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We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L1-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix…
Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
In this work, we consider the problem of recovering analysis-sparse signals from under-sampled measurements when some prior information about the support is available. We incorporate such information in the recovery stage by suitably tuning…
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
We study the use of very sparse random projections for compressed sensing (sparse signal recovery) when the signal entries can be either positive or negative. In our setting, the entries of a Gaussian design matrix are randomly sparsified…
The stability of sparse signal reconstruction is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique $\ell_1$ sparse recovery. One of our algorithm produces comparable results with the…
Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage…
Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
We consider the reconstruction problem in compressed sensing in which the observations are recorded in a finite number of bits. They may thus contain quantization errors (from being rounded to the nearest representable value) and saturation…
We consider the extensively studied problem of $\ell_2/\ell_2$ compressed sensing. The main contribution of our work is an improvement over [Gilbert, Li, Porat and Strauss, STOC 2010] with faster decoding time and significantly smaller…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world…
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…
In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the…