Related papers: Manifold Constrained Low-Rank Decomposition

Although recent deep learning methods, especially generative models, have shown good performance in fast magnetic resonance imaging, there is still much room for improvement in high-dimensional generation. Considering that internal…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

Computational reconstruction plays a vital role in computer vision and computational photography. Most of the conventional optimization and deep learning techniques explore local information for reconstruction. Recently, nonlocal low-rank…

Deep unfolding networks (DUNs) have achieved remarkable success and become the mainstream paradigm for spectral compressive imaging (SCI) reconstruction. Existing DUNs are derived from full-HSI imaging models, where each stage operates…

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data…

Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

Magnetic Resonance (MR) Fingerprinting is an emerging multi-parametric quantitative MR imaging technique, for which image reconstruction methods utilizing low-rank and subspace constraints have achieved state-of-the-art performance.…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

In this paper, we propose a robust representation learning model called Adaptive Structure-constrained Low-Rank Coding (AS-LRC) for the latent representation of data. To recover the underlying subspaces more accurately, AS-LRC seamlessly…

Parallel magnetic resonance imaging has served as an effective and widely adopted technique for accelerating scans. The advent of sparse sampling offers aggressive acceleration, allowing flexible sampling and better reconstruction.…

Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…

Low-dose computed tomography (LDCT) scans, which can effectively alleviate the radiation problem, will degrade the imaging quality. In this paper, we propose a novel LDCT reconstruction network that unrolls the iterative scheme and performs…

The low-rank matrix completion (LRMC) technology has achieved remarkable results in low-level visual tasks. There is an underlying assumption that the real-world matrix data is low-rank in LRMC. However, the real matrix data does not…

Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…

In recent years, large language models (LLMs) have driven advances in natural language processing. Still, their growing scale has increased the computational burden, necessitating a balance between efficiency and performance. Low-rank…

Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…

The overfitting is one of the cursing subjects in the deep learning field. To solve this challenge, many approaches were proposed to regularize the learning models. They add some hyper-parameters to the model to extend the generalization;…

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…