Related papers: A Trivial Observation related to Sparse Recovery
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
This work explores the fundamental problem of the recoverability of a sparse tensor being reconstructed from its compressed embodiment. We present a generalized model of block-sparse tensor recovery as a theoretical foundation, where…
Hard thresholding pursuit (HTP) is a recently proposed iterative sparse recovery algorithm which is a result of combination of a support selection step from iterated hard thresholding (IHT) and an estimation step from the orthogonal…
The performance of Large Language Models (LLMs) is increasingly governed by data efficiency rather than raw scaling volume. However, existing selection methods often decouple global distribution balancing from local instance selection,…
Applying the theory of compressive sensing in practice always takes different kinds of perturbations into consideration. In this paper, the recovery performance of greedy pursuits with replacement for sparse recovery is analyzed when both…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
Structured prediction requires searching over a combinatorial number of structures. To tackle it, we introduce SparseMAP: a new method for sparse structured inference, and its natural loss function. SparseMAP automatically selects only a…
We consider the problem of constructing a linear map from a Hilbert space $\mathcal{H}$ (possibly infinite dimensional) to $\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\mathcal{S} \subset…
This paper considers approximately sparse signal and low-rank matrix's recovery via truncated norm minimization $\min_{x}\|x_T\|_q$ and $\min_{X}\|X_T\|_{S_q}$ from noisy measurements. We first introduce truncated sparse approximation…
Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…
We give a suitable RI-Property under which recent results for trace regression translate into strong risk bounds for multivariate regression. This pseudo-RIP is compatible with the setting $n < p$.
In the field of compressed sensing, a key problem remains open: to explicitly construct matrices with the restricted isometry property (RIP) whose performance rivals those generated using random matrix theory. In short, RIP involves…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations $\mathrm{y}$ and the redundant dictionary…
Motivated by the well-known Papoulis-Gerchberg algorithm, an iterative thresholding algorithm for recovery of sparse signals from few observations is proposed. The sequence of iterates turns out to be similar to that of the thresholded…
In this study, we introduce a novel model, termed the Weighted Basis Pursuit Dequantization ($\omega$-BPDQ$_p$), which incorporates prior support information by assigning weights on the $\ell_1$ norm in the $\ell_1$ minimization process and…
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…
Sparse signals (i.e., vectors with a small number of non-zero entries) build the foundation of most kernel (or nullspace) results, uncertainty relations, and recovery guarantees in the sparse signal processing and compressive sensing…
One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the…
Persistent homology of the Rips filtration allows to track topological features of a point cloud over scales, and is a foundational tool of topological data analysis. Unfortunately, the Rips-filtration is exponentially sized, when…