Fusion of algorithms for compressed sensing

For compressed sensing (CS), we develop a new scheme inspired by data fusion principles. In the proposed fusion based scheme, several CS reconstruction algorithms participate and they are executed in parallel, independently. The final estimate of the underlying sparse signal is derived by fusing the estimates obtained from the participating algorithms. We theoretically analyze this fusion based scheme and derive sufficient conditions for achieving a better reconstruction performance than any participating algorithm. Through simulations, we show that the proposed scheme has two specific advantages: 1) it provides good performance in a low dimensional measurement regime, and 2) it can deal with different statistical natures of the underlying sparse signals. The experimental results on real ECG signals shows that the proposed scheme demands fewer CS measurements for an approximate sparse signal reconstruction.

En Masse relay selection algorithms for multi-source, multi-relay, decode-and-forward cooperative systems

Opportunistic relay selection in a multiple source-destination (MSD) cooperative system requires quickly allocating to each source-destination (SD) pair a suitable relay based on channel gains. Since the channel knowledge is available only locally at a relay and not globally, efficient relay selection algorithms are needed. For an MSD system, in which the SD pairs communicate in a time-orthogonal manner with the help of decode-and-forward relays, we propose three novel relay selection algorithms, namely, contention-free en masse assignment (CFEA), contention-based en masse assignment (CBEA), and a hybrid algorithm that combines the best features of CFEA and CBEA. En masse assignment exploits the fact that a relay can often aid not one but multiple SD pairs, and, therefore, can be assigned to multiple SD pairs. This drastically reduces the average time required to allocate an SD pair when compared to allocating the SD pairs one by one. We show that the algorithms are much faster than other selection schemes proposed in the literature and yield significantly higher net system throughputs. Interestingly, CFEA is as effective as CBEA over a wider range of system parameters than in single SD pair systems.

Polynomial time and parameterized approximation algorithms for boxicity

The boxicity (cubicity) of a graph G, denoted by box(G) (respectively cub(G)), is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes (cubes) in ℝ k . The problem of computing boxicity (cubicity) is known to be inapproximable in polynomial time even for graph classes like bipartite, co-bipartite and split graphs, within an O(n 0.5 − ε ) factor for any ε > 0, unless NP = ZPP. We prove that if a graph G on n vertices has a clique on n − k vertices, then box(G) can be computed in time n22O(k2logk) . Using this fact, various FPT approximation algorithms for boxicity are derived. The parameter used is the vertex (or edge) edit distance of the input graph from certain graph families of bounded boxicity - like interval graphs and planar graphs. Using the same fact, we also derive an O(nloglogn√logn√) factor approximation algorithm for computing boxicity, which, to our knowledge, is the first o(n) factor approximation algorithm for the problem. We also present an FPT approximation algorithm for computing the cubicity of graphs, with vertex cover number as the parameter.

Maximum likelihood algorithms for joint estimation of synchronisation impairments and channel in multiple input multiple output-orthogonal frequency division multiplexing system

Maximum likelihood (ML) algorithms, for the joint estimation of synchronisation impairments and channel in multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system, are investigated in this work. A system model that takes into account the effects of carrier frequency offset, sampling frequency offset, symbol timing error and channel impulse response is formulated. Cramer-Rao lower bounds for the estimation of continuous parameters are derived, which show the coupling effect among different impairments and the significance of the joint estimation. The authors propose an ML algorithm for the estimation of synchronisation impairments and channel together, using the grid search method. To reduce the complexity of the joint grid search in the ML algorithm, a modified ML (MML) algorithm with multiple one-dimensional searches is also proposed. Further, a stage-wise ML (SML) algorithm using existing algorithms, which estimate less number of parameters, is also proposed. Performance of the estimation algorithms is studied through numerical simulations and it is found that the proposed ML and MML algorithms exhibit better performance than SML algorithm.

Joint estimation of synchronization impairments in MIMO-OFDM system

A joint Maximum Likelihood (ML) estimation algorithm for the synchronization impairments such as Carrier Frequency Offset (CFO), Sampling Frequency Offset (SFO) and Symbol Timing Error (STE) in single user MIMO-OFDM system is investigated in this work. A received signal model that takes into account the nonlinear effects of CFO, SFO, STE and Channel Impulse Response (CIR) is formulated. Based on the signal model, a joint ML estimation algorithm is proposed. Cramer-Rao Lower Bound (CRLB) for the continuous parameters CFO and SFO is derived for the cases of with and without channel response effects and is used to compare the effect of coupling between different estimated parameters. The performance of the estimation method is studied through numerical simulations.

FUSION OF ALGORITHMS FOR COMPRESSED SENSING

Numerous algorithms have been proposed recently for sparse signal recovery in Compressed Sensing (CS). In practice, the number of measurements can be very limited due to the nature of the problem and/or the underlying statistical distribution of the non-zero elements of the sparse signal may not be known a priori. It has been observed that the performance of any sparse signal recovery algorithm depends on these factors, which makes the selection of a suitable sparse recovery algorithm difficult. To take advantage in such situations, we propose to use a fusion framework using which we employ multiple sparse signal recovery algorithms and fuse their estimates to get a better estimate. Theoretical results justifying the performance improvement are shown. The efficacy of the proposed scheme is demonstrated by Monte Carlo simulations using synthetic sparse signals and ECG signals selected from MIT-BIH database.

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO-OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO-OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator. (C) 2013 Elsevier GmbH. All rights reserved.

Progressive fusion of reconstruction algorithms for low latency applications in compressed sensing

Recently, it has been shown that fusion of the estimates of a set of sparse recovery algorithms result in an estimate better than the best estimate in the set, especially when the number of measurements is very limited. Though these schemes provide better sparse signal recovery performance, the higher computational requirement makes it less attractive for low latency applications. To alleviate this drawback, in this paper, we develop a progressive fusion based scheme for low latency applications in compressed sensing. In progressive fusion, the estimates of the participating algorithms are fused progressively according to the availability of estimates. The availability of estimates depends on computational complexity of the participating algorithms, in turn on their latency requirement. Unlike the other fusion algorithms, the proposed progressive fusion algorithm provides quick interim results and successive refinements during the fusion process, which is highly desirable in low latency applications. We analyse the developed scheme by providing sufficient conditions for improvement of CS reconstruction quality and show the practical efficacy by numerical experiments using synthetic and real-world data. (C) 2013 Elsevier B.V. All rights reserved.

Connectivity analysis of multichannel EEG signals using recurrence based phase synchronization technique

Real world biological systems such as the human brain are inherently nonlinear and difficult to model. However, most of the previous studies have either employed linear models or parametric nonlinear models for investigating brain function. In this paper, a novel application of a nonlinear measure of phase synchronization based on recurrences, correlation between probabilities of recurrence (CPR), to study connectivity in the brain has been proposed. Being non-parametric, this method makes very few assumptions, making it suitable for investigating brain function in a data-driven way. CPR's utility with application to multichannel electroencephalographic (EEG) signals has been demonstrated. Brain connectivity obtained using thresholded CPR matrix of multichannel EEG signals showed clear differences in the number and pattern of connections in brain connectivity between (a) epileptic seizure and pre-seizure and (b) eyes open and eyes closed states. Corresponding brain headmaps provide meaningful insights about synchronization in the brain in those states. K-means clustering of connectivity parameters of CPR and linear correlation obtained from global epileptic seizure and pre-seizure showed significantly larger cluster centroid distances for CPR as opposed to linear correlation, thereby demonstrating the superior ability of CPR for discriminating seizure from pre-seizure. The headmap in the case of focal epilepsy clearly enables us to identify the focus of the epilepsy which provides certain diagnostic value. (C) 2013 Elsevier Ltd. All rights reserved.

Performance evaluation of typical approximation algorithms for nonconvex l(p)-minimization in diffuse optical tomography

The sparse estimation methods that utilize the l(p)-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These l(p)-norm-based regularizations make the optimization function nonconvex, and algorithms that implement l(p)-norm minimization utilize approximations to the original l(p)-norm function. In this work, three such typical methods for implementing the l(p)-norm were considered, namely, iteratively reweighted l(1)-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of l(p)-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images. (C) 2014 Optical Society of America

Study of phase synchronization in multichannel seizure EEG using nonlinear recurrence measure

Complex biological systems such as the human brain can be expected to be inherently nonlinear and hence difficult to model. Most of the previous studies on investigations of brain function have either used linear models or parametric nonlinear models. In this paper, we propose a novel application of a nonlinear measure of phase synchronization based on recurrences, correlation between probabilities of recurrence (CPR), to study seizures in the brain. The advantage of this nonparametric method is that it makes very few assumptions thus making it possible to investigate brain functioning in a data-driven way. We have demonstrated the utility of CPR measure for the study of phase synchronization in multichannel seizure EEG recorded from patients with global as well as focal epilepsy. For the case of global epilepsy, brain synchronization using thresholded CPR matrix of multichannel EEG signals showed clear differences in results obtained for epileptic seizure and pre-seizure. Brain headmaps obtained for seizure and preseizure cases provide meaningful insights about synchronization in the brain in those states. The headmap in the case of focal epilepsy clearly enables us to identify the focus of the epilepsy which provides certain diagnostic value. Comparative studies with linear correlation have shown that the nonlinear measure CPR outperforms the linear correlation measure. (C) 2014 Elsevier Ltd. All rights reserved.

Efficient simulation of unitary operators by combining two numerical algorithms: An NMR simulation of the mirror-inversion propagator of an XY spin chain

Precise experimental implementation of unitary operators is one of the most important tasks for quantum information processing. Numerical optimization techniques are widely used to find optimized control fields to realize a desired unitary operator. However, finding high-fidelity control pulses to realize an arbitrary unitary operator in larger spin systems is still a difficult task. In this work, we demonstrate that a combination of the GRAPE algorithm, which is a numerical pulse optimization technique, and a unitary operator decomposition algorithm Ajoy et al., Phys. Rev. A 85, 030303 (2012)] can realize unitary operators with high experimental fidelity. This is illustrated by simulating the mirror-inversion propagator of an XY spin chain in a five-spin dipolar coupled nuclear spin system. Further, this simulation has been used to demonstrate the transfer of entangled states from one end of the spin chain to the other end.

Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model.

Parameterized Algorithms for MAX COLORABLE INDUCED SUBGRAPH Problem on Perfect Graphs

We address the parameterized complexity ofMaxColorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril IPL 1987] showed that this problem is NP-complete even on split graphs if q is part of input, but gave a n(O(q)) algorithm on chordal graphs. We first observe that the problem is W2]-hard parameterized by q, even on split graphs. However, when parameterized by l, the number of vertices in the solution, we give two fixed-parameter tractable algorithms. The first algorithm runs in time 5.44(l) (n+#alpha(G))(O(1)) where #alpha(G) is the number of maximal independent sets of the input graph. The second algorithm runs in time q(l+o()l())n(O(1))T(alpha) where T-alpha is the time required to find a maximum independent set in any induced subgraph of G. The first algorithm is efficient when the input graph contains only polynomially many maximal independent sets; for example split graphs and co-chordal graphs. The running time of the second algorithm is FPT in l alone (whenever T-alpha is a polynomial in n), since q <= l for all non-trivial situations. Finally, we show that (under standard complexitytheoretic assumptions) the problem does not admit a polynomial kernel on split and perfect graphs in the following sense: (a) On split graphs, we do not expect a polynomial kernel if q is a part of the input. (b) On perfect graphs, we do not expect a polynomial kernel even for fixed values of q >= 2.