

Diffusion probabilistic model (DPM) recently becomes one of the hottest topic in computer vision. Its image generation application such as Imagen, Latent Diffusion Models and Stable Diffusion have shown impressive generation capabilities,…

Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…

The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…

We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…

Segmentation of structural and diffusion MRI (sMRI/dMRI) is usually performed independently in neuroimaging pipelines. However, some brain structures (e.g., globus pallidus, thalamus and its nuclei) can be extracted more accurately by…

Learning dictionaries suitable for sparse coding instead of using engineered bases has proven effective in a variety of image processing tasks. This paper studies the optimization of dictionaries on image data where the representation is…

Dictionary learning consists of finding a sparse representation from noisy data and is a common way to encode data-driven prior knowledge on signals. Alternating minimization (AM) is standard for the underlying optimization, where gradient…

Dictionary learning aims at seeking a dictionary under which the training data can be sparsely represented. Methods in the literature typically formulate the dictionary learning problem as an optimization w.r.t. two variables, i.e.,…

Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…

We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this…

Although various distributed machine learning schemes have been proposed recently for pure linear models and fully nonparametric models, little attention has been paid on distributed optimization for semi-paramemetric models with…