We propose a novel SPARsity and Clustering (SPARC) regularizer, which is a modified version of the previous octagonal shrinkage and clustering algorithm for regression (OSCAR), where, the proposed regularizer consists of a K-sparse constraint and a pair-wise l∞ norm restricted on the K largest components in magnitude. The proposed regularizer is able to separably enforce K-sparsity and encourag...

Tensor factorization and distanced based models play important roles in knowledge graph completion (KGC). However, the relational matrices KGC methods often induce a high model complexity, bearing risk of overfitting. As remedy, researchers propose variety different regularizers such as tensor nuclear norm regularizer. Our motivation is on observation that previous work only focuses “size” para...

We propose computational algorithms for incorporating total varia-tional (TV) regularization in positron emission tomography (PET). The motivation for using TV is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations. This feature makes it particularly attractive for those applications of PET where the objective is to identify the shape of objects...

We examine the performance of Total Variation (TV) smoothing for processing of noisy Electrocardiogram (ECG) recorded by an ambulatory device. The TV smoothing is compared with traditionally-used bandpass filtering using ECG with artificially added noise, as well as with real-world noise obtained during physiological monitoring. The fundamental difference between TV smoothing and traditional ba...

The use of total variation as a regularization term in imaging problems was motivated by its ability to recover the image discontinuities.This is at the basis of its numerous applications to denoising, optical flow, stereo imaging and D surface reconstruction, segmentation, or interpolation to mention some of them. On one hand, we review here the main theoretical arguments that have been given...

Total variation regularization and anisotropic filtering have been established as standard methods for image denoising because of their ability to detect and keep prominent edges in the data. Both methods, however, introduce artifacts: In the case of anisotropic filtering, the preservation of edges comes at the cost of the creation of additional structures out of noise; total variation regulari...

We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure tensor and is suitable for both grayscale and vector-valued images. It generalizes several existing variational penalties, including the tot...

Abstract. In this paper we analyze iterative regularization with the Bregman distance of the total variation semi norm. Moreover, we prove existence of a solution of the corresponding flow equation as introduced in [8] in a functional analytical setting using methods from convex analysis. The results are generalized to variational denoising methods with L-norm fit-to-data terms and Bregman dist...

Semi-supervised inductive learning concerns how to learn a decision rule from a data set containing both labeled and unlabeled data. Several boosting algorithms have been extended to semi-supervised learning with various strategies. To our knowledge, however, none of them takes local smoothness constraints among data into account during ensemble learning. In this paper, we introduce a local smo...

The use of convex regularizers allow for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones. However, the resultant optimization problem is much harder. In this paper, for a large class of nonconvex regularizers, we propose to move the nonconvexity fro...