Related papers: Low-Rank and Sparse Matrix Decomposition with a-pr…

Three dimensional surface reconstruction based on two dimensional sparse information in the form of only a small number of level lines of the surface with moderately complex structures, containing both structured and unstructured…

In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…

The earlier works in the context of low-rank-sparse-decomposition (LRSD)-driven stationary synthetic aperture radar (SAR) imaging have shown significant improvement in the reconstruction-decomposition process. Neither of the proposed…

Magnetic Resonance Imaging (MRI) is a powerful imaging technique widely used for visualizing structures within the human body and in other fields such as plant sciences. However, there is a demand to develop fast 3D-MRI reconstruction…

High spatiotemporal resolution dynamic magnetic resonance imaging (MRI) is a powerful clinical tool for imaging moving structures as well as to reveal and quantify other physical and physiological dynamics. The low speed of MRI necessitates…

Low-field magnetic resonance imaging (MRI) offers a cost-effective alternative for medical imaging in resource-limited settings. However, its widespread adoption is hindered by two key challenges: prolonged scan times and reduced image…

Dynamic Magnetic Resonance Imaging (MRI) is a crucial non-invasive method used to capture the movement of internal organs and tissues, making it a key tool for medical diagnosis. However, dynamic MRI faces a major challenge: long…

Three-dimensional coronary magnetic resonance angiography (CMRA) demands reconstruction algorithms that can significantly suppress the artifacts from a heavily undersampled acquisition. While unrolling-based deep reconstruction methods have…

Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless…

Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing,…

Magnetic resonance imaging has been widely applied in clinical diagnosis, however, is limited by its long data acquisition time. Although imaging can be accelerated by sparse sampling and parallel imaging, achieving promising reconstruction…

We introduce a novel framework for an approxi- mate recovery of data matrices which are low-rank on graphs, from sampled measurements. The rows and columns of such matrices belong to the span of the first few eigenvectors of the graphs…

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…

Adaptive intelligence aims at empowering machine learning techniques with the additional use of domain knowledge. In this work, we present the application of adaptive intelligence to accelerate MR acquisition. Starting from undersampled…

In this paper, we consider the problem of recovering compressively sensed ultrasound images. We build on prior work, and consider a number of existing approaches that we consider to be the state-of-the-art. The methods we consider take…

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…

Increasing demand for high field magnetic resonance (MR) scanner indicates the need for high-quality MR images for accurate medical diagnosis. However, cost constraints, instead, motivate a need for algorithms to enhance images from low…

The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…