Related papers: Adaptive non-uniform B-spline dictionaries on a co…

Dictionary learning and sparse coding have been widely studied as mechanisms for unsupervised feature learning. Unsupervised learning could bring enormous benefit to the processing of hyperspectral images and to other remote sensing data…

In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…

Dictionary learning is a challenge topic in many image processing areas. The basic goal is to learn a sparse representation from an overcomplete basis set. Due to combining the advantages of generic multiscale representations with learning…

Prediction without justification has limited utility. Much of the success of neural models can be attributed to their ability to learn rich, dense and expressive representations. While these representations capture the underlying complexity…

We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions,…

This paper presents a new method for modelling periodic signals having an aperiodic trend, using the method of variable projection. It is a major extension to the IEEE-standard 1057 by permitting the background to be time varying;…

In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributions. We give a constructive proof of the existence of minimal…

In a sparse representation based recognition scheme, it is critical to learn a desired dictionary, aiming both good representational power and discriminative performance. In this paper, we propose a new dictionary learning model for…

Interpretability benefits the theoretical understanding of representations. Existing word embeddings are generally dense representations. Hence, the meaning of latent dimensions is difficult to interpret. This makes word embeddings like a…

Continuous-time trajectory representation has recently gained popularity for tasks where the fusion of high-frame-rate sensors and multiple unsynchronized devices is required. Lie group cumulative B-splines are a popular way of representing…

This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…

A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…

This paper introduces the class of ambiguity sparse processes, containing subsets of popular nonstationary time series such as locally stationary, cyclostationary and uniformly modulated processes. The class also contains aggregations of…

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by L\'evy white noises. A recent paper showed that these processes are limits in law of…

Sparse representation models a signal as a linear combination of a small number of dictionary atoms. As a generative model, it requires the dictionary to be highly redundant in order to ensure both a stable high sparsity level and a low…

Based on the continuous interpretation of deep learning cast as an optimal control problem, this paper investigates the benefits of employing B-spline basis functions to parameterize neural network controls across the layers. Rather than…

This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of…

A new representation of splines that targets efficiency in the analysis of functional data is implemented. The efficiency is achieved through two novel features: using the recently introduced orthonormal spline bases, the so-called {\it…

The estimation of functions with varying degrees of smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose the LABS (L\'{e}vy Adaptive B-Spline regression) model, an extension of the LARK…