Incremental Gaussian Elimination Approach to Implement OMP for Sparse Signal Measurement

An efficient architecture of the orthogonal matching pursuit (OMP) algorithm is proposed to recover signals compressively measured at the sub-Nyquist rate. The proposed architecture is implemented on the field-programmable gate array (FPGA) for performance validation. In the 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 the OMP algorithm. The proposed design is targeted to the Virtex6 FPGA device to compare with other reported works for <inline-formula> <tex-math notation="LaTeX">$K=256$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$N=1024$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$m=36$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> is the number of samples, <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> is the measurement vector length, and <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> 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 the 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 and faster, and consumes low dynamic power than other existing designs. The proposed design is hardware-efficient even for the higher value of <inline-formula> <tex-math notation="LaTeX">$m/K$ </tex-math></inline-formula>.

[1]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[2]  Abbes Amira,et al.  FPGA Implementation of Orthogonal Matching Pursuit for Compressive Sensing Reconstruction , 2015, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[3]  Wenyao Xu,et al.  A single-precision compressive sensing signal reconstruction engine on FPGAs , 2013, 2013 23rd International Conference on Field programmable Logic and Applications.

[4]  Yuan-Hao Huang,et al.  A High-SNR Projection-Based Atom Selection OMP Processor for Compressive Sensing , 2016, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[5]  Avi Septimus,et al.  Compressive sampling hardware reconstruction , 2010, Proceedings of 2010 IEEE International Symposium on Circuits and Systems.

[6]  Ajit Kumar Sahoo,et al.  Low-Complexity Architecture of Orthogonal Matching Pursuit Based on QR Decomposition , 2019, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[7]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[8]  Amar Rouane,et al.  Simple and Efficient Compressed Sensing Encoder for Wireless Body Area Network , 2014, IEEE Transactions on Instrumentation and Measurement.

[9]  Lei Wang,et al.  An FPGA-Based Architecture for High-Speed Compressed Signal Reconstruction , 2017, ACM Trans. Embed. Comput. Syst..

[10]  Sujuan Liu,et al.  The Implementation of the Improved OMP for AIC Reconstruction Based on Parallel Index Selection , 2017, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[11]  Steffen Paul,et al.  Rapid digital architecture design of orthogonal matching pursuit , 2016, 2016 24th European Signal Processing Conference (EUSIPCO).

[12]  Abbes Amira,et al.  High level prototyping and FPGA implementation of the orthogonal matching pursuit algorithm , 2012, 2012 11th International Conference on Information Science, Signal Processing and their Applications (ISSPA).

[13]  Dejan Markovic,et al.  A Configurable 12–237 kS/s 12.8 mW Sparse-Approximation Engine for Mobile Data Aggregation of Compressively Sampled Physiological Signals , 2016, IEEE Journal of Solid-State Circuits.

[14]  Hubert Kaeslin,et al.  High-speed compressed sensing reconstruction on FPGA using OMP and AMP , 2012, 2012 19th IEEE International Conference on Electronics, Circuits, and Systems (ICECS 2012).

[15]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[16]  Tinoosh Mohsenin,et al.  Low-complexity FPGA implementation of compressive sensing reconstruction , 2013, 2013 International Conference on Computing, Networking and Communications (ICNC).

[17]  Fan Yang,et al.  Fast compressive sensing reconstruction algorithm on FPGA using Orthogonal Matching Pursuit , 2016, 2016 IEEE International Symposium on Circuits and Systems (ISCAS).

[18]  Tinoosh Mohsenin,et al.  Low Overhead Architectures for OMP Compressive Sensing Reconstruction Algorithm , 2017, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Justin K. Romberg,et al.  Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals , 2009, IEEE Transactions on Information Theory.

[20]  Tinoosh Mohsenin,et al.  High performance compressive sensing reconstruction hardware with QRD process , 2012, 2012 IEEE International Symposium on Circuits and Systems.

[21]  Yu Hen Hu,et al.  Random Triggering-Based Sub-Nyquist Sampling System for Sparse Multiband Signal , 2017, IEEE Transactions on Instrumentation and Measurement.

[22]  Yi Li,et al.  An extensible and real-time compressive sensing reconstruction hardware for WBANs using OMP , 2013, 2013 IEEE 10th International Conference on ASIC.