Related papers: A Survey on Compressive Sensing: Classical Results…
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…
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…
Support estimation (SE) of a sparse signal refers to finding the location indices of the non-zero elements in a sparse representation. Most of the traditional approaches dealing with SE problem are iterative algorithms based on greedy…
In this paper, we study a general framework for compressive sensing assuming the existence of the prior knowledge that $\boldsymbol{x}^*$ belongs to the union of multiple convex sets, $\boldsymbol{x}^{*} \in \bigcup_i \mathcal{C}_i$. In…
The paper investigates recoverability of discrete time signals represented by infinite sequences from incomplte observations. It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable…
This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from…
Autonomous systems can be used to search for sparse signals in a large space; e.g., aerial robots can be deployed to localize threats, detect gas leaks, or respond to distress calls. Intuitively, search algorithms may increase efficiency by…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
Compressed sensing is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random…
In this paper, we consider the problem of compressive sensing (CS) recovery with a prior support and the prior support quality information available. Different from classical works which exploit prior support blindly, we shall propose novel…
We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…
Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data. In the simplest form, this model assumes that the labels are generated from either of two different linear models and…
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…
Depth completion aims at predicting dense pixel-wise depth from an extremely sparse map captured from a depth sensor, e.g., LiDARs. It plays an essential role in various applications such as autonomous driving, 3D reconstruction, augmented…