compressed sensing

This work addresses the low reconstruction accuracy and poor stability of compressed sensing (CS) in practical signal recovery. We systematically analyze its mathematical foundations—sparse representation and underdetermined system solving—and propose an improved optimization framework integrating adaptive thresholding with a weighted ℓ₁-norm. Methodologically, leveraging convex optimization theory and iterative soft-thresholding algorithms, we explicitly model the pathological effects of measurement noise and sparsity mismatch to enhance algorithmic robustness. Experimental results demonstrate that, at sampling rates below 30%, our method achieves an average 2.8 dB PSNR gain and 37% reduction in reconstruction error over classical OMP and ISTA. Moreover, it preserves high fidelity on real-world signals—including EEG and MRI data. This study not only strengthens the theoretical interpretability of CS but also delivers an efficient, stable, and deployment-ready reconstruction solution.

This paper addresses the support recovery of sparse signals under noise using sparse measurement matrices. To characterize the trade-off between sample complexity and measurement sparsity, we introduce the notion of “sparsity cost,” quantifying the additional sample overhead induced by matrix sparsification. Leveraging probabilistic analysis, information-theoretic lower bounds, and random matrix theory—under standard regularity assumptions—we derive sharp phase-transition thresholds and sufficient sampling conditions for exact support recovery. Our theoretical results establish that when $ds/p o infty$, the information-theoretic limit is $n_{ ext{INF}}^{ ext{SP}} = Thetaig(s log(p/s) / log(ds/p)ig)$; when $s = alpha p$ and $d = psi p$, the required sample size scales as $Theta(p / psi^2)$. To our knowledge, this is the first work to precisely quantify how measurement sparsity fundamentally limits support recovery performance, providing a foundational theoretical benchmark for the design of sparse-sensing systems.

This paper addresses sparse signal recovery in underdetermined linear systems $x = Qs$. We propose a novel greedy algorithmic framework that directly optimizes in the $s$-domain, unifying solution-space characterization and iterative mechanics. The framework supports both $ell_2$- and $ell_1$-norm measures and incorporates CoSaMP’s atom selection strategy. Our $ell_2$-based variant significantly outperforms classical OMP, while the $ell_1$-based variant substantially surpasses Basis Pursuit (BP). Both algorithms exhibit strong robustness to measurement noise and ill-conditioning of the sensing matrix $Q$. Theoretical analysis establishes guarantees for high-dimensional sparse modeling and numerical stability. Extensive experiments on synthetic data and real-world images demonstrate marked improvements in reconstruction accuracy, with computational complexity comparable to that of OMP.

This work addresses sparse recovery of real-world signals exhibiting group-symmetric structure under structured measurements generated via random group orbits. We propose a unified group-orbit measurement model, distinguishing between fixed and random sampling sets. Leveraging group representation theory, random matrix analysis, and probabilistic methods, we establish a compressed sensing framework explicitly incorporating group-action structure and derive restricted isometry property (RIP) conditions parameterized by representation-theoretic characteristics of the underlying group. We obtain sharp lower bounds on the minimum number of measurements required to guarantee RIP with high probability—significantly generalizing classical structured sensing matrices such as circulant ensembles. Theoretical analysis confirms that canonical representations—including the left-regular representation—achieve optimal or near-optimal recovery performance, thereby introducing a novel paradigm for structured sparse reconstruction.

This work addresses the problem of efficiently recovering sparse signals from random compressive measurements without solving optimization problems or linear systems. The authors propose a novel method that utilizes only Θ(log n) random sensing matrices to accurately recover the support set and reconstruct the signal in O(kn log n) time, where k = Θ(s log n) and s denotes the number of non-zero entries. To the best of the authors’ knowledge, this is the first approach to achieve efficient sparse recovery without relying on optimization or linear system solvers. Experimental results on binary signals demonstrate the effectiveness of the proposed method, showing superior performance compared to several existing optimization-based algorithms.

This work addresses the challenge of unifying diverse structured sparsity patterns for efficient model compression and acceleration. The authors propose S³, an algebraic framework that formally integrates three core components—View (tensor reshaping), Block (atomic pruning units), and Scope (sparsity decision range)—to express a wide spectrum of sparsity patterns, ranging from fine-grained N:M sparsity to coarse-grained channel pruning, within a single formalism. Notably, S³ enables cross-tensor collaborative sparsification. Building upon this framework, the authors incorporate Optimal Brain Damage and Surgeon algorithms to develop structured variants of OBS/OBD. These methods significantly outperform current state-of-the-art second-order heuristic approaches in terms of output reconstruction accuracy.

This study addresses the challenges of model stability and parameter tuning in the recovery of structured signals—such as sparse signals—from noisy measurements. It systematically investigates three constrained optimization models grounded in distinct structural priors. Through rigorous theoretical analysis, the work establishes a fundamental trade-off between sample complexity and mismatch error, and formally proves the robust stability of these models under both measurement noise and parameter perturbations. By incorporating structural priors like sparsity into regularized formulations, the proposed approach offers a principled framework that ensures both noise robustness and parameter stability, thereby providing strong theoretical guarantees for applications in imaging reconstruction, wireless communications, and related domains.