Related papers: Sparsest Error Detection via Sparsity Invariant Tr…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm…
We consider the compressed sensing problem, where the object $x_0 \in \bR^N$ is to be recovered from incomplete measurements $y = Ax_0 + z$; here the sensing matrix $A$ is an $n \times N$ random matrix with iid Gaussian entries and $n < N$.…
Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
We present a novel feature selection technique, Sparse Linear Centroid-Encoder (SLCE). The algorithm uses a linear transformation to reconstruct a point as its class centroid and, at the same time, uses the $\ell_1$-norm penalty to filter…
Underdetermined or ill-posed inverse problems require additional information for \ldd{d} sound solutions with tractable optimization algorithms. Sparsity yields consequent heuristics to that matter, with numerous applications in signal…
Sparse optimization is a fundamental challenge in various practical applications. A popular approach to sparse optimization is $\ell_p$ regularization. However, it may encounter optimization instability due to the unbounded gradients when…
This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab…
The Sparse Approximation problem asks to find a solution $x$ such that $||y - Hx|| < \alpha$, for a given norm $||\cdot||$, minimizing the size of the support $||x||_0 := \#\{j \ |\ x_j \neq 0 \}$. We present valid inequalities for Mixed…
In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted $\ell_1$ minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into…
This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…
We present a novel sparse signal reconstruction method "ISD", aiming to achieve fast reconstruction and a reduced requirement on the number of measurements compared to the classical l_1 minimization approach. ISD addresses failed…
We consider the decomposition of a signal over an overcomplete set of vectors. Minimization of the $\ell^1$-norm of the coefficient vector can often retrieve the sparsest solution (so-called "$\ell^1/\ell^0$-equivalence"), a generally…
Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this…
Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
We discuss a strategy of sparse approximation that is based on the use of an overcomplete basis, and evaluate its performance when a random matrix is used as this basis. A small combination of basis vectors is chosen from a given…
In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…