Related papers: Dictionary Learning for the Almost-Linear Sparsity…
This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the…
A recent line of work shows that a deep neural network with ReLU nonlinearities arises from a finite sequence of cascaded sparse coding models, the outputs of which, except for the last element in the cascade, are sparse and unobservable.…
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…
We formulate a unified framework for the separation of signals that are sparse in "morphologically" different redundant dictionaries. This formulation incorporates the so-called "analysis" and "synthesis" approaches as special cases and…
Symbolic library -- or Koopman dictionary -- selection is a fundamental challenge in data-driven dynamical systems. Extended Dynamic Mode Decomposition (EDMD), Sparse Identification of Nonlinear Dynamics (SINDy), and Kolmogorov--Arnold…
We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature…
In this paper, a novel semi-supervised dictionary learning and sparse representation (SS-DLSR) is proposed. The proposed method benefits from the supervisory information by learning the dictionary in a space where the dependency between the…
The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…
Greedy approaches in general, and orthogonal matching pursuit in particular, are the most commonly used sparse recovery techniques in a wide range of applications. The complexity of these approaches is highly dependent on the size of the…
We consider a learning problem of identifying a dictionary matrix D (M times N dimension) from a sample set of M dimensional vectors Y = N^{-1/2} DX, where X is a sparse matrix (N times P dimension) in which the density of non-zero entries…
This paper presents a dictionary learning-based method with region-specific image patches to maximize the utility of the powerful sparse data processing technique for CT image reconstruction. Considering heterogeneous distributions of image…
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…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
The problem of identifying a dynamical system from its dynamics is of great importance for many applications. Recently it has been suggested to impose sparsity models for improved recovery performance. In this paper, we provide recovery…
The sparse representation problem of recovering an N dimensional sparse vector x from M < N linear observations y = Dx given dictionary D is considered. The standard approach is to let the elements of the dictionary be independent and…
The power of sparse signal coding with learned dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these…
Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades…
Sparsity priors are commonly used in denoising and image reconstruction. For analysis-type priors, a dictionary defines a representation of signals that is likely to be sparse. In most situations, this dictionary is not known, and is to be…
This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level $O(\bar{k})$, then OMP can recover a $\bar{k}$-sparse signal…
We consider the recovery of sparse signals subject to sparse interference, as introduced in Studer et al., IEEE Trans. IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of…