A team of researchers led by Professor Sun Zhong of Peking University recently presented an analog hardware approach to recover compressed real-time sensing. Their findings were documented in a recently published article. Science Developments.

This paper presents a design based on resistive memory (also known as memristor) to realize instantaneous matrix-matrix-vector multiplication (MMVM) for the first time. Based on this module, an analog matrix calculation circuit is described that solves compressed sensing (CS) recovery in one step (within a few microseconds).

The value of CS in modern technology

CS is the cornerstone of modern signal and image processing in many important areas such as medical imaging, wireless communications, object tracking, and single-pixel cameras. In CS, sparse signals can have significantly undersampling at the forward sensor, violating the Nyquist ratio and thus greatly increasing sampling efficiency.

In the internal processor, the output signals can be accurately reconstructed by solving the sparse approximation problem. However, the CS recovery algorithm is often very complex and involves highly complex matrix-matrix operations and pointwise nonlinear functions. As a result, in-processor CS recovery has become a common bottleneck in the CS pipeline, preventing its application in high-speed real-time signal processing scenarios.

Challenges and Innovations in CS Recovery

To accelerate CS recovery calculations, two-line efforts have been implemented in the traditional digital domain using advanced algorithms (e.g., deep learning) or parallel processors (e.g., GPUs, FPGAs, and ASICs). However, the efficiency of calculations is fundamentally limited by the polynomial complexity of matrix operations in digital processors.

To this end, analog computing has been considered an effective approach to accelerate CS recovery due to inherent computational parallelism. However, again due to the high complexity of CS recovery algorithms, previous analog computing solutions either rely on precomputed matrix matrix multiplication, which has cubic complexity, or involve a discrete iterative process that requires expensive but frequent analog-to-matrix operations. digital transformations. . Therefore, solving the CS recovery problem in one step remains a great challenge.

Practical application and future potential

To solve this problem, a team from Peking University first developed an in-memory analog computing module that implements MMVM in a single step, thus eliminating the preliminary calculation of matrix-matrix multiplication. By connecting this MMVM module to other analog components to create a feedback loop, the resulting circuit accurately reflects a local competitive algorithm (LCA) that solves CS recovery in a single step without separate iterations.

To test the circuit, the team fabricated a resistive memory array using a standard semiconductor process in which an LCA circuit is built on a printed circuit board to perform CS recovery. The compressed data was converted into an input voltage signal in the circuit, and the reconstructed signals were received continuously.

Using this scheme, restoration of 1D sparse signals, 2D native RGB images, and magnetic resonance images (MRI) have been demonstrated in experiments. The normalized mean square error (NMSE) is around 0.01 and the peak signal-to-noise ratio (PSNR) of the images is 27 dB. The speed of this scheme is estimated to be 1-2 times faster than traditional digital approaches such as deep learning and better than other electronic or photonic analog computing solutions. The scheme is very promising for implementation in an internal CS processor to provide real-time processing capabilities in the microsecond regime; This may include advanced medical, visual and communication techniques.