Fast OMP Algorithm Based on Bayesian Test for Multiple Measurement Vectors Model

Publication in the conference proceedings of EUSIPCO, Bucharest, Romania, 2012

Pattern transformation-invariant schemes for wireless sensor networks based on an edge detection gradient-based mechanism

A directional pursuit algorithm is proposed to reconstruct an unknown sparse signal from noisy measurements. The algorithm offered an iterative update direction for improving the reconstructive accuracy of compressive sensing. Unlike traditional directional pursuit methods which only select the atoms owning higher correlation with the residual signal, the proposed algorithm not only values the higher correlation atoms but also reserves the lower correlation atoms with the residual signal. In the lower correlation atoms, only a few are active which usually impact the reconstructive performance and decide the reconstruction dynamic range of directional pursuit methods. The others are inactive. In order to avoid redundant atoms impacting the reconstructive accuracy, Bayesian hypothesis testing model is used to identify active atoms and eliminate redundant ones. Simulation results of the proposed algorithm show that the reconstructive accuracy and reconstructive dynamic range can indeed be improved. Furthermore, better noisy immunity compared with the traditional directional pursuit methods can be obtained.

Synthetic aperture radar (SAR) is widely used for ground observations owing to its all-weather and all-time capabilities. Sparse SAR reconstruction imaging, which can enhance SAR imaging performance, has emerged as a significant research area. The traditional sparse SAR reconstruction imaging method was successfully applied to raw SAR data processing. However, the computational complexity makes sparse reconstruction imaging difficult for large scenes. Meanwhile, because raw data are usually kept confidential, only limited data are available. To address the issue of how to use publicly available complex image data for sparse reconstruction and effectively improve image quality, this study proposes a joint L1- and F-norm edge-preservation-based sparse SAR reconstruction algorithm for complex images. The algorithm uses the gradient descent (GD) technique to optimize the L1-norm regularization and reconstruct the overall image information; the iterative soft thresholding algorithm (ISTA) to optimize the F-norm regularization and reconstruct the high-frequency image information; and fuses the two sets of reconstructed information to obtain SAR reconstructed images with characteristics such as edge preservation, clear texture, and high quality. The results show that, compared with traditional matched filtering (MF) imaging results, the joint L1- and F-norm results obtained for complex images have lower sidelobes, higher signal-to-noise ratio, and better target resolution ability; compared with the F-norm-based sparse SAR reconstruction imaging results, the joint L1- and F-norm method provides images with better edge texture clarity.

The medial axis can be viewed as a compact representation for an arbitrary model; it is an essential geometric structure in many applications. A number of practical algorithms for its computation have been aimed at speeding up its computation and at addressing its instabilities. In this paper we propose a new algorithm to compute the medial axis with arbitrary precision. It exhibits several desirable properties not previously combined in a practical and efficient algorithm. First, it allows for a tradeoff between computation time and accuracy, making it well-suited for applications in which an approximation of the medial axis suffices, but computational efficiency is of particular concern. Second, it is output sensitive: the computation complexity of the algorithm does not depend on the size of the representation of a model, but on the size of the representation of the resulting medial axis. Third, the densities of the approximated medial axis points in different areas are adaptive to local free space volumes, based on the assumption that a coarser approximation in wide open area can still suffice the requirements of the applications. We present theoretical results, bounding the error introduced by the approximation process. The algorithm has been implemented and experimental results are presented that illustrate its computational efficiency and robustness.

This paper addresses the problem of compressively sensing a set of temporally correlated sources, in order to achieve faithful sparse signal reconstruction from noisy multiple measurement vectors (MMV). To this end, a simple sensing mechanism is proposed, which does not require the restricted isometry property (RIP) to hold near the sparsity level, whilst it provides additional degrees of freedom to better capture and suppress the inherent sampling noise effects. In particular, a reduced set of MMVs is generated by projecting the source signals onto random vectors drawn from isotropic multivariate stable laws. Then, the correlated sparse signals are recovered from the random MMVs by means of a recently introduced sparse Bayesian learning algorithm. Experimental evaluations on synthetic data with varying number of sources, correlation values, and noise strengths, reveal the superiority of our proposed sensing mechanism, when compared against well-established RIP-based compressive sensing schemes.

This work addresses the problem of recovering multi-echo T1 or T2 weighted images from their partial K-space scans. Recent studies have shown that the best results are obtained when all the multi-echo images are reconstructed by simultaneously exploiting their intra-image spatial redundancy and inter-echo correlation. The aforesaid studies either stack the vectorised images (formed by row or columns concatenation) as columns of a Multiple Measurement Vector (MMV) matrix or concatenate them as a long vector. Owing to the inter-image correlation, the thus formed MMV matrix or the long concatenated vector is row-sparse or group-sparse respectively in a transform domain (wavelets). Consequently the reconstruction problem was formulated as a row-sparse MMV recovery or a group-sparse vector recovery. In this work we show that when the multi-echo images are arranged in the MMV form, the thus formed matrix is low-rank. We show that better reconstruction accuracy can be obtained when the information about rank-deficiency is incorporated into the row/group sparse recovery problem. Mathematically, this leads to a constrained optimization problem where the objective function promotes the signal's groups-sparsity as well as its rank-deficiency; the objective function is minimized subject to data fidelity constraints. The experiments were carried out on ex vivo and in vivo T2 weighted images of a rat's spinal cord. Results show that this method yields considerably superior results than state-of-the-art reconstruction techniques.

Monte Carlo (MC) dose calculation algorithms are regarded as the gold standard in intensity-modulated radiation therapy (IMRT). Simply adding a MC dose calculation engine to a standard IMRT optimization framework is possible but computationally inefficient. Thus, the optimization would be too time consuming for clinical practice. In this work we developed a hybrid algorithm for the treatment plan optimization that combines the accuracy of MC simulations with the efficiency of less precise dose calculation algorithms. Two methods are introduced that allow a rapid convergence of the iterative optimization algorithm and preserve the efficiency of the MC dose calculation. The performance of the hybrid optimization algorithm is analyzed on different treatment sites. The results are compared against a reference optimization algorithm, which is based on MC simulations in the standard IMRT framework. For this comparison we evaluated several indicators of treatment plan quality, convergence properties, calculation times and efficiency ratios. The efficiency of the optimization could be improved from originally 10-30% to 80-95%. Due to this improvement the calculation times could be reduced to 2-28 minutes, depending on the treatment plan complexity. At the same time, the treatment plan quality could be maintained compared to the reference algorithm.

Extreme UltraViolet (EUV) lithography is a new technology for production of integrated circuits. In EUV lithographic machines, optical elements are heated by absorption of exposure energy. Heating induces thermoelastic deformations of optical elements and consequently, it creates wavefront aberrations. These Thermally Induced Wavefront Aberrations (TIWA) can significantly degrade the resolution of EUV lithographic machines. One of the ways to correct TIWA and consequently, to improve the resolution of EUV lithographic machines, is to use the Adaptive Optics (AO) technique and predictive control algorithms. However, the predictive control of TIWA is a challenging problem, mainly because the dynamical behavior of TIWA is described by thermoelastic Partial Differential Equations (PDEs). By discretizing the thermoelastic equations using the finite difference or finite element methods, large-scale state-space models can be obtained. A striking feature of these state-space models is that they have sparse (multi) banded matrices. Consequently, these state-space models can be interpreted as large-scale networks of local subsystems. All this implies that the problem of correcting TIWA can be placed in a much more general context of identifying, estimating and controlling large-scale interconnected (distributed) systems. However, currently used estimation and control algorithms are not computationally feasible for large-scale systems. For this reason, this thesis focuses on the development of computationally efficient identification, estimation and control algorithms for large-scale interconnected systems. In this thesis, we prove that the inverses of (finite-time) Gramians of large-scale interconnected systems, obtained by discretizing PDEs, belong to a class of off-diagonally decaying matrices. Consequently, these inverses can be approximated by sparse (multi) banded matrices with O(N) complexity, where N is the number of local subsystems. To compute the approximate inverses, the Chebyshev approximation method and the Newton iteration are used. On the basis of these theoretical results, we develop novel estimation and identification algorithms for large-scale interconnected systems. The computational and memory complexity of these methods scale with O(N). This is the main advantage over the traditional estimation and identification methods, which complexity is O(N^3). Furthermore, in this thesis we develop and experimentally verify AO control algorithms for predictive correction of TIWA. The experimental results give a good first indication for a possible implementation of the developed predictive control algorithms in EUV lithographic machines. Finally, we develop and experimentally test an iterative learning control algorithm for high performance correction of wavefront aberrations.

Aiming at the problems of synthetic-aperture radar (SAR), such as high sampling rate and vulnerability to noise interference in imaging, a sparse reconstruction algorithm based on approximate observation and L1/2 threshold iteration is proposed in this paper. To solve the problem of the large dimension and high computational complexity of the measurement matrix, a sparse reconstruction model based on approximate observation is constructed, and a threshold iterative algorithm to rapidly solve the L1/2 regularization problem is introduced, which can realize sparse signal reconstruction with fewer sampling data and quickly solve the problem. The simulation results of point targets and the measured data of spaceborne SAR show that compared with the traditional matched filtering algorithm and L1 threshold algorithm based on a two-step iteration, the proposed sparse reconstruction algorithm has a faster iteration speed and improves the image quality.

Uncovering brain activity from magnetoencephalography (MEG) data requires solving an ill-posed inverse problem, greatly confounded by noise, interference, and correlated sources. Sparse reconstruction algorithms, such as Champagne, show great promise in that they provide focal brain activations robust to these confounds. In this paper, we address the technical considerations of statistically thresholding brain images obtained from sparse reconstruction algorithms. The source power distribution of sparse algorithms makes this class of algorithms ill-suited to “conventional” techniques. We propose two non-parametric resampling methods hypothesized to be compatible with sparse algorithms. The first adapts the maximal statistic procedure to sparse reconstruction results and the second departs from the maximal statistic, putting forth a less stringent procedure that protects against spurious peaks. Simulated MEG data and three real data sets are utilized to demonstrate the efficacy of the proposed methods. Two sparse algorithms, Champagne and generalized minimum-current estimation (G-MCE), are compared to two non-sparse algorithms, a variant of minimum-norm estimation, sLORETA, and an adaptive beamformer. The results, in general, demonstrate that the already sparse images obtained from Champagne and G-MCE are further thresholded by both proposed statistical thresholding procedures. While non-sparse algorithms are thresholded by the maximal statistic procedure, they are not made sparse. The work presented here is one of the first attempts to address the problem of statistically thresholding sparse reconstructions, and aims to improve upon this already advantageous and powerful class of algorithm.

Blade tip-timing measurements (BTT) are increasingly used in the monitoring of aero-engine blades. BTT signal is heavily under-sampled, which is difficult to recover. In order to solve this problem, the sparse reconstruction algorithm has been applied in many studies. However, the speed of sparse reconstruction for the BTT signal has been rarely mentioned till now. In this paper, for the purpose of improving computation speed, an improved sparse reconstruction algorithm is proposed Besides, a series of simulation results are performed to verify that with higher accuracy, the improved method can significantly shorten computing time compared with traditional sparse reconstruction algorithm. Therefore, the improved method can enhance accuracy and real-time performance of BTT, for which its advantage of online measurement can be better shown.

Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-of- arrival estimation. Recently, this problem has been address using prior information in form of a jointly sparse signal structure. A prominent approach for exploiting joint sparsity considers mixed-norm minimization in which, however, the problem size grows with the number of measurements and the desired resolution, respectively. In this work we derive an equivalent, compact reformulation of the $\ell_{2,1}$ mixed-norm minimization problem which provides new insights on the relation between different existing approaches for jointly sparse signal reconstruction. The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the jointly sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we derive in this case from our compact problem formulation the exact equivalence between the $\ell_{2,1}$ mixed-norm minimization and the atomic-norm minimization. Additionally, for the case of irregular sampling or a large number of samples, we present a low complexity, grid-based implementation based on the coordinate descent method.

– This paper analyses the performance of Multiple Input Multiple Output (MIMO) wireless communication system by combining it with an efficient algorithm Diagonal Reduction (DR). DR is a powerful tool to achieve more efficiently a high performance with less complexity. This paper proposes a DR algorithm in order to reduce its complexity named Greedy Diagonal Reduction (GDR) algorithm which gives reduced complexity with efficient performance at the receiver using the MATLAB communication tool box version 7.0 as a simulation tool. From the simulation results of various reduction algorithms it is observed that, DR can reduce the number of iterations using size reduction operations. Proposed DR algorithm gives identical Bit Error Rate (BER) performance with LLL algorithms when applied to Successive Interference cancellation (SIC) decoding. Greedy DR reduces the computational complexity in Multiple Input Multiple Output systems by improving the efficiency in terms of size reduction operations. Sphere Decoding (SD) technique gives better BER performance on comparing with Successive Interference cancellation decoding technique.

Modern radio systems require accurate radio channel estimates in the presence of fast fading. This paper proposes an iterative radio channel estimation system where the detected and decoded symbols from the previous iteration are used as ‘virtual’ pilot symbols to improve estimation accuracy. In each iteration of the receiver algorithm, a low order Kalman filter provides a rough estimate of the channel gains. This rough estimate is refined to a more accurate radio channel estimate with a zero phase de-noising filter. This two stage channel estimation system is capable of providing near optimal channel estimation at a much lower computational cost than prior art. It is demonstrated that the proposed radio channel estimation is capable of supporting low error data reception at high fading rates. The algorithm can be implemented efficiently on modern multicore computing systems.