A regularisation-selection method combining systematic parameter search with random forest regression investigates the relationship between replica phase diagrams of annealing-based binary compressive sensing. Reference parameters are selected from a candidate grid by minimising mean squared reconstruction error over repeated simulated annealing (SA) trials under noiseless Gaussian measurements with known sparsity. The fitted model predicts these reference values from signal dimension, sampling ratio, and sparsity.

Predicted regularisation enables the SA recovery transition to broadly follow the asymptotic reference boundary for box-constrained l1 recovery at the larger signal dimensions examined. Work originating from Tohoku University, Sigma-i Co., Research and Education Institute for Semiconductors and Informatics, and Institute of Science Tokyo demonstrates that without retraining, performance degrades significantly.

Predictive modelling streamlines parameter selection in sparse reconstruction algorithms

A hybrid solver achieves smaller mean squared reconstruction errors, in parts of the evaluated parameter space across evaluated parameter spaces, than simulated annealing. Previously, comparable improvements necessitated exhaustive re-optimisation of regularisation parameters with each new instance. The novel method predicts optimal values for these crucial settings utilising random forest regression trained on systematic searches from simulated annealing trials. Consequently, information acquired during initial optimisation is reusable, avoiding computationally expensive candidate evaluations when signal dimensions, sampling ratios or sparsity levels differ.

Streamlining signal reconstruction has potential applications spanning medical imaging and communications systems thanks to successful prediction of regularisation parameters. However, the current work depends upon carefully controlled conditions which may not mirror real-world scenarios. While performance demonstrably improves using hybrid quantum, classical solvers compared to solely relying on simulated annealing, a key question remains: how does this predictive power hold up if sparsity isn’t known *a priori* and must be estimated directly from noisy measurements.

Within certain parameter ranges, applying these predicted settings also yielded smaller mean squared reconstruction errors than standard simulated annealing. The significance of this predictive capability is undiminished despite its present reliance on known sparsity levels; signal reconstruction efficiency has been improved with both conventional simulated annealing and advanced quantum, classical hybrid solvers. Tohoku University researchers, alongside collaborators at other institutions, have devised a method for predicting effective regularisation parameters within binary compressed sensing techniques, enabling signal reconstruction using fewer measurements than previously achievable.

Training a random forest regression model on data obtained through simulated annealing trials created tools that bypass repetitive optimisation when problem characteristics change, such as differing dimensions or sparsity in signals. The team from the University of Tokyo and JST have demonstrated an approach to optimising signal reconstruction by forecasting necessary parameters for efficient rebuilding of data via standard and quantum-enhanced computing methods, offering a valuable tool which reduces computational demands without extensive parameter searching.

The researchers developed a method to predict optimal regularisation parameters within binary compressed sensing techniques using random forest regression trained on simulated annealing trials. This prediction allows for more efficient signal reconstruction with fewer measurements than previously possible across varying signal dimensions and sparsity levels.

The predicted values were successfully applied to both conventional simulated annealing and a hybrid quantum, classical solver, yielding smaller mean squared reconstruction errors in some instances. By reusing information from initial searches, the process avoids repetitive optimisation when problem characteristics change; this improves efficiency while working under defined conditions of known sparsity.

👉 More information
🗞 Phase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization
✍️ Xiaoxin Huang and Masayuki Ohzeki
🧠 ArXiv: https://arxiv.org/abs/2609.16712

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