Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing With Prior Information

Compressed sensing (CS) is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper, we apply the iterative hard thresholding (IHT) algorithm for compressed sensing on the speech signal. The interested speech signal is transformed to the frequency domain using Discrete Fourier Transform (DCT) and then compressed sensing is applied to that signal. The compressed signal can be reconstructed using the recently introduced Iterative Hard Thresholding (IHT) algorithm and also by the tradditional \( \ell_{1} \) minimization (basic pursuit) for comparison. It is shown that the compressed sensing can provide better root mean square error (RMSE) than the tradition DCT compression method, given the same compression ratio.

This paper develops a low-complexity channel estimation (CE) scheme based on compressive sensing (CS) for time-domain synchronous (TDS) orthogonal frequency-division multiplexing (OFDM) to overcome the performance loss under doubly selective fading channels. Specifically, an overlap-add method of the time-domain training sequence is first proposed to obtain the coarse estimates of the channel length, path delays and path gains of the wireless channel, by exploiting the channel's temporal correlation to improve the robustness of the coarse CE under the severe fading channel with long delay spread. We then propose the priori-information aided (PA) iterative hard threshold (IHT) algorithm, which utilizes the priori information of the acquired coarse estimate for the wireless channel and therefore is capable of obtaining an accurate channel estimate of the doubly selective fading channel. Compared with the classical IHT algorithm whose convergence requires the $l_2$ norm of the measurement matrix being less than 1, the proposed PA-IHT algorithm exploits the priori information acquired to remove such a limitation as well as to reduce the number of required iterations. Compared with the existing CS based CE method for TDS-OFDM, the proposed PA-IHT algorithm significantly reduces the computational complexity of CE as well as enhances the CE accuracy. Simulation results demonstrate that, without sacrificing spectral efficiency and changing the current TDS-OFDM signal structure, the proposed scheme performs better than the existing CE schemes for TDS-OFDM in various scenarios, especially under severely doubly selective fading channels.

The recently proposed compressed sensing theory equips us with methods to recover exactly or approximately, high resolution images from very few encoded measurements of the scene. The traditional ill-posed problem of MRI image recovery from heavily under-sampled κ-space data can be thus solved using CS theory. Differing from the soft thresholding methods that have been used earlier in the case of CS MRI, we suggest a simple iterative hard thresholding algorithm which efficiently recovers diagnostic quality MRI images from highly incomplete κ-space measurements. The new multi-scale redundant systems, curvelets and contourlets having high directionality and anisotropy, and thus best suited for curved-edge representation are used in this iterative hard thresholding framework for CS MRI reconstruction and their performance is compared. The κ-space under-sampling schemes such as the variable density sampling and the more conventional radial sampling are experimented at the same sampling rate and the effect of encoding scheme on iterative hard thresholding compressed sensing reconstruction is studied.

Iterative hard thresholding algorithm (IHT) is a novel and efficient method to solve signal and image reconstruction in compressed sensing, but it is sensitive to the initial point and converges to a local optimal solution. Therefore, to overcome its shortcoming, in this paper a hybrid hard thresholding algorithm (HHT) is derived by introducing the simulated annealing algorithm (SA) into the IHT. And a series of experiments are provided on signal and image reconstruction to assess performance of the algorithm. The experiments and applications show that the proposed algorithm uses less sampling to construct the signal and image and is more stable, as compared with IHT.

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.

Compressive radar imaging has attracted considerable attention because it substantially reduces imaging time through directly compressive sampling. However, a problem that must be addressed for compressive radar imaging systems is the high computational complexity of reconstruction of sparse signals. In this paper, a novel algorithm, called two-dimensional (2D) normalized iterative hard thresholding (NIHT) or 2D-NIHT algorithm, is proposed to directly reconstruct radar images in the matrix domain. The reconstruction performance of 2D-NIHT algorithm was validated by an experiment on recovering a synthetic 2D sparse signal, and the superiority of the 2D-NIHT algorithm to the NIHT algorithm was demonstrated by a comprehensive comparison of its reconstruction performance. Moreover, to be used in compressive radar imaging systems, a 2D sampling model was also proposed to compress the range and azimuth data simultaneously. The practical application of the 2D-NIHT algorithm in radar systems was validated by recovering two radar scenes with noise at different signal-to-noise ratios, and the results showed that the 2D-NIHT algorithm could reconstruct radar scenes with a high probability of exact recovery in the matrix domain. In addition, the reconstruction performance of the 2D-NIHT algorithm was compared with four existing efficient reconstruction algorithms using the two radar scenes, and the results illustrated that, compared to the other algorithms, the 2D-NIHT algorithm could dramatically reduce the computational complexity in signal reconstruction and successfully reconstruct 2D sparse images with a high probability of exact recovery.

In this letter, a novel robust two-dimensional nearfield millimeter-wave (MMW) image reconstruction algorithm is developed based on compressed sensing (CS) in the presence of impulsive measurement noise. To enable the sparse MMW image recovery, the CS algorithm usually employs the popular l 2 -norm as the data fidelity term and a combination of multiple sparsityinduced functions as the penalty term. The l 2 -norm is non-robust against impulsive noise since the Gaussian noise distribution assumption is not valid, and the presence of impulsive noise will severely degrade the robustness of the compressive MMW image recovery. To gain more robustness performance, a complex correntropy based data-fitting term, namely complex correntropic loss (CC-loss), is used to replace the l2-norm for the near-field MMW measurement contaminated by impulsive noise. In order to solve the corresponding minimization problem, an additive half quadratic method is used to transform the CC-loss term to its convex form, and then a parallel primal-dual process is used to guarantee the convergence of the proposed algorithm. In total, 150-GHz MMW experimental results show that the proposed algorithm can achieve accurate image reconstruction from compressive measurements under different impulsive noise levels.

In this letter, the authors propose block normalised iterative hard thresholding (BNIHT) algorithm for the recovery of block sparse signal, in which the non-zero elements are presented in clusters. Based on block restricted isometry property, the sufficient conditions to guarantee the convergence of BNIHT are derived. In addition, the number of required iterations is obtained. The simulation experiment shows that BNIHT algorithm is superior to the block IHT (BIHT) algorithm when the step size satisfies μ < 1 .

The direct sequence-code division multiple accesses (DS-CDMA) signals are transmitted over multipath channels that introduce fading and shadowing. Combined effect of multipath fading and shadowing along with multiple access interference (MAI) and inter-symbol interference (ISI) worsens the system performance. Further, experimental results have confirmed the presence of impulsive noise in wireless mobile communication channels. Hence, this paper presents a comprehensive learning particle swarm optimization (CLPSO) based multiuser detection technique for DS-CDMA systems over generalized-K (GK) fading channels in presence of impulsive noise. Maximal ratio combining (MRC) receive diversity is also incorporated to mitigate the effects of fading and shadowing. Performance of proposed M-decorrelator is studied by evaluating average error rate. Simulation results show that the proposed M-decorrelator performs better in the presence of fading, shadowing and heavy-tailed impulsive noise when compared to least squares, Huber and Hampel M-estimator based detectors.

As an essential task for enabling dynamic spectrum sharing, spectrum sensing in wideband cognitive radio (CR) networks becomes quite challenging due to high sampling pressure, huge data transmission overheads and serious channel fading. To overcome these challenges, this paper proposes a collaborative spectrum sensing scheme based on 1-bit compressed sensing (CS). Each SU performs local 1-bit CS and obtains its own estimated support set via signal reconstruction. To make use of joint sparsity, all the support sets are fused in the fusion center (FC) and the fused result is used as priori information to guide the next local signal reconstruction. The weighted binary iterative hard thresholding (BIHT) algorithm with support estimate vector is proposed to implement the second reconstruction. Simulation results show that our proposed scheme can achieve effective spectrum detection at low communication and computation load.

In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. This requires careful characterization of robust complex-valued loss functions as well as Huber's criterion function for the multivariate sparse regression problem. We devise a greedy algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Unlike the conventional SNIHT method, our algorithm, referred to as HUB-SNIHT, is robust under heavy-tailed non-Gaussian noise conditions, yet has a negligible performance loss compared to SNIHT under Gaussian noise. Usefulness of the method is illustrated in source localization application with sensor arrays.

The paper proposes a novel signal reconstruction algorithm through substituting the gradient descent method in the iterative hard thresholding algorithm with a faster sparse randomized Kaczmarz method. By designing a series of gradually attenuated weights for the matrix rows whose indexes lie outside of the support set of the original sparse signal, we can focus the iterations on the effective support rows of the measurement matrix. The experiment results show that the proposed algorithm presents a faster convergence rate and more accurate reconstruction accuracy than the state-of-the-art algorithms. Meanwhile, the successful reconstruction probability of the proposed algorithm is higher than that of other algorithms. Moreover, the characteristics of the proposed signal reconstruction algorithm are also analyzed in detail through numerical experiments.

Iterative hard thresholding for compressed sensing

Generalized [formula omitted]-sparse algorithms for constructing fault tolerant RBF networks

Impulsive noise is always present in real-world image Compressive Sensing (CS) acquisition systems, where existing CS reconstruction performance may seriously deteriorate. In this article, we propose a robust CS formulation for image reconstruction to suppress outliers in the presence of impulsive noise. To address this issue, we consider a novel truncated-Cauchy loss function as the metric of residual error to elevate the reconstruction robustness. Specifically, we design a complementary priors model to incorporate nonconvex nonlocal low-rank prior and deep denoiser prior for high-accuracy image reconstruction. By means of the half-quadratic optimization theory and generalized soft-thresholding technique, we also develop an alternative optimization algorithm for solving the induced nonconvex optimization problem. Numerical simulations demonstrate the robustness and accuracy of the proposed robust CS method compared to some recent CS methods for image reconstruction in impulsive noise.