Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit

This paper demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with $m$ nonzero entries in dimension $d$ given ${rm O}(m ln d)$ random linear measurements of that signal. This is a massive improvement over previous results, which require ${rm O}(m^{2})$ measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems

Applications of sparse approximation in communications

Sparse approximation problems abound in many scientific, mathematical, and engineering applications. These problems are defined by two competing notions: we approximate a signal vector as a linear combination of elementary atoms and we require that the approximation be both as accurate and as concise as possible. We introduce two natural and direct applications of these problems and algorithmic solutions in communications. We do so by constructing enhanced codebooks from base codebooks. We show that we can decode these enhanced codebooks in the presence of Gaussian noise. For MIMO wireless communication channels, we construct simultaneous sparse approximation problems and demonstrate that our algorithms can both decode the transmitted signals and estimate the channel parameters

Sparse Approximation Via Iterative Thresholding

The well-known shrinkage technique is still relevant for contemporary signal processing problems over redundant dictionaries. We present theoretical and empirical analyses for two iterative algorithms for sparse approximation that use shrinkage. The GENERAL IT algorithm amounts to a Landweber iteration with nonlinear shrinkage at each iteration step. The BLOCK IT algorithm arises in morphological components analysis. A sufficient condition for which General IT exactly recovers a sparse signal is presented, in which the cumulative coherence function naturally arises. This analysis extends previous results concerning the Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) algorithms to IT algorithms

Simultaneous sparse approximation via greedy pursuit

A simple sparse approximation problem requests an approximation of a given input signal as a linear combination of T elementary signals drawn from a large, linearly dependent collection. An important generalization is simultaneous sparse approximation. Now one must approximate several input signals at once using different linear combinations of the same T elementary signals. This formulation appears, for example, when analyzing multiple observations of a sparse signal that have been contaminated with noise. A new approach to this problem is presented here: a greedy pursuit algorithm called simultaneous orthogonal matching pursuit. The paper proves that the algorithm calculates simultaneous approximations whose error is within a constant factor of the optimal simultaneous approximation error. This result requires that the collection of elementary signals be weakly correlated, a property that is also known as incoherence. Numerical experiments demonstrate that the algorithm often succeeds, even when the inputs do not meet the hypotheses of the proof

Improved sparse approximation over quasi-incoherent dictionaries

This paper discusses a new greedy algorithm for solving the sparse approximation problem over quasi-incoherent dictionaries. These dictionaries consist of waveforms that are uncorrelated "on average," and they provide a natural generalization of incoherent dictionaries. The algorithm provides strong guarantees on the quality of the approximations it produces, unlike most other methods for sparse approximation. Moreover, very efficient implementations are possible via approximate nearest-neighbor data structure

Algorithmic linear dimension reduction in the l_1 norm for sparse vectors

This paper develops a new method for recovering m-sparse signals that is simultaneously uniform and quick. We present a reconstruction algorithm whose run time, O(m log^2(m) log^2(d)), is sublinear in the length d of the signal. The reconstruction error is within a logarithmic factor (in m) of the optimal m-term approximation error in l_1. In particular, the algorithm recovers m-sparse signals perfectly and noisy signals are recovered with polylogarithmic distortion. Our algorithm makes O(m log^2 (d)) measurements, which is within a logarithmic factor of optimal. We also present a small-space implementation of the algorithm. These sketching techniques and the corresponding reconstruction algorithms provide an algorithmic dimension reduction in the l_1 norm. In particular, vectors of support m in dimension d can be linearly embedded into O(m log^2 d) dimensions with polylogarithmic distortion. We can reconstruct a vector from its low-dimensional sketch in time O(m log^2(m) log^2(d)). Furthermore, this reconstruction is stable and robust under small perturbations

Language and Intergroup Contact: Investigating the Impact of Bilingual Instruction on Children’s Intergroup Attitudes

This study examined the impact of bilingual versus English-only instruction on the intergroup attitudes of White, English-speaking children in kindergarten through second grade. Replicating prior research, White children generally showed a clear preference toward the ingroup in terms of positive evaluations, friendship preference, and perceived similarity to the self. However, all three effects were significantly smaller among children who were in classrooms with a significant amount of Spanish instruction (i.e. bilingual classes). The smaller preference for the ingroup over the outgroup found in bilingual classes resulted from higher evaluations of, greater selection of friends among, and greater perceived similarity to Latino targets, and not from changes in preference for White ingroup targets. Furthermore, comparisons with English-only classes that had substantial Latino representation shows that the positive impact of bilingual instruction can be only partially explained by the greater representation of Latino children in bilingual classes. Finally, these positive patterns of intergroup attitudes found in bilingual classes were not associated with any negative effects on White children’s personal self-evaluation

Progress of Diamond Digital Low Level RF

The first version of digital low level RF (DLLRF) for the Diamond Light Source storage ring and booster was developed with ALBA Synchrotron. Six systems have been built so far. Two of them are in routine operation controlling two normal conducting HOM-damped cavi-ties in the Diamond storage ring. A third system is being used for cavity testing in the RF test facility (RFTF). The fourth system is being commissioned to control the sec-ond normal conducting booster cavity. The fifth DLLRF system is being prepared for the third normal conducting RF cavity in the storage ring. A new DLLRF system based on SIS8300-KU with RTM has been developed and tested in the last few years. We are aiming to develop a common platform for the differ-ent RF systems in Diamond, including the storage ring, the booster and the Linac. It will also be our baseline design for the future Diamond II. Firmware, software and supporting hardware have been developed and tested. The Linac version with arbitrary waveform generator mode was tested successfully to generate flat top pulse from SLED in the high power test in the Linac. The stor-age ring version was also tested successfully in RFTF.Comment: Poster presented at LLRF Workshop 2022 (LLRF2022, arXiv:2208.13680

Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case

This report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(mln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems

Differential behavioral state-dependence in the burst properties of CA3 and CA1 neurons

Brief bursts of fast high-frequency action potentials are a signature characteristic of CA3 and CA1 pyramidal neurons. Understanding the factors determining burst and single spiking is potentially significant for sensory representation, synaptic plasticity and epileptogenesis. A variety of models suggest distinct functional roles for burst discharge, and for specific characteristics of the burst in neural coding. However, little in vivo data demonstrate how often and under what conditions CA3 and CA1 actually exhibit burst and single spike discharges. The present study examined burst discharge and single spiking of CA3 and CA1 neurons across distinct behavioral states (awake-immobility and maze-running) in rats. In both CA3 and CA1 spike bursts accounted for less than 20% of all spike events. CA3 neurons exhibited more spikes per burst, greater spike frequency, larger amplitude spikes and more spike amplitude attenuation than CA1 neurons. A major finding of the present study is that the propensity of CA1 neurons to burst was affected by behavioral state, while the propensity of CA3 to burst was not. CA1 neurons exhibited fewer bursts during maze running compared with awake-immobility. In contrast, there were no differences in burst discharge of CA3 neurons. Neurons in both subregions exhibited smaller spike amplitude, fewer spikes per burst, longer inter-spike intervals and greater spike amplitude attenuation within a burst during awake-immobility compared with maze running. These findings demonstrate that the CA1 network is under greater behavioral state-dependent regulation than CA3. The present findings should inform both theoretic and computational models of CA3 and CA1 function. © 2006 IBRO