In this paper, we introduce a framework of distributed orthogonal approximate message passing for recovering sparse vector based on sensing by multiple nodes. The iterative recovery process consists of local computation at each node, and global computation performed either by a particular node or joint computation on the overall network by exchanging messages. We then propose a method to reduce the communication cost between the nodes while maintaining the recovery performance.

Compressed sensing is a rapidly growing research field in signal and image processing, machine learning, statistics, and systems control. In this survey paper, we provide a review of the theoretical foundations of compressed sensing and present state-of-the-art algorithms for solving the corresponding optimization problems. Additionally, we discuss several practical applications of compressed sensing, such as group testing, sparse system identification, and sparse feedback gain design, and demonstrate their effectiveness through Python programs. This survey paper aims to contribute to the advancement of compressed sensing research and its practical applications in various scientific disciplines.

A super-resolution algorithm is proposed to solve the problem of measuring the thin thickness of oil slick using compressed sensing theory. First, a mathematical model of a single pulse underwater ultrasonic echo is established. Then, the estimation model of the transmit time of flight (TOF) of ultrasonic echo within oil slick is given based on the sparsity of echo signals. At last, the super-resolution TOF value can be obtained by solving the sparse convex optimization problem. Simulations and experiments are conducted to validate the performance of the proposed method.

In the massive machine-type communication scenario, aiming at the problems of active user detection and channel estimation in the grant-free non-orthogonal multiple access (NOMA) system, new sets of non-orthogonal spreading sequences are proposed by using the zero/low correlation zone sequence set with low correlation among multiple sets. The simulation results show that the resulting sequence set has low coherence, which presents reliable performance for channel estimation and active user detection based on compressed sensing. Compared with the traditional Zadoff-Chu (ZC) sequences, the new non-orthogonal spreading sequences have more flexible lengths, and lower peak-to-average power ratio (PAPR) and smaller alphabet size. Consequently, these sequences will effectively solve the problem of high PAPR of time domain signals and are more suitable for low-cost devices in massive machine-type communication.

It has been widely recognized that in compressed sensing, many restricted isometry property (RIP) conditions can be easily obtained by using the null space property (NSP) with its null space constant (NSC) 0<θ≤1 to construct a contradicted method for sparse signal recovery. However, the traditional NSP with θ=1 will lead to conservative RIP conditions. In this paper, we extend the NSP with 0<θ<1 to a scale NSP, which uses a factor τ to scale down all vectors belonged to the Null space of a sensing matrix. Following the popular proof procedure and using the scale NSP, we establish more relaxed RIP conditions with the scale factor τ, which guarantee the bounded approximation recovery of all sparse signals in the bounded noisy through the constrained l1 minimization. An application verifies the advantages of the scale factor in the number of measurements.

We propose a sampling method that incorporates a normally distributed sampling series for EEG measurements using compressed sensing. We confirmed that the ADC sampling count and amount of wirelessly transmitted data can be reduced by 11% while maintaining a reconstruction accuracy similar to that of the conventional method.

The application of compressed sensing (CS) theory to non-orthogonal multiple access (NOMA) systems has been investigated recently. As described in this paper, we propose a quality-of-service (QoS)-aware, low-complexity, CS-based user selection and power allocation scheme with adaptive resource block selection for downlink NOMA systems, where the tolerable interference threshold is designed mathematically to achieve a given QoS requirement by being relaxed to a constrained l1 norm optimization problem. The proposed scheme adopts two adaptive resource block (RB) selection algorithms that assign proper RB to user pairs, i.e. max-min channel assignment and two-step opportunistic channel assignment. Simulation results show that the proposed scheme is more effective at improving the user rate than other reference schemes while reducing the required complexity. The QoS requirement is approximately satisfied as long as the required QoS value is feasible.

Reducing the power consumption of capsule endoscopy is essential for its further development. We introduce K-SVD dictionary learning to design a dictionary for sparse coding, and improve reconstruction accuracy of capsule endoscopic images captured using compressed sensing. At a compression ratio of 20%, the proposed method improves image quality by approximately 4.4 dB for the peak signal-to-noise ratio.

In the user identification (UI) scheme for a multiple-access fading channel based on a randomly generated (0, 1, -1)-signature code, previous studies used the signature code over a noisy multiple-access adder channel, and only the user state information (USI) was decoded by the signature decoder. However, by considering the communication model as a compressed sensing process, it is possible to estimate the channel coefficients while identifying users. In this study, to improve the efficiency of the decoding process, we propose an iterative deep neural network (DNN)-based decoder. Simulation results show that for the randomly generated (0, 1, -1)-signature code, the proposed DNN-based decoder requires less computing time than the classical signal recovery algorithm used in compressed sensing while achieving higher UI and channel estimation (CE) accuracies.

Expectation propagation (EP) is a powerful algorithm for signal recovery in compressed sensing. This letter proposes correction of a variance message before denoising to improve the performance of EP in the high signal-to-noise ratio (SNR) regime for finite-sized systems. The variance massage is replaced by an observation-dependent consistent estimator of the mean-square error in estimation before denoising. Massive multiple-input multiple-output (MIMO) is considered to verify the effectiveness of the proposed correction. Numerical simulations show that the proposed variance correction improves the high SNR performance of EP for massive MIMO with a few hundred transmit and receive antennas.

We propose a spectrum regeneration and demodulation method for multiple direct RF undersampled real signals by using a new algorithm. Many methods have been proposed to regenerate the RF spectrum by using undersampling because of its simple circuit architecture. However, it is difficult to regenerate the spectrum from a real signal that has a band wider than a half of the sampling frequency, because it is difficult to include complex conjugate relation of the folded spectrum into the linear algebraic equation in this case. We propose a new spectrum regeneration method from direct undersampled real signals that uses multiple clocks and an extended algorithm considering the complex conjugate relation. Simulations are used to verify the potential of this method. The validity of the proposed method is verified by using the simulation data and the measured data. We also apply this algorithm to the demodulation system.

Cognitive radio provides a feasible solution for alleviating the lack of spectrum resources by enabling secondary users to access the unused spectrum dynamically. Spectrum sensing and learning, as the fundamental function for dynamic spectrum sharing in 5G evolution and 6G wireless systems, have been research hotspots worldwide. This paper reviews classic narrowband and wideband spectrum sensing and learning algorithms. The sub-sampling framework and recovery algorithms based on compressed sensing theory and their hardware implementation are discussed under the trend of high channel bandwidth and large capacity to be deployed in 5G evolution and 6G communication systems. This paper also investigates and summarizes the recent progress in machine learning for spectrum sensing technology.

This letter reports on the effectiveness of applying the K-singular value decomposition (SVD) dictionary learning to the electroencephalogram (EEG) compressed sensing framework with outlier detection and independent component analysis. Using the K-SVD dictionary matrix with our design parameter optimization, for example, at compression ratio of four, we improved the normalized mean square error value by 31.4% compared with that of the discrete cosine transform dictionary for CHB-MIT Scalp EEG Database.

Sparse modeling is one of the most active research areas in engineering and science. The technique provides solutions from far fewer samples exploiting sparsity, that is, the majority of the data are zero. This paper reviews sparse modeling in radio techniques. The first half of this paper introduces direction-of-arrival (DOA) estimation from signals received by multiple antennas. The estimation is carried out using compressed sensing, an effective tool for the sparse modeling, which produces solutions to an underdetermined linear system with a sparse regularization term. The DOA estimation performance is compared among three compressed sensing algorithms. The second half reviews channel state information (CSI) acquisitions in multiple-input multiple-output (MIMO) systems. In time-varying environments, CSI estimated with pilot symbols may be outdated at the actual transmission time. We describe CSI prediction based on sparse DOA estimation, and show excellent precoding performance when using the CSI prediction. The other topic in the second half is sparse Bayesian learning (SBL)-based channel estimation. A base station (BS) has many antennas in a massive MIMO system. A major obstacle for using the massive MIMO system in frequency-division duplex mode is an overhead for downlink CSI acquisition because we need to send many pilot symbols from the BS and to get the feedback from user equipment. An SBL-based channel estimation method can mitigate this issue. In this paper, we describe the outline of the method, and show that the technique can reduce the downlink pilot symbols.

Sparse orthogonal matrices are proposed to improve the convergence property of expectation propagation (EP) for sparse signal recovery from compressed linear measurements subject to known dense and ill-conditioned multiplicative noise. As a typical problem, this letter addresses generalized spatial modulation (GSM) in over-loaded and spatially correlated multiple-input multiple-output (MIMO) systems. The proposed sparse orthogonal matrices are used in precoding and constructed efficiently via a generalization of the fast Walsh-Hadamard transform. Numerical simulations show that the proposed sparse orthogonal precoding improves the convergence property of EP in over-loaded GSM MIMO systems with known spatially correlated channel matrices.

This paper proposes a novel compressed sensing (CS) framework for reconstructing electroencephalogram (EEG) signals. A feature of this framework is the application of independent component analysis (ICA) to remove the interference from artifacts after undersampling in a data processing unit. Therefore, we can remove the ICA processing block from the sensing unit. In this framework, we used a random undersampling measurement matrix to suppress the Gaussian. The developed framework, in which the discrete cosine transform basis and orthogonal matching pursuit were used, was evaluated using raw EEG signals with a pseudo-model of an eye-blink artifact. The normalized mean square error (NMSE) and correlation coefficient (CC), obtained as the average of 2,000 results, were compared to quantitatively demonstrate the effectiveness of the proposed framework. The evaluation results of the NMSE and CC showed that the proposed framework could remove the interference from the artifacts under a high compression ratio.

This paper proposes a deterministic pilot pattern placement optimization scheme based on the quantum genetic algorithm (QGA) which aims to improve the performance of sparse channel estimation in orthogonal frequency division multiplexing (OFDM) systems. By minimizing the mutual incoherence property (MIP) of the sensing matrix, the pilot pattern placement optimization is modeled as the solution of a combinatorial optimization problem. QGA is used to solve the optimization problem and generate optimized pilot pattern that can effectively avoid local optima traps. The simulation results demonstrate that the proposed method can generate a sensing matrix with a smaller MIP than a random search or the genetic algorithm (GA), and the optimized pilot pattern performs well for sparse channel estimation in OFDM systems.

Analyzing aging-induced delay degradations of ring oscillators (ROs) is an effective way to detect recycled field-programmable gate arrays (FPGAs). However, it requires a large number of RO measurements for all FPGAs before shipping, which increases the measurement costs. We propose a cost-efficient recycled FPGA detection method using a statistical performance characterization technique called virtual probe (VP) based on compressed sensing. The VP technique enables the accurate prediction of the spatial process variation of RO frequencies on a die by using a very small number of sample RO measurements. Using the predicted frequency variation as a supervisor, the machine-learning model classifies target FPGAs as either recycled or fresh. Through experiments conducted using 50 commercial FPGAs, we demonstrate that the proposed method achieves 90% cost reduction for RO measurements while preserving the detection accuracy. Furthermore, a one-class support vector machine algorithm was used to classify target FPGAs with around 94% detection accuracy.

In the context of compressed sensing (CS), simultaneous orthogonal matching pursuit (SOMP) algorithm is an important iterative greedy algorithm for multiple measurement matrix vectors sharing the same non-zero locations. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the convergence of CS algorithms. Based on the RIP of measurement matrix, this paper shows that for the K-row sparse recovery, the restricted isometry constant (RIC) is improved to $delta_{K+1}<rac{sqrt{4K+1}-1}{2K}$ for SOMP algorithm. In addition, based on this RIC, this paper obtains sufficient conditions that ensure the convergence of SOMP algorithm in noisy case.

To efficiently collect sensor readings in cluster-based wireless sensor networks, we propose a structural compressed network coding (SCNC) scheme that jointly considers structural compressed sensing (SCS) and network coding (NC). The proposed scheme exploits the structural compressibility of sensor readings for data compression and reconstruction. Random linear network coding (RLNC) is used to re-project the measurements and thus enhance network reliability. Furthermore, we calculate the energy consumption of intra- and inter-cluster transmission and analyze the effect of the cluster size on the total transmission energy consumption. To that end, we introduce an iterative reweighed sparsity recovery algorithm to address the all-or-nothing effect of RLNC and decrease the recovery error. Experiments show that the SCNC scheme can decrease the number of measurements required for decoding and improve the network's robustness, particularly when the loss rate is high. Moreover, the proposed recovery algorithm has better reconstruction performance than several other state-of-the-art recovery algorithms.