Related papers: Total Variation Regularized Tensor-on-scalar Regre…
In this paper, we propose the Graph-Fused Multivariate Regression (GFMR) via Total Variation regularization, a novel method for estimating the association between a one-dimensional or multidimensional array outcome and scalar predictors.…
Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…
Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…
In our paper, we have studied the tensor completion problem when the sampling pattern is deterministic. We first propose a simple but efficient weighted HOSVD algorithm for recovery from noisy observations. Then we use the weighted HOSVD…
Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…
The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…
We introduce mixed model trace regression (MMTR), a mixed model linear regression extension for scalar responses and high-dimensional matrix-valued covariates. MMTR's fixed effects component is equivalent to trace regression, with an…
While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…
Direction-guided structure tensor total variation (DSTV) is a recently proposed regularization term that aims at increasing the sensitivity of the structure tensor total variation (STV) to the changes towards a predetermined direction.…
Heterogeneous but complementary sources of data provide an unprecedented opportunity for developing accurate statistical models of systems. Although the existing methods have shown promising results, they are mostly applicable to situations…
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor…
In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…
We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…
We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our…
We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distributed counts. Tensors, or multi-dimensional arrays, composed…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide…
Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor…