4 Nearby scalp channels in multi-channel EEG data exhibit high correlation. A question that naturally arises is whether it is required to record signals from all the electrodes in a group of closely spaced electrodes in a typical measurement setup. One could save on the number of channels that are recorded, if it were possible to reconstruct the omitted channels to the accuracy needed for ident...

We give lower bounds for the problem of stable sparse recovery from adaptive linear measurements. In this problem, one would like to estimate a vector x ∈ R from m linear measurements A1x, . . . , Amx. One may choose each vector Ai based on A1x, . . . , Ai−1x, and must output x̂ satisfying ‖x̂− x‖p ≤ (1 + ) min k-sparse x′ ‖x− x‖p with probability at least 1−δ > 2/3, for some p ∈ {1, 2}. For p = ...

Manuscript received ; revised . Copyright (c) 2010 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. A. Carmi is with the Asher Space Research Institute, Technion – Israel Institute of Technology, Haifa 32000, Israel. P. Gurfil is with the Faculty of ...

It has been recently shown that incorporating priori knowledge significantly improves the performance of basic compressive sensing based approaches. We have managed to successfully exploit this idea for recovering a matrix as a summation of a Low-rank and a Sparse component from compressive measurements. When applied to the problem of construction of 4D Cardiac MR image sequences in real-time f...

This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the results in the area, we illustrate why an approach that is common for synthesis sparse signals fails and different techniques are necessary. Lastly, we discuss a generalizations of recent results for Gaussian measureme...

We discuss the applicability of compressed sensing theory. We take a genuine look at both experimental results and theoretical works. We answer the following questions: 1) What can compressed sensing really do? 2) More importantly, why? I. WHAT CAN COMPRESSED SENSING DO? Compressed sensing theory is described and studied as a panacea in many fields of science and engineering, evidenced by the w...