相关论文: Improved Bounds on RIP for Generalized Orthogonal …
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…
Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any $n$-dimensional vector that is $k$-sparse (with $k\ll n$) can be fully recovered using…
In this paper, an efficient distributed approach for implementing the approximate message passing (AMP) algorithm, named distributed AMP (DAMP), is developed for compressed sensing (CS) recovery in sensor networks with the sparsity K…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
In this paper, we compare and catalog the performance of various greedy quantized compressed sensing algorithms that reconstruct sparse signals from quantized compressed measurements. We also introduce two new greedy approaches for…
The optimization problems with a sparsity constraint is a class of important global optimization problems. A typical type of thresholding algorithms for solving such a problem adopts the traditional full steepest descent direction or…
We address the exact recovery of the support of a k-sparse vector with Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) in a noiseless setting. We consider the scenario where OMP/OLS have selected good atoms during the…
Greedy sparse recovery has become a popular tool in many applications, although its complexity is still prohibitive when large sparsifying dictionaries or sensing matrices have to be exploited. In this paper, we formulate first a new class…
Isotonic regression is a nonparametric approach for fitting monotonic models to data that has been widely studied from both theoretical and practical perspectives. However, this approach encounters computational and statistical overfitting…
For any $\varepsilon > 0$, we prove that $k$-Dimensional Matching is hard to approximate within a factor of $k/(12 + \varepsilon)$ for large $k$ unless $\textsf{NP} \subseteq \textsf{BPP}$. Listed in Karp's 21 $\textsf{NP}$-complete…
We present AQMP, a novel image codec combining Adaptive Quadtree Refinement with Matching Pursuit. Unlike conventional Matching Pursuit methods that operate on fixed-size sub-images, AQMP dynamically adapts block sizes to local image…
Applications of compressed sensing motivate the possibility of using different operators to encode and decode a signal of interest. Since it is clear that the operators cannot be too different, we can view the discrepancy between the two…
Region-of-Interest (ROI)-based image compression allocates bits unevenly according to the semantic importance of different regions. Such differentiated coding typically induces a sharp-peaked and heavy-tailed distribution. This distribution…
Imitation Learning (IL) holds great potential for learning repetitive manipulation tasks, such as those in industrial assembly. However, its effectiveness is often limited by insufficient trajectory precision due to compounding errors. In…
This paper addresses the challenge of reconstructing full-field structural mode shapes from sparse sensor data. While Gaussian Process Regression (GPR) offers a robust non-parametric framework for spatial interpolation and uncertainty…
We obtain mproved bounds for one bit sensing. For instance, let $ K_s$ denote the set of $ s$-sparse unit vectors in the sphere $ \mathbb S ^{n}$ in dimension $ n+1$ with sparsity parameter $ 0 < s < n+1$ and assume that $ 0 < \delta < 1$.…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
Recently, it has been observed that a sparse trigonometric polynomial, i.e. having only a small number of non-zero coefficients, can be reconstructed exactly from a small number of random samples using Basis Pursuit (BP) or Orthogonal…
There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach starts with a geometric constraint on the measurement matrix and then uses linear programming to decode information…