Adaptive regularization improves binary compressed sensing recovery accuracy
Phase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization
Information Theory
Summary
The paper studies how choosing the right regularization helps recover hidden binary signals from limited measurements using a type of search called simulated annealing. The authors develop a method using machine learning to pick the best regularization parameters based on signal size, sparsity, and measurement strength. This method predicts good parameters without needing repeated searches every time, making recovery more efficient. They also show that a quantum-classical hybrid solver can sometimes outperform traditional annealing when using these parameters.
What this means in practice
- •For signal processing engineers: Optimize parameter settings for annealing algorithms to improve binary signal recovery from limited data.
- •For quantum computing developers: Use predicted regularization values to enhance quantum-classical hybrid algorithms for compressed sensing problems.
Authors
Xiaoxin Huang, Masayuki Ohzeki
Abstract
Regularization choice changes the recovery phase diagrams of annealing-based binary compressed sensing. We develop a regularization-selection method that combines systematic parameter search with random forest regression. Under noiseless Gaussian measurements with known sparsity, reference parameters are selected from a candidate grid by minimizing mean squared reconstruction error over repeated simulated annealing (SA) trials. The fitted model predicts these reference values from signal dimension, sampling ratio, and sparsity. With predicted regularization, the SA recovery transition broadly follows the asymptotic reference boundary for box-constrained $\ell_1$ recovery at the larger signal dimensions examined. Without retraining, the same predictor supplies identical regularization values to SA and a quantum--classical hybrid solver. On matched problem instances, the hybrid solver yields smaller mean squared reconstruction errors than SA in parts of the evaluated parameter space. The resulting rule reuses the searched information for subsequent reconstruction without repeating candidate searches at each setting. The results quantify empirical performance under the stated finite candidate grid and solver settings; they do not constitute a solver-independent recovery guarantee or a time-to-solution comparison.