Comparison of Image Reconstruction Algorithms using Compressive Sensing

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 orthogonal matching pursuit (OMP) algorithm is widely used because of its simple algorithmic structure, the linear magnitude of its computational complexity and other advantages. Algorithms of improved and extended OMP types are continually emerging. To make the OMP algorithm more suitable for the new transmission requirements of the fifth-generation (5G) network, the orthogonal matching pursuit with multiple users (OMP_mu) algorithm is proposed for cell-free massive multi-input multi-output (MIMO) networks with multiuser spatial index modulation. The OMP_mu algorithm considers the constraint condition for the sparsity of each user on the basis of each iterative search in the OMP algorithm until all users meet the constraint. The simulation results show that compared with the original OMP algorithm, the OMP_mu algorithm has a greatly improved demodulation performance. Compared with the orthogonal matching pursuit step-by-step (OMP_step) algorithm, which takes the user sparsity constraint condition into account in two steps, the OMP_mu algorithm greatly reduces the operation time and number of iterations while achieving a slightly better performance. The OMP_mu algorithm provides an effective reference for the application of spatial index modulation in cell-free massive MIMO networks.

In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm, without any loss of accuracy.

Compressed sensing is a new paradigm to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper, a new structured Wilkinson matrix is proposed as a measurement matrix to improve the performance of the block compressive sensing technique which is based on the orthogonal matching pursuit (OMP) algorithm. OMP is simpler to implement and potentially faster than linear programming algorithms but it suffers from two problems: the lack of reconstruction quality, and the need for a large number of measurements. The use of the new structured Wilkinson matrix has improved the OMP reconstruction quality, increased the compression ratio and reduced the computational time. In our experiments, the proposed method was applied to three different test images: Lenna, Barbara and heart MRI. Compared to conventional CS algorithms, the proposed method improves the reconstruction quality by approximately 10 dB with less computational time.

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

The recovery algorithm is a crucial issue of the compressed sensing (CS). This paper presents a greedy algorithm called optimized orthogonal matching pursuit (OOMP) for sparse signal recovery. The OOMP algorithm improves the orthogonal matching pursuit (OMP) algorithm via providing the projection onto the subspace generated by the selected measurements and minimizing the corresponding residual error at each iteration. Compared with the OMP algorithm, the simulation results show that the proposed algorithm provides a better approximation of a given signal and reduces measurements needed to recover the signal accurately.

In this paper, we present a novel architecture based on field-programmable gate arrays (FPGAs) for the reconstruction of compressively sensed signal using the orthogonal matching pursuit (OMP) algorithm. We have analyzed the computational complexities and data dependence between different stages of OMP algorithm to design its architecture that provides higher throughput with less area consumption. Since the solution of least square problem involves a large part of the overall computation time, we have suggested a parallel low-complexity architecture for the solution of the linear system. We have further modeled the proposed design using Simulink and carried out the implementation on FPGA using Xilinx system generator tool. We have presented here a methodology to optimize both area and execution time in Simulink environment. The execution time of the proposed design is reduced by maximizing parallelism by appropriate level of unfolding, while the FPGA resources are reduced by sharing the hardware for matrix-vector multiplication across the data-dependent sections of the algorithm. The hardware implementation on the Virtex6 FPGA provides significantly superior performance in terms of resource utilization measured in the number of occupied slices, and maximum usable frequency compared with the existing implementations. Compared with the existing similar design, the proposed structure involves 328 more DSP48s, but it involves 25,802 less slices and 1.85 times less computation time for signal reconstruction with N = 1024, K = 256, and m = 36, where N is the number of samples, K is the size of the measurement vector, and m is the sparsity. It also provides a higher peak signal-to-noise ratio value of 38.9 dB with a reconstruction time of 0.34 s, which is twice faster than the existing design. In addition, we have presented a performance metric to implement the OMP algorithm in resource constrained FPGA for the better quality of signal reconstruction.

FOMP algorithm for Direction of Arrival estimation

We investigate ultra-wideband (UWB) channel estimation based on compressive sampling (CS), where the orthogonal matching pursuit (OMP) algorithm is employed to recover the channel waveform from noisy measurements. In order to boost the robustness of OMP in the presence of additive Gaussian noise (AWGN), we propose a weighted OMP (WOMP) algorithm. For a given sparse dictionary, weighting factors are assigned to the atoms and a weighted matching process is performed by WOMP. Simulation results show that the proposed WOMP is more robust than the original OMP and can be used to gain better channel estimation precision.

Acoustic emission(AE) dynamic monitoring of HRB400 welding specimens during tension process will collect a large number of mixed noise data, increasing the storage space and transmission time of data. And the sparsity of the signal changes with the change of ambient noise, which affects the reconstruction performance of the orthogonal matching pursuit (OMP) algorithm under fixed sparse degree. An adaptive threshold piecewise weak orthogonal matching pursuit (SWOMP) algorithm is proposed to reconstruct the signal, which is solved the problem of data quantity and guarantees the quality of real-time monitoring and reconstruction. The simulation results show that the reconstruction error of SWOMP and OMP algorithm decreases with the increase of measurement value, and the reconstruction performance of SWOMP algorithm is obviously better than that of OMP algorithm. The reconstructed quality of OMP algorithm fluctuates greatly when reconstructing multi-segment signals, while the reconstructed error of SWOMP algorithm is stable at about 0.05, which can reconstruct signals effectively and has high adaptability.

Sparse signals can be reconstructed from a small set of measurements basing on the theory of compressive sensing (CS), whereas the key points are the selection of the measurement matrix and the reconstruction algorithm. This paper presents an imaging algorithm for ground penetrating radar based on CS. The measurement matrix is selected via random filters, which can reduce the number of nonzero elements in the measurement matrix effectively. We adopt the simple orthogonal matching pursuit (OMP) algorithm to reconstruct signal with less data storage and lower computational complexity. Simulation results are provided to illustrate the performance of the proposed method.

Due to the application of power electronics and wind power generation equipment in power systems, broadband oscillation events constantly appear, which makes broadband oscillation difficult to detect due to the limitations of communication bandwidth and the sampling theorem. To ensure the safety and stability of the system, and to detect and recognize the broadband oscillation information timely and accurately, this paper presents a multi-mode recognition method of broadband oscillation based on compressed sensing (CS) and the adaptive Variational Mode Decomposition (VMD) algorithm. Firstly, the high-dimensional oscillation signal data collected by the Phasor Measurement Unit (PMU) is compressed and sampled by a Gaussian random matrix, and the obtained low-dimensional data are uploaded to the main station. Secondly, the orthogonal matching pursuit (OMP) algorithm of the master station is used to reconstruct the low-dimension signal, and the original high-dimension signal data are recovered without losing the main features of the signal. Finally, an adaptive VMD algorithm with energy loss minimization as a threshold is used to decompose the reconstructed signal, and the Intrinsic Mode Function (IMF) components with broadband oscillation information are obtained. By constructing oscillating signals with different frequencies, Gaussian white noise with a signal-to-noise ratio of 10 dB to 30 dB is added successively. After the signal is compressed and reconstructed by the proposed method, the signal-to-noise ratio can reach 18.8221 dB to 40.0794 dB, etc., and the oscillation frequency and amplitude under each signal-to-noise ratio can be accurately identified. The results show that the proposed method not only has good robustness to noise, but also has good denoising effect to noise. By using the simulation measurement model, the original oscillation signal is compressed and reconstructed, and the reconstruction error is 0.1263. The basic characteristics of the signal are restored, and the frequency and amplitude of the oscillation mode are accurately identified, which proves that the method is feasible and accurate.

Reconstruction of atomic force microscopy image using compressed sensing

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.

Sparse signal approximations have become a new tool in signal processing with wide ranging applications from source separation to signal acquisition. Recently, many algorithms for sparse signal reconstruction have been developed, however, greedy algorithms, such as Orthogonal Matching Pursuit algorithm, can have better performance than the other algorithms. Approximate orthogonal matching pursuit algorithms, such as gradient pursuit algorithm and conjugate gradient pursuit algorithm, can lead to fast approximations to Orthogonal Matching Pursuit. In this paper Newton pursuit algorithm for sparse signal reconstruction is proposed. The algorithm is a kind of directional pursuit algorithms with the same computational complexity compared to orthogonal matching pursuit algorithm, but it can have better performance than approximate orthogonal matching pursuit algorithms.