Related papers: Fast and Efficient Compressive Sensing using Struc…
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…
Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non- adaptive linear projection observations, provided that the objects…
Random column sampling is not guaranteed to yield data sketches that preserve the underlying structures of the data and may not sample sufficiently from less-populated data clusters. Also, adaptive sampling can often provide accurate low…
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
Deep learning has been used to image compressive sensing (CS) for enhanced reconstruction performance. However, most existing deep learning methods train different models for different subsampling ratios, which brings additional hardware…
Compressive sensing involves the inversion of a mapping $SD \in \mathbb{R}^{m \times n}$, where $m < n$, $S$ is a sensing matrix, and $D$ is a sparisfying dictionary. The restricted isometry property is a powerful sufficient condition for…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
Magnetic resonance imaging (MRI) is a powerful imaging modality that revolutionizes medicine and biology. The imaging speed of high-dimensional MRI is often limited, which constrains its practical utility. Recently, low-rank tensor models…
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…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…
In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass and without any iterations. Due to its noniterative nature,…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
The resources required to characterise the dynamics of engineered quantum systems-such as quantum computers and quantum sensors-grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce…