Related papers: Deformable Groupwise Image Registration using Low-…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…

Many registration problems are ill-posed in homogeneous or noisy regions, and dense voxel-wise decoders can be unnecessarily high-dimensional. A sparse control-point parameterisation provides a compact, smooth deformation representation…

High-dimensional data often exhibit dependencies among variables that violate the isotropic-noise assumption under which principal component analysis (PCA) is optimal. For cases where the noise is not independent and identically distributed…

Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…

Sparse principal component analysis (sPCA) enhances the interpretability of principal components (PCs) by imposing sparsity constraints on loading vectors (LVs). However, when used as a precursor to independent component analysis (ICA) for…

Motion correction of dynamic contrast enhanced magnetic resonance images (DCE-MRI) is a challenging task, due to changes in image appearance. In this study a groupwise registration, using a principle component analysis (PCA) based metric,1…

In the field of data mining, how to deal with high-dimensional data is an inevitable problem. Unsupervised feature selection has attracted more and more attention because it does not rely on labels. The performance of spectral-based…

Video background subtraction is one of the fundamental problems in computer vision that aims to segment all moving objects. Robust principal component analysis has been identified as a promising unsupervised paradigm for background…

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover dynamic magnetic resonance images from undersampled measurements. We introduce a generalized formulation that is capable of handling a wide class of…

Group sparse representation has shown promising results in image debulrring and image inpainting in GSR [3] , the main reason that lead to the success is by exploiting Sparsity and Nonlocal self-similarity (NSS) between patches on natural…

Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…

Deformable image registration is fundamental to many medical imaging applications. Registration is an inherently ambiguous task often admitting many viable solutions. While neural network-based registration techniques enable fast and…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…

In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…

In this paper, we propose a non-convex formulation to recover the authentic structure from the corrupted real data. Typically, the specific structure is assumed to be low rank, which holds for a wide range of data, such as images and…