A group of scientists at Peking University lead by Professor Sun Zhong has presented an analog hardware method for real-time compressed sensing recovery. An article that was just published in Science Advances details their findings.
In this study, an instantaneous matrix-matrix-vector multiplication (MMVM) design based on a resistive memory (sometimes called memristor) array is first presented. This module serves as the foundation for the subsequent disclosure of an analog matrix computing circuit that resolves compressed sensing (CS) recovery in a single step (a few microseconds).
The role of computer science in modern technology
In numerous crucial domains like medical imaging, wireless communications, object tracking, and single-pixel cameras, CS has become the cornerstone of contemporary signal and image processing. In CS, it is possible to break past the Nyquist rate and greatly increase sampling efficiency by drastically undersampling sparse signals in the front-end sensor.
A sparse approximation problem can be solved in the back-end processor to reconstruct the original signals with accuracy. On the other hand, pointwise nonlinear functions and high-complexity matrix-matrix operations are typically seen in the CS recovery procedure, which is typically quite complex. Therefore, it is no longer possible to apply CS recovery in high-speed, real-time signal processing scenarios because it has become the acknowledged bottleneck in the CS pipeline at the back-end processor.
Compressed Sensing Recovery Innovations and Challenges
In the classical digital world, two approaches have been used to speed up the CS recovery computation: either employing parallel processors (such as GPU, FPGA, and ASIC) or advanced algorithms (like deep learning). However, in digital computers, the polynomial complexity of matrix operations imposes a basic limit on computing efficiency.
Because of its built-in processing parallelism, analog computing has been seen as an effective method for quickening the recovery of computer systems. However, as previously mentioned, because of the high complexity of CS recovery algorithms, prior analog computing solutions either depend on pre-calculated matrix-matrix multiplication, which has a cubic complexity, or use a discrete iterative process that necessitates costly but frequent analog-digital conversions. Thus, it is still quite difficult to solve CS recovery in a single step.
Useful Applications and Possibilities for the Future
The Peking University team decided to avoid pre-calculating matrix-matrix multiplication by first creating an analog in-memory computing module that implements MMVM in a single step. The local competitive algorithm (LCA), which solves CS recovery in a single step without discrete iterations, is precisely mapped onto the final circuit by joining this MMVM module with other analog components to design a feedback loop.
The researchers built the LCA circuit on a PCB for carrying out CS recovery after validating the circuit by fabricating a resistive memory array using a conventional semiconductor method. The recovered signals were obtained in a continuous-time fashion after the compressed data was transformed into input voltage signals for the circuit.
It has been proved in studies that this circuit can recover 1D sparse signals, 2D natural RGB images, and magnetic resonance imaging (MRI). The peak signal-to-noise ratio (PSNR) of the pictures is 27 dB, and the normalized mean square error (NMSE) is approximately 0.01. According to estimates, this circuit performs better than other electronic or photonic analog computing methods and is 1-2 orders of magnitude faster than conventional digital techniques like deep learning. Advanced medical, visual, and communication approaches may be made possible by implementing the circuit in the back-end CS processor, which has great potential to deliver real-time processing capacity in the microsecond range.
Reference: “In-memory analog solution of compressed sensing recovery in one step,” published in Science Advances on December 13, 2023, by Shiqing Wang, Yubiao Luo, Pushen Zuo, Lunshuai Pan, Yongxiang Li, and Zhong Sun.