Related papers: Constrained low-rank quaternion approximation for …
This paper presents a randomized quaternion singular value decomposition (QSVD) algorithm for low-rank matrix approximation problems, which are widely used in color face recognition, video compression, and signal processing problems. With…
One of the most powerful methods of color image recognition is the two-dimensional principle component analysis (2DQPCA) approach, which is based on quaternion representation and preserves color information very well. However, the current…
Low-rank quaternion tensor completion method, a novel approach to recovery color videos and images is proposed in this paper. We respectively reconstruct a color image and a color video as a quaternion matrix (second-order tensor) and a…
The ability of capturing fine spectral discriminative information enables hyperspectral images (HSIs) to observe, detect and identify objects with subtle spectral discrepancy. However, the captured HSIs may not represent true distribution…
Due to the high flexibility and remarkable performance, low-rank approximation methods has been widely studied for color image denoising. However, those methods mostly ignore either the cross-channel difference or the spatial variation of…
In this work we present Low-rank Deconvolution, a powerful framework for low-level feature-map learning for efficient signal representation with application to signal recovery. Its formulation in multi-linear algebra inherits properties…
Color image denoising is frequently encountered in various image processing and computer vision tasks. One traditional strategy is to convert the RGB image to a less correlated color space and denoise each channel of the new space…
We study the 2-D super-resolution multi-reference alignment (SR-MRA) problem: estimating an image from its down-sampled, circularly-translated, and noisy copies. The SR-MRA problem serves as a mathematical abstraction of the structure…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics…
Reduced biquaternion (RB), as a four-dimensional algebra highly suitable for representing color pixels, has recently garnered significant attention from numerous scholars. In this paper, for color image processing problems, we introduce a…
Quantitative magnetic resonance imaging (qMRI) provides tissue-specific parameters vital for clinical diagnosis. Although simultaneous multi-parametric qMRI (MP-qMRI) technologies enhance imaging efficiency, robustly reconstructing qMRI…
Multispectral images contain many clues of surface characteristics of the objects, thus can be widely used in many computer vision tasks, e.g., recolorization and segmentation. However, due to the complex illumination and the geometry…
Post-training quantization (PTQ) is essential for deploying large diffusion transformers on resource-constrained hardware, but aggressive 4-bit quantization significantly degrades generative performance. Low-rank approximation methods have…
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
Recently, quaternion collaborative representation-based classification (QCRC) and quaternion sparse representation-based classification (QSRC) have been proposed for color face recognition. They can obtain correlation information among…
Low-rank Deconvolution (LRD) has appeared as a new multi-dimensional representation model that enjoys important efficiency and flexibility properties. In this work we ask ourselves if this analytical model can compete against Deep Learning…
We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…
Inspired by the fact that the matrix formulated by nonlocal similar patches in a natural image is of low rank, the rank approximation issue have been extensively investigated over the past decades, among which weighted nuclear norm…