Related papers: Dictionary Learning with Convex Update (ROMD)
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…
This paper seeks to combine dictionary learning and hierarchical image representation in a principled way. To make dictionary atoms capturing additional information from extended receptive fields and attain improved descriptive capacity, we…
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
This paper proposes a novel approach to image deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some…
We study the problem of robust matrix completion (RMC), where the partially observed entries of an underlying low-rank matrix is corrupted by sparse noise. Existing analysis of the non-convex methods for this problem either requires the…
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…
Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…
Dictionary learning for sparse representations is traditionally approached with sequential atom updates, in which an optimized atom is used immediately for the optimization of the next atoms. We propose instead a Jacobi version, in which…
Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the…
State-of-the-art learned reconstruction methods often rely on black-box modules that, despite their strong performance, raise questions about their interpretability and robustness. Here, we build on a recently proposed image reconstruction…
This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to…
Short-and-sparse deconvolution (SaSD) aims to recover a short kernel and a long and sparse signal from their convolution. In the literature, formulations of blind deconvolution is either a convex programming via a matrix lifting of…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the…
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient,…
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
We propose an efficient online dictionary learning algorithm for kernel-based sparse representations. In this framework, input signals are nonlinearly mapped to a high-dimensional feature space and represented sparsely using a virtual…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…