This work considers reconstructing a target signal in a context of distributed sparse sources. We propose an efficient reconstruction algorithm with the aid of other given sources as multiple side information (SI). The proposed algorithm takes advantage of compressive sensing (CS) with SI and adaptive weights by solving a proposed weighted @math - @math minimization. The proposed algorithm computes the adaptive weights in two levels, first each individual intra-SI and then inter-SI weights are iteratively updated at every reconstructed iteration. This two-level optimization leads the proposed reconstruction algorithm with multiple SI using adaptive weights (RAMSIA) to robustly exploit the multiple SIs with different qualities. We experimentally perform our algorithm on generated sparse signals and also correlated feature histograms as multiview sparse sources from a multiview image database. The results show that RAMSIA significantly outperforms both classical CS and CS with single SI, and RAMSIA with higher number of SIs gained more than the one with smaller number of SIs.
In this section, we review a fundamental problem of signal recovery from low-dimensional signals @cite_4 @cite_1 @cite_5 and CS with SI @cite_6 @cite_14 @cite_15 @cite_8 @cite_3 @cite_12 .
@cite_14 @cite_4 @cite_8 @cite_1 @cite_6 @cite_3 @cite_5 @cite_15 @cite_12
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In this paper, we study the problem of one-bit compressed sensing (1-bit CS), where the goal is to design a measurement matrix A and a recovery algorithm such that a k-sparse unit vector x* can be efficiently recovered from the sign of its linear measurements, i.e., b = sign(Ax*). This is an important problem for signal acquisition and has several learning applications as well, e.g., multi-label classification (, 2009). We study this problem in two settings: a) support recovery: recover the support of x*, b) approximate vector recovery: recover a unit vector x such that ||x - x*||2 = e. For support recovery, we propose two novel and efficient solutions based on two combinatorial structures: union free families of sets and expanders. In contrast to existing methods for support recovery, our methods are universal i.e. a single measurement matrix A can recover all the signals. For approximate recovery, we propose the first method to recover a sparse vector using a near optimal number of measurements. We also empirically validate our algorithms and demonstrate that our algorithms recover the true signal using fewer measurements than the existing methods. The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a union of subspaces, respectively. A stable analytic reconstruction procedure of low complexity is given. Additionally it is proven that signal recovery from these measurements can be solved exactly via a semidefinite program. A practical implementation with 4 deterministic diffraction patterns is provided and some numerical experiments with noisy measurements complement the analytic approach. This paper studies the problem of recovering a sparse signal x ∈ ℝn from highly corrupted linear measurements y = Ax + e ∈ ℝm, where e is an unknown error vector whose nonzero entries may be unbounded. Motivated by an observation from face recognition in computer vision, this paper proves that for highly correlated (and possibly overcomplete) dictionaries A, any sufficiently sparse signal x can be recovered by solving an l1 -minimization problem min ||x||1 + ||e||1 subject to y = Ax + e. More precisely, if the fraction of the support of the error e is bounded away from one and the support of a: is a very small fraction of the dimension m, then as m becomes large the above l1 -minimization succeeds for all signals x and almost all sign-and-support patterns of e. This result suggests that accurate recovery of sparse signals is possible and computationally feasible even with nearly 100 of the observations corrupted. The proof relies on a careful characterization of the faces of a convex polytope spanned together by the standard crosspolytope and a set of independent identically distributed (i.i.d.) Gaussian vectors with nonzero mean and small variance, dubbed the "cross-and-bouquet" (CAB) model. Simulations and experiments corroborate the findings, and suggest extensions to the result. Can we recover a signal f 2 R N from a small number of linear measurements? A series of recent papers developed a collection of results showing that it is surprisingly possible to reconstruct certain types of signals accurately from limited measurements. In a nutshell, suppose that f is compressible in the sense that it is well-approximated by a linear combination of M vectors taken from a known basis . Then not knowing anything in advance about the signal, f can (very nearly) be recovered from about M logN generic nonadaptive measurements only. The recovery procedure is concrete and consists in solving a simple convex optimization program. In this paper, we show that these ideas are of practical significance. Inspired by theoretical developments, we propose a series of practical recovery procedures and test them on a series of signals and images which are known to be well approximated in wavelet bases. We demonstrate empirically that it is possible to recover an object from about 3M ‐5M projections onto generically chosen vectors with the same accuracy as the ideal M -term wavelet approximation. We briefly discuss possible implications in the areas of data compression and medical imaging.