相关论文: Local Identification of Overcomplete Dictionaries

The problem of consistently estimating the sparsity pattern of a vector $\betastar \in \real^\mdim$ based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in…

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 $\mathbb{R}^{n\times m}$…

A locally threshold testable language L is a language with the property that for some non negative integers k and l, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k > 1 and (2) the…

Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…

In traditional compressed sensing theory, the dictionary matrix is given a priori, whereas in real applications this matrix suffers from random noise and fluctuations. In this paper we consider a signal model where each column in the…

This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its discrete gradient from an incomplete subset of its discrete Fourier coefficients which have been corrupted with…

Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free electron lasers, high harmonic generation, soft X-ray laser and…

This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…

In the noisy population recovery problem of Dvir et al., the goal is to learn an unknown distribution $f$ on binary strings of length $n$ from noisy samples. For some parameter $\mu \in [0,1]$, a noisy sample is generated by flipping each…

Much of the existing literature in sparse recovery is concerned with the following question: given a sparsity pattern and a corresponding regularizer, derive conditions on the dictionary under which exact recovery is possible. In this…

For sequence transduction tasks like speech recognition, a strong structured prior model encodes rich information about the target space, implicitly ruling out invalid sequences by assigning them low probability. In this work, we propose…

We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…

In this paper, we derive a new dimension-free non-asymptotic upper bound for the quadratic $k$-means excess risk related to the quantization of an i.i.d sample in a separable Hilbert space. We improve the bound of order $\mathcal{O} \bigl(…

This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact…

Orthogonal Matching Pursuit (OMP) is a simple, yet empirically competitive algorithm for sparse recovery. Recent developments have shown that OMP guarantees exact recovery of K-sparse signals with K or more than K iterations if the…

The purpose of this note is to establish a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for compressed sensing. For fulfilling D-RIP, the constant $\delta_k$ is used in the definition: $(1…

As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm…

To provide constraints on their inversion, ocean sound speed profiles (SSPs) often are modeled using empirical orthogonal functions (EOFs). However, this regularization, which uses the leading order EOFs with a minimum-energy constraint on…

In this paper, we account for approaches of sparse recovery from large underdetermined linear models with perturbation present in both the measurements and the dictionary matrix. Existing methods have high computation and low efficiency.…