High‐throughput and low‐area implementation of orthogonal matching pursuit algorithm for compressive sensing reconstruction (original) (raw)
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IET Circuits, Devices & Systems, 2021
Compressed sensing-based radio frequency signal acquisition systems call for higher reconstruction speed and low dynamic power. In this study, a novel low power fast orthogonal matching pursuit (LPF-OMP) algorithm is proposed for faster reconstruction of sparse signals from their compressively sensed samples and the reconstruction circuit consumes very low dynamic power. The searching time to find the best column is reduced by reducing the number of columns to be searched in successive iterations. A novel architecture of the proposed LPF-OMP algorithm is also presented here. The proposed architecture is implemented on field programmable gate array for demonstrating the performance enhancement. Computation of pseudoinverse in OMP is avoided to save time and storage requirement to store the pseudoinverse matrix. The proposed design incorporates a novel strategy to stop the algorithm without consuming any extra circuitry. A case study is carried out to reconstruct the RADAR test pulses. The design is implemented for K = 256, N = 1024 using XILINX Virtex6 device and supports maximum of K/4 iterations. The proposed design is faster, hardware efficient and consumes very less dynamic power than the previous implementations of OMP. In addition, the proposed implementation proves to be efficient in reconstructing low sparse signals. 1 | INTRODUCTION High-frequency radio frequency (RF) signals, such as RADAR pulses, are sparse in nature in the transform domain. Exploiting this sparsity property, modern signal measurement systems use compressed sensing (CS) [1,2] in place of other existing sampling techniques [3] to acquire RF signals. CSbased acquisition systems can work with low speed analog-todigital converters due to sampling at sub-Nyquist rate [4]. In CS-based sampling paradigm, random measurements are taken from the signal and then the original signal is recovered from the measurement samples using signal recovery algorithms. Orthogonal matching pursuit (OMP) [5,6] is a well known recovery algorithm. Unlike the other greedy pursuit algorithms, OMP provides better performance with moderate computational complexity. OMP estimates a sparse signal by executing two steps in every iteration, viz., perform the atom searching (AS) and solve a least squares (LS) problem. In AS step, OMP identifies an atom or a column of the sampling matrix which gives maximum correlation with the current residual. Subsequently the signal is estimated by solving an LS problem. The timing complexity of the AS step is very high as it is a linear function of the signal sparsity and the number of samples. Many techniques are reported in literature to reduce the timing complexity of AS step. In [7] authors applied clustering algorithms to group the similar columns and reported a tree-based pursuit algorithm. But such algorithm has no reports of implementation. Researchers reported parallel selection of multiple columns to address the timing complexity problem in [8,9]. Multiple selection of columns reduces the timing complexity but with greater chances of choosing wrong columns. Many implementations are reported based on either field programmable gate arrays (FPGAs) or application-specific integrated circuits. The LS problem is solved in different ways in current research works. The implementations of OMP reported in [9-15] used modified Cholesky factorization [16] to solve the LS problem. The LS problem is solved by lowerupper decomposition [16] in [17]. QR decomposition [16] is another powerful matrix factorization technique which is used This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
VLSI Architecture for OMP to Reconstruct Compressive Sensing Image
Advances in Science, Technology and Engineering Systems Journal
A real-time embedded system requires plenty of measurements to fallow the Nyquist criteria. The hardware built for such a large number of measurements, is facing the challenges like storage and transmission rate. Practically it is very much complex to build such costly hardware. Compressive Sensing (CS) will be a future alternate technique for the Nyquist rate, specific to some applications where sparsity property plays a major role. Software implementation of Compressive Sensing takes more time to reconstruct a signal from CS measurements using the Matching Pursuit (MP) algorithm because of fetching, decoding, and execution policy. It is necessary to build hardware in CS. The author proposes one such VLSI Architecture (Hardware) for 256 256 and 512 512image. Various random matrices like Bernoulli, Partial Hadmard, Uniform Spherical, and Random Matrix are used to build hardware. FHT (Foreward Transform) with ±2 6 threshold is applied to get CS measurements. The reconstruction time, Signal to Noise ratio (SNR), and Mean Square Error (MSE) are measured. Multiple time experiments are carried out and results show that for an image of size 256 256, SNR is 25 and MSE is 166. For the image of size 512 512, the values are 27 and 182. However, both the input images are resized to 256 256 so the reconstruction time is 2.62µ which is less is compared to software implementation.
Incremental Gaussian Elimination Approach to Implement OMP for Sparse Signal Measurement
IEEE Transactions on Instrumentation and Measurement, 2019
An efficient architecture of Orthogonal Matching Pursuit (OMP) algorithm is proposed to recover signals compressively measured at sub-Nyquist rate. The proposed architecture is implemented on Field Programmable Gate Array (FPGA) for performance validation. In place of matrix factorization based pseudoinverse computation, Gaussian Elimination (GE) is used to compute the signal estimate. A novel Incremental Gaussian Elimination (IGE) algorithm is proposed and used in OMP algorithm. The proposed design is targeted to Virtex6 FPGA device to compare with other reported works for K = 256, N = 1024 and m = 36 where N is the number of samples, K is the measurement vector length and m is the signal sparsity level. The recovery signal-to-noise ratio (RSNR) of 23.98 dB is achieved. The proposed work is validated by implementing it on Artix7 FPGA device by taking compressed measurements from an analog to information converter (AIC). The input signal is synthesized as a random combination of sine waves with different frequencies. The proposed architecture is hardware efficient, faster and consumes low dynamic power than other existing designs. The proposed design is hardware efficient even for the higher value of m/K.
Indonesian Journal of Electrical Engineering and Computer Science, 2022
Orthogonal matching pursuit (OMP) is the most efficient algorithm used for the reconstruction of compressively sampled data signals in the implementation of compressive sensing. OMP operates in an iteration-based nature, which involves optimisation and least-square problem (LSP) as the main processes. However, optimisation and LSP processes comprise complex mathematical operations that are computationally demanding, and software-based implementations are slow, power-consuming, and unfit for real-time applications. To fill the research gap, we reviewed the optimisation and LSP techniques implemented on the FPGA platform as the hardware accelerator. Aspects that contributed to the performance, algorithm, and methods involved in the implemented works were discussed and compared. The methods were found to be improved when modified or combined. However, the best approach still depends on the requirement of the system to be developed, and this review is significant as a reference.
Efficient Implementations for Orthogonal Matching Pursuit
Electronics
Based on the efficient inverse Cholesky factorization, we propose an implementation of OMP (called as version 0, i.e., v0) and its four memory-saving versions (i.e., the proposed v1, v2, v3 and v4). In the simulations, the proposed five versions and the existing OMP implementations have nearly the same numerical errors. Among all the OMP implementations, the proposed v0 needs the least computational complexity, and is the fastest in the simulations for almost all problem sizes. As a tradeoff between computational complexities/time and memory requirements, the proposed v1 seems to be better than all the existing ones when only considering the efficient OMP implementations storing G (i.e., the Gram matrix of the dictionary), the proposed v2 and v3 seem to be better than the only existing one when only considering the efficient implementations not storing G, and the proposed v4 seems to be better than the naive implementation that has the (known) minimum memory requirements. Moreover, ...
FPGA implementation of LSD-OMP for real-time ECG signal reconstruction
2021
Compressed sensing is widely used to compress electrocardiogram (ECG) signals, but the major challenges of the compressed sensing algorithms are their highly complex signal reconstruction processes. In this paper, a reconfigurable high-speed and low-power field-programmable gate array (FPGA) implementation of the least support denoising-orthogonal matching pursuit (LSD-OMP) algorithm for the real-time reconstruction of the ECG signals is presented. The contribution of this study is twofold: Firstly, LSD-OMP can pick more than one element at each iteration and reconstruct the sparse signal using less number of iterations as compared to the standard OMP algorithms. Latency of the proposed design is therefore reduced by exploiting the multiple index selection feature of LSD-OMP. Secondly, the proposed architecture is the first reconfigurable LSD-OMP reconstruction architecture which can take different signal sizes and different sparsity levels. The proposed design also includes an efficient inverse wavelet transform (IWT) module to convert the reconstructed signal back into the time-domain. Together with the overhead of the IWT module, the proposed design demonstrates faster execution times while consuming lower power than the existing FPGA implementations; therefore, it can be utilized in wireless body area networks as a back-end unit to reconstruct the compressed ECG signals.
Indonesian Journal of Electrical Engineering and Computer Science, 2020
Synthetic Aperture Radar (SAR) is an imaging system based on the processing of radar echoes. The produced images have a huge amount of data which will be stored onboard or transmitted as a digital signal to the ground station via downlink to be processed. Therefore, some methods of compression on the raw images provides an attractive option for SAR systems design. One of these techniques which used for image reconstruction is the Orthogonal Matching Pursuit (OMP). OMP is an iterative algorithm which need high computational operations. The computational complexity of the iterative algorithms is high due to updating operations of the measurement vector and large number of iterations that are used to reconstruct the images successfully. This paper presents a new adaptive OMP algorithm to overcome this issue by using certain threshold. The new adaptive OMP algorithm is compared with the classical OMP algorithm using the Receiver Operating Characteristic (ROC) curves. The MATLAB simulati...
2011
Modern multicore architectures require adapted, parallel algorithms and implementation strategies for many applications. As a non-trivial example we chose in this paper a patch-based sparse coding algorithm called Orthogonal Matching Pursuit (OMP) and discuss parallelization and implementation strategies on current hardware. The OMP algorithm is used in imaging and involves heavy computations on many small blocks of pixels called patches. From a global view the patches within the image can be processed completely in parallel but within one patch the algorithm is hard to parallelize. We compare the performance on the Cell Broadband Engine Architecture (CBEA), different GPUs, and current multicore CPUs.
A Single-Precision Compressive Sensing Signal Reconstruction Engine on FPGAs
Proceedings of the 23rd International Conference on Field-Programmable Logic and Applications (FPL'13), 2013
Compressive sensing (CS) is a promising technology for the low-power and cost-effective data acquisition in wireless healthcare systems. However, its efficient realtime signal reconstruction is still challenging, and there is a clear demand for hardware acceleration. In this paper, we present the first single-precision floating-point CS reconstruction engine implemented a Kintex-7 FPGA using the orthogonal matching pursuit (OMP) algorithm. In order to achieve high performance with maximum hardware utilization, we propose a highly parallel architecture that shares the computing resources among different tasks of OMP by using configurable processing elements (PEs). By fully utilizing the FPGA recourses, our implementation has 128 PEs in parallel and operates at 53.7 MHz. In addition, it can support 2x larger problem size and 10x more sparse coefficients than prior work, which enables higher reconstruction accuracy by adding finer details to the recovered signal. Hardware results from the ECG reconstruction tests show the same level of accuracy as the double-precision C program. Compared to the execution time of a 2.27 GHz CPU, the FPGA reconstruction achieves an average speed-up of 41x.
Batch Look Ahead Orthogonal Matching Pursuit
2018 Twenty Fourth National Conference on Communications (NCC), 2018
Compressed sensing (CS) is a sampling paradigm that enables sampling signals at sub Nyquist rates by exploiting the sparse nature of signals. One of the main concerns in CS is the reconstruction of the signal after sampling. Many reconstruction algorithms have been proposed in the literature for the recovery of the sparse signals-Basis Pursuit, Orthogonal Matching Pursuit (OMP), Look Ahead Orthogonal Matching Pursuit (LAOMP) are some of the popular reconstruction algorithms. LAOMP, a modification of OMP, improves the reconstruction accuracy of OMP by employing a look ahead procedure. But LAOMP suffers from the drawback of being very expensive in terms of the computational time. In this paper we propose a modified version of the LAOMP algorithm called Batch-LAOMP which has a lesser computational complexity and also gives better performance in terms of reconstruction accuracy as seen from the results of the numerical experiments.