Related papers: Deformable Groupwise Image Registration using Low-…

This paper considers the use of Robust PCA in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of column-row factorizations of matrices $\mathbf{D}=\mathbf{L}+\mathbf{S}$ where…

Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier…

We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…

Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…

Group-based sparse representation has shown great potential in image denoising. However, most existing methods only consider the nonlocal self-similarity (NSS) prior of noisy input image. That is, the similar patches are collected only from…

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank…

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…

We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Group sparsity has shown great potential in various low-level vision tasks (e.g, image denoising, deblurring and inpainting). In this paper, we propose a new prior model for image denoising via group sparsity residual constraint (GSRC). To…

Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

The segmentation of animals from camera-trap images is a difficult task. To illustrate, there are various challenges due to environmental conditions and hardware limitation in these images. We proposed a multi-layer robust principal…

Hyperspectral images (HSIs) are often degraded by complex mixed noise during acquisition and transmission, making effective denoising essential for subsequent analysis. Recent hybrid approaches that bridge model-driven and data-driven…

It is known that the decomposition in low-rank and sparse matrices (\textbf{L+S} for short) can be achieved by several Robust PCA techniques. Besides the low rankness, the local smoothness (\textbf{LSS}) is a vitally essential prior for…

In this paper, we consider a new variant for principal component analysis (PCA), aiming to capture the grouping and/or sparse structures of factor loadings simultaneously. To achieve these goals, we employ a non-convex truncated…