Construction on the measurement matrix A is a central problem in compressed sensing. Although using random matrices is proven optimal and successful in both theory and applications. A deterministic construction on the measurement matrix is still very important and interesting. In fact, it is still an open problem proposed by T. Tao. In this paper, we shall provide a new deterministic constructi...

Abstract. There are well-known relationships between compressed sensing and the geometry of the finite-dimensional lp spaces. A result of Kashin and Temlyakov [20] can be described as a characterization of the stability of the recovery of sparse vectors via l1minimization in terms of the Gelfand widths of certain identity mappings between finitedimensional l1 and l2 spaces, whereas a more recen...

where the second inequality follows from Cauchy-Schwartz. Furthermore, the CauchySchwartz inequality holds with equality for all vectors x in the one-dimensional subspace spanned by the all-ones vector. Therefore, it is not difficult to achieve Property 1 when the subspace X has small dimension. But we want the dimension to be very large, let us say, dim(X) = Ω(N). As it turns out, even with th...

In this paper the authors describe the problem of acquisition of interfered signals and formulate a filtering problem. A frequency-selective compressed sensing technique is proposed as a solution to this problem. Signal acquisition is critical in facilitating frequency-selective compressed sensing. The authors propose a filtering compressed sensing parameter, which allows to assess if a given a...

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 identif...

Suppose one has n points, X = {x1, . . . , xn}, in Rd (with d very large). If d > n, since the points have to lie in a subspace of dimension n it is clear that one can consider the projection f : Rd → Rn of the points to that subspace without distorting the geometry of X. In particular, for every xi and xj , ‖f(xi)− f(xj)‖ = ‖xi − xj‖, meaning that f is an isometry in X. Suppose now we allow a ...

Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal, this extra information can be successfully exploited to enhance recovery performance. In particular, weighted l1-minimization with suitable choice of weights ha...