Related papers: Sparse Linear Representation
A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from the sparse codes. We verify that the new…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary…
Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
We consider approximations of signals by the elements of a frame in a complex vector space of dimension $N$ and formulate both the noiseless and the noisy sparse representation problems. The noiseless representation problem is to find…
Sparse representation with respect to an overcomplete dictionary is often used when regularizing inverse problems in signal and image processing. In recent years, the Convolutional Sparse Coding (CSC) model, in which the dictionary consists…
Sparse linear regression is a vast field and there are many different algorithms available to build models. Two new papers published in Statistical Science study the comparative performance of several sparse regression methodologies,…
Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representations map an input $x \in \mathbb{R}^d$ to…
A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…
The dictionary-aided sparse regression (SR) approach has recently emerged as a promising alternative to hyperspectral unmixing (HU) in remote sensing. By using an available spectral library as a dictionary, the SR approach identifies the…
This work proposes a research problem of finding sparse solution of undetermined Linear system with some applications. Two approaches how to solve the compressive sensing problem: using l_1 approach , the l_q approach with 0 < q < 1.…
The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology…
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…
The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously. In this paper we show how to bring the number of…
A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…