相关论文: Is the 1-norm the best convex sparse regularizatio…
In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its…
Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the $\ell_1$-norm of the part of the solution vector which is known to be sparse. Such a problem is closely…
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be…
To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the…
Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex…
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
Analysis sparsity is a common prior in inverse problem or machine learning including special cases such as Total Variation regularization, Edge Lasso and Fused Lasso. We study the geometry of the solution set (a polyhedron) of the analysis…
This paper investigates recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing…
This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…
We want to exactly reconstruct a sparse signal f (a vector in R^n of small support) from few linear measurements of f (inner products with some fixed vectors). A nice and intuitive reconstruction by Linear Programming has been advocated…
In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the…
Image quality is the basis of image communication and understanding tasks. Due to the blur and noise effects caused by imaging, transmission and other processes, the image quality is degraded. Blind image restoration is widely used to…
It is known that a high-dimensional sparse vector x* in R^n can be recovered from low-dimensional measurements y= A^{m*n} x* (m<n) . In this paper, we investigate the recovering ability of l_p-minimization (0<=p<=1) as p varies, where…
We present novel analysis and algorithms for solving sparse phase retrieval and sparse principal component analysis (PCA) with convex lifted matrix formulations. The key innovation is a new mixed atomic matrix norm that, when used as…
Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…
This paper studies the problem of recovering a non-negative sparse signal $\x \in \Re^n$ from highly corrupted linear measurements $\y = A\x + \e \in \Re^m$, where $\e$ is an unknown error vector whose nonzero entries may be unbounded.…
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…