A Subspace Projection-Based Joint Sparse Recovery Method for Structured Biomedical Signals

Sparse signals can be reconstructed from a reduced set of signal samples using compressive sensing (CS) methods. The discrete cosine transform (DCT) can provide highly concentrated representations of audio signals. This property implies the DCT as a good sparsity domain for the audio signals. In this paper, the DCT is studied within the context of sparse audio signal processing using the CS theory and methods. The DCT coefficients of a sparse signal, calculated with a reduced set of available samples, can be modeled as random variables. It has been shown that the statistical properties of these variables are closely related to the unique reconstruction conditions. The main result of this paper is in an exact formula for the mean-square reconstruction error in the case of approximately sparse and nonsparse noisy signals reconstructed under the sparsity assumption. Based on the presented analysis, a simple and computationally efficient reconstruction algorithm is proposed. The presented theoretical concepts and the efficiency of the reconstruction algorithm are verified numerically, including examples with synthetic and recorded audio signals with unavailable or corrupted samples. Random disturbances and disturbances simulating clicks or inpainting in audio signals are considered. Statistical verification is done on a dataset with experimental signals. Results are compared with some classical and recent methods used in similar signal and disturbance scenarios.

The impulsive noise and the time-varying channel are two major detrimental factors which greatly constrain the performance of underwater acoustic communications (UACs). Utilizing the joint sparsity of the impulsive noise and the channel impulse response, the paper proposes the generalized approximate message passing (GAMP)-based sparse Bayesian learning (SBL) frameworks for joint impulsive noise mitigation and channel estimation and tracking for orthogonal frequency division multiplexing (OFDM) UACs. Firstly, the SBL framework for the joint estimation is employed. To reduce the computational complexity, the GAMP is introduced into the expectation-maximization (EM) algorithm, and a low-complexity GAMP based SBL framework is formulated without performance degradation. To further estimate and track the impulsive noise and channel state information in the slow time-varying scenarios, we propose a novel GAMP-based temporal SBL framework. The factor graph and GAMP are used to achieve the approximated estimation for the posterior statistics of both the channel state information and the impulsive noise. The algorithm formulates the message passing scheduling for the EM algorithm to solve the joint multiple sparse signal recovery problem. Simulations and sea-trial results demonstrate that the proposed algorithms significantly improve the performance in terms of the mean square error of channel estimation, impulsive noise estimation, bit error rate and computational complexity compared with their corresponding SBL-based counterparts.

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

This chapter briefly overviews the digital signal processing with an outline of introduction and importance of biomedical signal processing. Biomedical signal processing plays an important role in analysis of human body. For this, bioelectric potential needs to be recorded digitally and processed through digital processing system. In general, all the real-world signals are analog in nature. Initially, these analog signals are converted into digital signals, and then digital filters and other signal processing techniques are applied over them. Same is also followed in case of biomedical signals. A brief overview of this conversion process is also given in this chapter. Mainly, this chapter explores about generation process, recording, signal processing and common problems of electrocardiogram (ECG), electroencephalogram (EEG), electromyogram (EMG), and electrooculogram (EOG) signals. Real signals are also visualized that are taken from known datasets. This chapter provides a good base for any beginner in the field of biomedical signal processing.

A parallel VLSI architecture of Kalman-filter-based algorithms for signal reconstruction

The problem of improving the performance of the implementation in VLSI technology of Kalman-based algorithms for signal reconstruction in real time is discussed. A systolic approach is proposed to develop architecture expressly for this specific application. Implemented algorithms are based on the steady-state version of the Kalman filter, which performs for a broad field of specific applications, but the use of a co-processor for the Kalman gain is allowed. We show that the autoregressive model of Kalman filtering is particularly adapted to parallel processing and is well suited for implementation. Although intended to improve signal reconstruction, other applications where a similar autoregressive model of Kalman filtering is required are allowed. The performance of the systolic architecture is validated by comparison with Motorola's general-purpose DSP56002 digital signal for real-world spectrometric signal reconstruction.

Received signal strength (RSS) measurement based source localization is highly dependent on the propagation model. However, such propagation model is not easy to be captured in the practical applications. In this paper, we address the multiple sources localization (MSL) problem while jointly estimating parametric propagation model. Specifically, we model the localization problem as being parameterized by the unknown source locations and propagation parameters. Then, the localization problem is reformulated as a joint parametric sparsifying dictionary learning (PSDL) and sparse signal recovery (SSR) problem. Finally, the problem is solved under the framework of sparse Bayesian learning with parametric dictionary approximation. We compare the proposed method with the state-of-the-art MSL algorithms as well as Cramer-Rao lower bound (CRLB). Numerical simulations highlight the effectiveness of the proposed method.

Received signal strength (RSS) based source localization method is popular due to its simplicity and low cost. However, this method is highly dependent on the propagation model which is not easy to be captured in practice. Moreover, most existing works only consider the single source and the identical measurement noise scenario, while in practice multiple co-channel sources may transmit simultaneously, and the measurement noise tends to be nonuniform. In this paper, we study the multiple co-channel sources localization (MSL) problem under unknown nonuniform noise, while jointly estimating the parametric propagation model. Specifically, we model the MSL problem as being parameterized by the unknown source locations and propagation parameters, and then reformulate it as a joint parametric sparsifying dictionary learning (PSDL) and sparse signal recovery (SSR) problem which is solved under the framework of sparse Bayesian learning with iterative parametric dictionary approximation. Furthermore, multiple snapshot measurements are utilized to improve the localization accuracy, and the Cramer-Rao lower bound (CRLB) is derived to analyze the theoretical estimation error bound. Comparing with the state-of-the-art sparsity-based MSL algorithms as well as CRLB, extensive simulations show the importance of jointly inferring the propagation parameters,and highlight the effectiveness and superiority of the proposed method.

In wireless communication systems, spoofing attack significantly impact the information security, for this attack is not hard to launch with little effort. Although traditional cryptographic authentication can be utilized for node identification, it is not desirable in some low power requirements application scenarios such as Wireless Sensor Networks (WSNs). In this paper, we formulate this problem as one of sparse signal processing. In order to identify the existence of the spoofing attacker, we explore using the feature extraction and fusion to establish an automatic representative selection algorithm. By examining the correlation between the two selected targets, we can determine the attacking situation. We evaluate our scheme through an experimental system, and the experimental results on real measured data show that our sparse signal processing can reach desired identification performance.

Wireless channels especially for OFDM transmissions can be precisely approximated by a time varying filter with sparse taps (in the time domain). Sparsity of the channel is a criterion which can highly improve the channel estimation task in mobile applications. In sparse signal processing, many efficient algorithms have been developed for finding the sparsest solution to linear equations (basis pursuit, matching pursuit) in the presence of noise. In current OFDM standards, a number of the ending subcarriers at both positive and negative frequencies are left unoccupied (for ease of analog filtering at the receiver) which results in an ill-conditioned frequency to time transformation matrix. This means that the initial estimate for the impulse response of the channel (in time) easily varies as the noise vector changes. Thus in this case we cannot use most of the proposed algorithms in sparse signal processing. In this paper, we propose iteration with adaptive thresholding and MMSE methods to overcome this difficulty. Simulation results indicate that the proposed method is almost perfect for stationary channels and only minor performance degradation is observed with increase of Doppler frequency.

In this work we derive fundamental limits for many linear and non-linear sparse signal processing models including group testing, quantized compressive sensing, multivariate regression and observations with missing features. In general, sparse signal processing problems can be characterized in terms of the following Markovian property. We are given a set of N variables X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , ..., X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> , and there is an unknown subset of variables S ⊂ {1, 2, ..., N} that are relevant for predicting outcomes/outputs Y. In other words, when Y is conditioned on {X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> } <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nϵS</sub> it is conditionally independent of the other variables, {X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> } <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n∉S</sub> . Our goal is to identify the set S from samples of the variables X and the associated outcomes Y. We characterize this problem as a version of the noisy channel coding problem. Using asymptotic information theoretic analyses, we establish mutual information formulas that provide sufficient and necessary conditions on the number of samples required to successfully recover the salient variables. These mutual information expressions unify conditions for both linear and non-linear observations. We then compute sample complexity bounds for the aforementioned models, based on the mutual information expressions.

BioSig is an open source software library for biomedical signal processing. The aim of the BioSig project is to foster research in biomedical signal processing by providing free and open source software tools for many different application areas. Some of the areas where BioSig can be employed are neuroinformatics, brain-computer interfaces, neurophysiology, psychology, cardiovascular systems, and sleep research. Moreover, the analysis of biosignals such as the electroencephalogram (EEG), electrocorticogram (ECoG), electrocardiogram (ECG), electrooculogram (EOG), electromyogram (EMG), or respiration signals is a very relevant element of the BioSig project. Specifically, BioSig provides solutions for data acquisition, artifact processing, quality control, feature extraction, classification, modeling, and data visualization, to name a few. In this paper, we highlight several methods to help students and researchers to work more efficiently with biomedical signals.

In the past decades, there has been an extensive research interest in the areas of both waveform diversity/design and advanced signal processing algorithms departing from the more classical solutions based on Linear Frequency Modulated (LFM) pulses and Matched Filters (MF). In the waveform diversity community, especially within the context of spectrum sharing, MIMO and cognitive radars, several waveform optimization and design methodologies have been studied, see [1], [2] and references therein. In parallel to waveform design, several signal processing techniques have also been proposed which exploit some kind of prior knowledge and/or iterative algorithms to improve the performance of the more classical MF, such as the Adaptive Pulse Compression(APC) [3], MUSIC [4], CLEAN [5] and Sparse Signal Processing (SSP) [6], [7]. In this paper we present some results and examples to show how the combination of waveform design with SSP can lead to improved performance in radar compared to the more classical approach.

Purpose: To investigate the impact of phase‐and amplitude‐based reconstruction algorithms in 4D treatment margin strategies in presence of respiratory irregularities. Methods: 4D CT images of Dynamic Thorax Phantom were acquired and the respiratory signal was tracked by the belt. Three irregular breathing patterns were simulated: amplitude, frequency, and combined amplitude and frequency variations. 4D CT image artifacts were analyzed for the phase‐and amplitude based reconstruction algorithms. To assess the impact of the 4D CT image artifacts on the dose distribution, twelve plans (three simulated breathing models for the two reconstruction algorithms and for the two margins strategies) were calculated with a Monte Carlo based TPS. The lung tumor was delineated according to the mid ventilation and the ITV‐based strategy. All the plans were evaluated for Dmin, Dmax, Dmean, homogeneity index and conformity index. Results: The amplitude‐based reconstruction shows a significant reduction of artifacts compared to the phase‐based only for breathing amplitude variations. Most of the observed artifacts are image blurring and incomplete structures. The dosimetric analysis shows that the mid‐ventilation strategy provides better tumor coverage than the ITV‐based strategy. In the mid‐ventilation strategy the selected phase is close to the exhale phase which is less subject to motion artifacts. In the ITV‐based strategy the influence of motion artifacts is more pronounced due to the contribution of different phases and leads to a blurred dose distribution. Conclusion: Amplitude‐based reconstruction algorithm reduces image distortions in the particular case of amplitude variations but not when frequency variations are present. Based on the impact of image artifacts on the definition of margin strategies we showed that the mid‐ventilation strategy is more robust than the ITV‐based strategy. The ITV‐based strategy is more prone to image artifacts which cause significant degradation in the dose distribution compare to the mid ventilation.

In this paper, we propose a new test response acquisition technique for high-speed devices-based on dual-frequency incoherent sub-sampling and sparse signal reconstruction. The proposed technique enables reconstruction of spectrally sparse wideband signals such as multi-tone signals and short pseudo-random bit sequences (PRBS) with enhanced time/frequency resolution as opposed to current methods. The sampling hardware utilizes dual analog-to-digital converters (ADCs) and dedicated sampling frequency synthesizers with a common frequency reference. As compared to other compressive sampling architectures [1], the proposed hardware architecture is easy to implement at low cost since it does not require accurate sampling clock phase adjustment or random timing generation. For digital signal reconstruction, the proposed technique requires less number of waveform samples than conventional equivalent-time sampling techniques. In addition, the use of an resolution-enhanced discrete Fourier transform (DFT) frame and basis pursuit algorithms minimizes spectral leakage of incoherently sub-sampled signals. This co-design of sampling hardware and signal reconstruction algorithms enables testing of spectrally sparse wideband signals with enhanced time/frequency resolution.