Liyan Qiao

A Simplified FRI Sampling System for Pulse Streams Based on Constraint Random Modulation

The recent finite rate of innovation (FRI) framework provides effective sub-Nyquist sampling of pulse streams, allowing recovery of such signals from a set of Fourier coefficients. In this brief, a multi-channel FRI sampling system is presented to sample distinct bands of Fourier coefficients. This is achieved through modulating the desired spectrum band to baseband and then filtering with a low-pass filter. However, the modulation process will lead to the spectrum aliasing and unavailability. A modulation frequency selection strategy is proposed to solve this problem, which allows obtaining reconfigurable Fourier coefficients from the aliasing spectrum. Combining with multi-channel structure, we present a simple and efficient way to sample distinct bands of the pulse streams’ spectrum. Finally, a design and implementation of the hardware prototype is presented. Simulation and hardware experiment results demonstrate the effectiveness and robustness of our system.

DE-RCO: Rotating Crossover Operator With Multiangle Searching Strategy for Adaptive Differential Evolution

Differential evolution (DE) is confirmed as a simple yet efficacious methodology to solve practical optimization problems. In this paper, we develop a new rotating crossover operator (RCO), to improve the optimization performance by utilizing multiangle searching strategy-based RCO. The proposed crossover scheme, different from conventional crossover operators, can generate trial vectors in control of the self-adaptive crossover parameter and rotation control vectors, which obey Lévy distribution. More specifically, trial vectors are generated diversely within circle regions around donor vectors and target vectors, by multiplying the rotation control vectors and difference of donor and target vectors. Rotation angles and radii are adjusted along with angles and moduli of the rotation control vectors. The proposed RCO operator can be easily applied to crossover strategies of other DE variants with minor changes. In order to verify the efficiency and generality of the algorithm, the proposed RCO scheme is respectively applied to the conventional DE variants and a state-of-the-art algorithm JADE, denoted as JADE-RCO. Further comparison experiments of JADE-RCO and other five efficient DE variants are conducted to confirm the superiority of the improved algorithm JADE-RCO. Series of experiments on a set of test functions in CEC 2013 demonstrate that the DE-RCO shows excellent performance in convergence rate and optimization ability comparing with classic and advanced evolutionary algorithms and it improves the performance of the original algorithms by 57%–96%.

Sparsity-based reconstruction method for signals with finite rate of innovation

In the last decade, it was shown that it is possible to reconstruct signals with finite rate of innovation (FRI signals) from the samples of their filtered versions. However, when noise is present, the present reconstruction algorithms tend to be low accuracy. In this work, a new sparsity-based reconstruction method for FRI signals is put forward. The streams of Diracs and exponential reproducing kernel are considered. Firstly, the analog time axis is quantified and aligned to grids. Secondly, selecting a finite subset of time delay parameters, the measurement vector is represented as a sparse linear combination of the amplitude parameters. Finally, the sparse solution is calculated by solving an optimization problem under L0 norm. The position of non-zero elements is approximation to the time delays, and the value of non-zero elements is the amplitude. Extensive numerical simulations demonstrate the accuracy and robustness of our method.

Image reconstruction method of electromagnetic tomography based on finite rate of innovation

In order to improve the image reconstruction quality of electromagnetic tomography (EMT), a new EMT image reconstruction method based on finite rate of innovation (FRI) is put forward in this paper. The FRI sampling process is used to extract the feature information and combined a new measurement equation. Firstly, the conductivity distribution of the target object inside pipeline is modeled as an one-dimensional FRI signal, and then be sampled with polynomial reproducing kernel in FRI sampling framework. Then, more measurements are obtained from these samples, which generate a new mathematical model for EMT image reconstruction problem. Finally, the original image signal is recovered by solving a L0 norm optimization problem with matching pursuit (OMP) algorithm. Experiment result shows that the image error and correlation coefficient of reconstructed images by the proposed method are much better than corresponding indicators obtained by Linear back-projection (LBP), Landweber and Total variation (TV) regularization algorithm. So it is a kind of EMT image reconstruction method with high efficiency and accuracy, which also provides a new method and means for EMT research.

Fast pursuit method for greedy algorithms in Distributed Compressive Sensing

This paper proposes a fast pursuit method for greedy algorithms when reconstructing multi-signals under Distributed Compressive Sensing (DCS) framework. DCS takes advantage of both intra- and inter-signal correlation structures to reduce the measurements required for signals recovery. Greedy algorithms, much faster than l0 and l1 minimization algorithms, are widely used in DCS. General approaches transform DCS model to Compressive Sensing (CS) model and then directly use greedy algorithms to reconstruct signals, but the recovery speed becomes very slow as the signal number n increasing. In this paper, we propose a fast pursuit method which exploits the structural features of joint measurement matrix to reduce the computational complexity form O(n2) to O(n) when calculating inner-product in greedy algorithms, which improves the recovery speed significantly without reducing recovery accuracy.

Compressive Blind Mixing Matrix Estimation of Audio Signals

Compressive sensing (CS) shows that, when a signal is sparse or compressible with respect to some basis, a small number of compressive measurements of the original signal can be sufficient for exact (or approximate) recovery. Distributed CS (DCS) takes advantage of both intra- and intersignal correlation structures to reduce the number of measurements required for multisignal recovery. In most cases of audio signal processing, only mixtures of the original sources are available for observation under the DCS framework, without prior information on both the source signals and the mixing process. To recover the original sources, estimating the mixing process is a key step. The underlying method for mixing matrix estimation reconstructs the mixtures by a DCS approach first and then estimates the mixing matrix from the recovered mixtures. The reconstruction step takes considerable time and also introduces errors into the estimation step. The novelty of this paper lies in verifying the independence and non-Gaussian property for the compressive measurements of audio signals, based on which it proposes a novel method that estimates the mixing matrix directly from the compressive observations without reconstructing the mixtures. Numerical simulations show that the proposed method outperforms the underlying method with better estimation speed and accuracy in both noisy and noiseless cases.

Compressive blind mixing matrix recovery algorithm based on gradient ascent

Compressed Sensing (CS) shows that, when signal is sparse or compressible with respect to some basis, only a small number of compressive measurements of original signal can be sufficient for exact (or approximate) recovery. While in some cases, only the mixtures of original sources are available for observation without knowing the priori information of both the source signals and the mixing process. To recover the original sources, estimating the mixing process is a key step. In this paper, we estimate the mixing matrix in the compressive measurement domain based on gradient ascent. The innovation lies in that, we recover the mixing matrix directly from the observed compressive measurements of mixture signals, without recovering the mixture signals at first. Numerical experiments show that the mixing matrix can be well estimated via the proposed method.

Sub-Nyquist Sampling and Recovery of Pulse Streams With the Real Parts of Fourier Coefficients

We consider the problem of sampling pulse streams with known shapes. The recent finite rate of innovation (FRI) framework has shown that such signals can be sampled with perfect reconstruction at their rate of innovation, which is usually much lower than the Nyquist rate. Although FRI sampling of pulse streams was treated in various works, either the work was unstable for high rate of innovation, or the sampling stage was complex and redundant. In this paper, we propose an FRI sampling and recovery method for pulse streams, which is based on the real parts of the Fourier coefficients. The proposed method is simple and efficient, and leads to stable recovery even when the rate of innovation is very high. This is achieved through modulating the input signal in each channel with a properly chosen cosine signal, followed by filtering with a low-pass filter. Since the modulating process will lead to the signal spectrum aliasing, we propose a spectrum de-aliasing algorithm to solve this problem, resulting in the real parts of a band of Fourier coefficients from each two channels. Combining with the multi-channel sampling structure, we propose a more efficient way to obtain arbitrary frequency bands from the aliased spectrum, which improves the utility of the signal spectrum. By using a sparsity-based recovery algorithm, the time delays and amplitudes of the pulse streams can be recovered from the obtained real parts of the Fourier coefficients. Finally, simulation results have shown that the proposed scheme is flexible and exhibits better noise robustness than previous approaches.

Directly Estimating Endmembers for Compressive Hyperspectral Images

The large volume of hyperspectral images (HSI) generated creates huge challenges for transmission and storage, making data compression more and more important. Compressive Sensing (CS) is an effective data compression technology that shows that when a signal is sparse in some basis, only a small number of measurements are needed for exact signal recovery. Distributed CS (DCS) takes advantage of both intra- and inter- signal correlations to reduce the number of measurements needed for multichannel-signal recovery. HSI can be observed by the DCS framework to reduce the volume of data significantly. The traditional method for estimating endmembers (spectral information) first recovers the images from the compressive HSI and then estimates endmembers via the recovered images. The recovery step takes considerable time and introduces errors into the estimation step. In this paper, we propose a novel method, by designing a type of coherent measurement matrix, to estimate endmembers directly from the compressively observed HSI data via convex geometry (CG) approaches without recovering the images. Numerical simulations show that the proposed method outperforms the traditional method with better estimation speed and better (or comparable) accuracy in both noisy and noiseless cases.

Blind separation of sufficiently sparse sources in multichannel compressed sensing

Conventional approaches for blind source separation (BSS) are almost based on the Nyquist sampling theory. Recently, compressed sensing (CS) theory is applied to BSS for the fact that the information of a signal can be preserved in a relatively small number of linear projections. The traditional method for compressive BSS mainly involves two steps: recovering mixed signals from compressed observations and separating source signals from the recovered mixed signals. This paper presents a novel framework for separating and reconstructing the sufficiently sparse sources from compressively sensed linear mixtures simultaneously. Compared with the traditional compressive BSS, the proposed approach can reduce the requirements of sampling speed and operating rate of the devices. Moreover, our approach has better reconstruction results. Simulation results demonstrate the proposed algorithm can separate multichannel sufficiently sparse sources successfully.