相关论文: On Deterministic Sketching and Streaming for Spars…
We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…
We study the robust one-bit compressed sensing problem whose goal is to design an algorithm that faithfully recovers any sparse target vector $\theta_0\in\mathbb{R}^d$ \textit{uniformly} via $m$ quantized noisy measurements. Specifically,…
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…
We consider the online convex optimization problem. In the setting of arbitrary sequences and finite set of parameters, we establish a new fast-rate quantile regret bound. Then we investigate the optimization into the L1-ball by…
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world…
Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
The recovery of signals that are sparse not in a basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard…
The paper discusses the recovery of signals in the case that signals are nearly sparse with respect to a tight frame $D$ by means of the $l_1$-analysis approach. We establish several new sufficient conditions regarding the $D$-restricted…
We present an algorithm for the maximum matching problem in dynamic (insertion-deletions) streams with *asymptotically optimal* space complexity: for any $n$-vertex graph, our algorithm with high probability outputs an $\alpha$-approximate…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
The stability of sparse signal reconstruction is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique $\ell_1$ sparse recovery. One of our algorithm produces comparable results with the…
Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study…
We consider algorithms and recovery guarantees for the analysis sparse model in which the signal is sparse with respect to a highly coherent frame. We consider the use of a monotone version of the fast iterative shrinkage- thresholding…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
The channel estimation is one of important techniques to ensure reliable broadband signal transmission. Broadband channels are often modeled as a sparse channel. Comparing with traditional dense-assumption based linear channel estimation…
Elastic-Sketch is a hash-based data structure for counting item's appearances in a data stream, and it has been empirically shown to achieve a better memory-accuracy trade-off compared to classical methods. This algorithm combines a heavy…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the…