In [1], we proved the asymptotic achievability of the Cramér-Rao bound in the compressive sensing setting in the linear sparsity regime. In the proof, we used an erroneous closed-form expression of ασ for the genie-aided Cramér-Rao bound σTr(AIAI) −1 from Lemma 3.5, which appears in Eqs. (20) and (29). The proof, however, holds if one avoids replacing σTr(AIAI) −1 by the expression of Lemma 3.5...

Corresponding author: Vasilis Ntziachristos Ingoldstädter Landstraße 1, 85764 ,Neuherberg, Germany; E-mail: [email protected]

In traditional compressed sensing MRI methods, single sparsifying transform limits the reconstruction quality because it cannot sparsely represent all types of image features. Based on the principle of basis pursuit, a method that combines sparsifying transforms to improve the sparsity of images is proposed. Simulation results demonstrate that the proposed method can well recover different type...

F. Krzakala , M. Mézard , F. Sausset , Y. F. Sun and L. Zdeborová 4 1 CNRS and ESPCI ParisTech, 10 rue Vauquelin, UMR 7083 Gulliver, Paris 75005, France. 2 Univ. Paris-Sud & CNRS, LPTMS, UMR8626, Bât. 100, 91405 Orsay, France. 3 LMIB and School of Mathematics and Systems Science, Beihang University, 100191 Beijing, China. 4 Institut de Physique Théorique, IPhT, CEA Saclay, and URA 2306, CNRS, 9...

Is it possible to obliviously construct a set of hyperplanes H such that you can approximate a unit vector x when you are given the side on which the vector lies with respect to every h ∈ H? In the sparse recovery literature, where x is approximately k-sparse, this problem is called onebit compressed sensing and has received a fair amount of attention the last decade. In this paper we obtain th...

Compressive sensing (CS) exploits the sparsity present in many signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in environments where the input ...

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, and demonstrating how it can be fruitfully exploited by the design of suitable sampling strategies in order to outperform more standard compressed sensing tech...

Performance guarantees for recovery algorithms employed in sparse representations, and compressed sensing highlights the importance of incoherence. Optimal bounds of incoherence are attained by equiangular unit norm tight frames (ETFs). Although ETFs are important in many applications, they do not exist for all dimensions, while their construction has been proven extremely difficult. In this pa...

We study the recovery results of lp-constrained compressive sensing (CS) with p ≥ 1 via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon (2014) from l2-constrained CS to lp-constrained case with p ≥ 1 and complements the reco...