Improved Matching Pursuits Image Coding

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15° using OMP algorithms to by > 5° using the proposed NSRomp algorithm.

The objective of this study is to propose an accurate emotion recognition methodology. To this end, a novel fusion framework based on wavelet transform (WT), and matching pursuit (MP) algorithm was offered. Electrocardiogram (ECG) and galvanic skin response (GSR) of 11 healthy students were collected while subjects listened to emotional music clips. In both fusion techniques, Coiflet wavelet (Coif5 at level 14) was chosen as a wavelet family and MP dictionary, respectively. After employing the proposed fusion framework, some statistical measures were extracted. To describe emotions, three schemes were adopted: two-dimensional model (five classes), valence-(three classes), and arousal-(three classes) based emotion categories. Subsequently, the probabilistic neural network (PNN) was applied to classify affective states. The experiments indicate that the MP-based fusion approach outperform the wavelet-based fusion technique or methods using only ECG or GSR indices. Considering the proposed fusion techniques, the maximum classification rate of 99.64% and 92.31% was reached for the fusion methodology based on the MP algorithm (five classes of emotion) and wavelet-based fusion technique (three classes of valence), respectively.

Matching pursuit (MP) uses a greedy search to construct a subset of vectors, from a larger set, which best represents a signal of interest. We extend this search for the best subset by keeping the K vectors which maximize the selection criterion at each iteration. This is termed the MP:K algorithm and represents a suboptimal search through the tree of all possible subsets where each node is limited to having K children. As a more suboptimal search, we can use the M-L search to select a subset of dictionary vectors, leading to the MP:M-L algorithm. We compare the computation and storage requirements for three variants of the MP algorithm using these searches. Through simulations, the significantly improved performance obtained using the MP:K and MP:M-L algorithms is demonstrated. We conclude that the modified matching pursuit (MMP) algorithm offers the best compromise between performance and complexity using these search techniques.

The matching pursuit algorithm has been successfully applied in many areas such as data compression and pattern recognition. The performance of matching pursuit is closely related to the selection of the dictionary. In this paper, we propose an algorithm to estimate the optimal dictionary distribution ratio and discuss the decay of the norm of residual signal in matching pursuit when the coefficients are quantized by a uniform scalar quantizer. It is proposed that if the approximation error E and the dimension of the space N are given, the optimal size of the dictionary and the optimal quantizer step should be obtained by minimizing the number of bits required to store the matching pursuit representation of any signal in the space to satisfy the error bound.

An FPGA implementation of the matching pursuit algorithm for a compressed sensing enabled e-Health monitoring platform

An improved method is presented for coding the atoms found by the matching pursuits algorithm used in compressing displaced frame difference (DFD) images in motion compensated video coding. A list of atoms is collected, which are then communicated in the order of their most significant bit plane, rather than being communicated as they are found. The atom positions are run length coded, with the sign, extra bits of magnitude and code-book entry sent as side information. The magnitudes are represented by the most significant bit plus a specified number of additional bits. The distortion is never worse than the standard coding method, and can be up to 1dB better. The magnitude precision for best PSNR is found to be 2 at low bit rates and 1 at high bit rates in the examples considered.

Broadband ultrasound signals will produce distortion in viscoacoustic medium, which may influence the accuracy of time-of-flight (TOF) measurement. Under the condition of single-frequency acoustic source, the wave propagation process in viscoacoustic medium was analyzed and an approximate solution of the wave propagation was given. Instances of broadband ultrasound were analyzed and simulated based on the single-frequency results. A single-frequency matching pursuits (SFMP) algorithm was then introduced to solve the waveform distortion problem. Time-frequency decomposition was applied to extracting the single-frequency compositions from broadband ultrasound signals, and then these compositions were sent to the matching pursuits (MP) algorithm for calculating the TOF parameters. Compared with the broadband signals, the shapes of extracted single-frequency signals change more slightly as distance and attenuation coefficient increase. The residuals of SFMP were far less than those of MP algorithm. Experimental results show that the SFMP algorithm is able to eliminate waveform distortion of broadband ultrasound in viscoacoustic medium, which helps improve the accuracy of TOF measurement.

Matching pursuit is a powerful and flexible optimisation technique that has found applications in different areas, including image and video compression. This paper proposes an underlying probabilistic model for the entropy coding of the parameters generated by the matching pursuit algorithm in the context of image coding. It also distinguishes between orthogonal and fully-orthogonal matching pursuit, and provides a formulation for rate-distortion optimized matching pursuit.

The matching pursuit algorithm can be used to derive signal decompositions in terms of the elements of a dictionary of time-frequency atoms. Using a structured overcomplete dictionary yields a signal model that is both parametric and signal adaptive. In this paper, we apply matching pursuit to the derivation of signal expansions based on damped sinusoids. It is shown that expansions in terms of complex damped sinusoids can be efficiently derived using simple recursive filter banks. We discuss a subspace extension of the pursuit algorithm that provides a framework for deriving real-valued expansions of real signals based on such complex atoms. Furthermore, we consider symmetric and asymmetric two-sided atoms constructed from underlying one-sided damped sinusoids. The primary concern is the application of this approach to the modeling of signals with transient behavior such as music; it is shown that time-frequency atoms based on damped sinusoids are more suitable for representing transients than symmetric Gabor atoms. The resulting atomic models are useful for signal coding and analysis modification synthesis.

State-of-the-art sparse recovery methods often rely on the restricted isometry property for their theoretical guarantees. However, they cannot explicitly incorporate metrics such as restricted isometry constants within their recovery procedures due to the computational intractability of calculating such metrics. This paper formulates an iterative algorithm, termed yet another matching pursuit algorithm (YAMPA), for recovery of sparse signals from compressive measurements. YAMPA differs from other pursuit algorithms in that: (i) it adapts to the measurement matrix using a threshold that is explicitly dependent on two computable coherence metrics of the matrix, and (ii) it does not require knowledge of the signal sparsity. Performance comparisons of YAMPA against other matching pursuit and approximate message passing algorithms are made for several types of measurement matrices. These results show that while state-of-the-art approximate message passing algorithms outperform other algorithms (including YAMPA) in the case of well-conditioned random matrices, they completely break down in the case of ill-conditioned measurement matrices. On the other hand, YAMPA and comparable pursuit algorithms not only result in reasonable performance for well-conditioned matrices, but their performance also degrades gracefully for ill-conditioned matrices. The paper also shows that YAMPA uniformly outperforms other pursuit algorithms for the case of thresholding parameters chosen in a clairvoyant fashion. Further, when combined with a simple and fast technique for selecting thresholding parameters in the case of ill-conditioned matrices, YAMPA outperforms other pursuit algorithms in the regime of low undersampling, although some of these algorithms can outperform YAMPA in the regime of high undersampling in this setting.

We consider efficient methods for active users detection in Multiple-Input Multiple-Output (MIMO) system. To support massive connectivities, all active users are allowed to transmit information simultaneously. We use greedy algorithm to get the set of active users and their channel state information(CSI) in limited time. The Block Orthogonal Matching Pursuit (BOMP) algorithm needs many iterations and the knowledge of sparsity level. To make explicit use of block sparsity, adaptive Compressive Sampling Matching Pursuit(ACoSaMP) algorithm is proposed to decrease the iterations we need. And new stop conditions has been found to get accurate sparsity level which is the number of active users. Combining those two methods, we can have better performance and lower complexity than BOMP at the same time.

Wearable ECG monitoring devices, often limited by power constraints, require efficient methods to reduce energy consumption and extend battery life for continuous health tracking. This work proposes a digital compressed sensing approach for ECG (DCS-ECG), featuring a suitable sensing matrix, effective sparse signal recovery algorithms, and an optimized number of bits for quantization (BM). The framework is designed to achieve high compression ratios (CR) with minimal signal distortion and parameter extraction without the reconstruction of the original signal. The following five sensing matrices are examined: deterministic block binary diagonal (DBBD) matrix, random binary (RBin) matrix, random Bernoulli (RBen) matrix, random Gaussian (RG) matrix, and random sparse fixed binary (RSB) matrix. These are paired with a sparsifying matrix (ψ), a hybrid of identity matrix (I), discrete sine transform matrix (S), and discrete cosine transform matrix (C) (i.e. ψ = [I S C]). The following five sparse reconstruction algorithms are evaluated: iterative hard thresholding (IHT) algorithm, orthogonal matching pursuit (OMP) algorithm, smoothed ℓ0 (SL0) algorithm, ℓ1 least square (L1LS) algorithm, and subspace matching pursuit (SMP) algorithm. The proposed DCS-ECG system was tested on ECG signals from the MIT-BIH arrhythmia database. The configuration using the DBBD sensing matrix and OMP recovery algorithm with the sparsifying matrix achieved a low average percentage of root mean square difference (PRD) of 3.75 ± 1.43% at CR = 12.5%, which also offers fast reconstruction. For CR = 12.5% and BM = 8, the CS measurement generation on the Arduino Due consumes 2.02 mJ, while reconstruction on the Raspberry Pi requires 1.13 J. The wireless transmission energy is 1.2973 J. Overall, the proposed CS-based system achieves an 86.24% total energy saving compared to the without CS approach, demonstrating its suitability for low-power IoT-enabled wearable edge ECG health monitoring applications.

The covariance-assisted matching pursuit (CAMP) algorithm has recently been proposed for recovering sparse signals f from noisy linear measurements based on a priori knowledge of the covariance and mean of the nonzero coefficients of f. It utilizes the a priori knowledge by incorporating the Gauss-Markov theorem into the orthogonal matching pursuit (OMP) algorithm and has a significantly better reconstruction performance than OMP. This letter develops sufficient conditions of exact support recovery of any k-sparse signals f via CAMP ink iterations, under the 12-bounded and Gaussian noises. These sufficient conditions are based on the restricted isometry constant of the sensing matrix and minimum magnitude of the nonzero elements of f, and are much better than the existing ones.

In most scenes of through-the-wall imaging (TWI), the observation zone is spares. So the radar signals could be processed using Compressive Sensing (CS) technique. Existing greedy algorithms for CS, such as orthogonal Matching Pursuit (OMP) algorithm and Compressive Sampling Matching pursuit (CoSaMP), suffer from artifacts and low resolution respectively. To cover the shortage of existing algorithms, a modified Compressive Sampling Matching Pursuit algorithm is proposed. By using the orthogonality among selected basis-signals and backtracking strategy for basis-signals reevaluation, the proposed algorithm could reconstruct radar signal. Then the image of observation zone could be got using Delay and Sum (DAS) beamforming method. Measurement results demonstrate the effectiveness of the proposed algorithm.

In this brief we present a new approach to fine relative position control in satellite formation flying. We focus on a situation involving two spacecraft, one of which (the “chaser”) is actively controlling its position with respect to the other (the “target”). The goal of the approach is to use the minimum number of thruster firings in order to keep the chaser following its reference position within a certain tolerance. We first present a method based on the matching pursuit (MP) algorithm, which proves to provide a solution to this problem in the open-loop case. Moreover, we show that a closed-loop version of the controller can be obtained as well by turning the method into a model predictive control (MPC) strategy, thanks to the fact that the computational cost of the method is small. An example of application is shown at the end for a mission scenario inspired by the PROBA3 mission, which is currently under development.