相关论文: Average Case Recovery Analysis of Tomographic Comp…

Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease…

The bound that arises out of sparse recovery analysis in compressed sensing involves input signal sparsity and some property of the sensing matrix. An effort has therefore been made in the literature to optimize sensing matrices for optimal…

While most existing sparse recovery results allow only minimal structure within the measurement scheme, many practical problems possess significant structure. To address this gap, we present a framework for structured measurements that are…

Fast scanning probe microscopy enabled via machine learning allows for a broad range of nanoscale, temporally resolved physics to be uncovered. However, such examples for functional imaging are few in number. Here, using piezoresponse force…

In this paper, we propose a general framework for designing sensing matrix $\boldsymbol{A} \in \mathbb{R}^{d\times p}$, for estimation of sparse covariance matrix from compressed measurements of the form $\boldsymbol{y} =…

Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and…

We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (i.e.…

Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing…

Compressed sensing (CS) is a signal processing technique that enables the efficient recovery of a sparse high-dimensional signal from low-dimensional measurements. In the multiple measurement vector (MMV) framework, a set of signals with…

Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…

We present a new recovery analysis for a standard compressed sensing algorithm, Iterative Hard Thresholding (IHT) (Blumensath and Davies, 2008), which considers the fixed points of the algorithm. In the context of arbitrary measurement…

From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…

Most existing bounds for signal reconstruction from compressive measurements make the assumption of additive signal-independent noise. However in many compressive imaging systems, the noise statistics are more accurately represented by…

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…

Closed-loop architecture is widely utilized in automatic control systems and attain distinguished performance. However, classical compressive sensing systems employ open-loop architecture with separated sampling and reconstruction units.…

The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…

Performing a large number of spatial measurements enables high-resolution photoacoustic imaging without specific prior information. However, the acquisition of spatial measurements is time-consuming, costly, and technically challenging. By…

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…

In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…

Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…