A shrinkage-backtracking algorithm for gamma radiation field reconstruction under sparse and limited measurements

This paper proposes a Shrinkage–Backtracking Algorithm (SBA) for high-quality gamma radiation field reconstruction under sparse and limited measurements. The method is developed within the Compressed Sensing (CS) framework and formulates the reconstruction as a non-negative sparse regression problem. An initial solution is obtained using non-negative Lasso, followed by an adaptive F-test–based pruning and backtracking strategy that dynamically refines the coefficient structure. When pruning leads to increased reconstruction error, a backtracking step restores the relevant coefficients, thereby preventing over-simplification and enhancing reconstruction accuracy. Validation across three Monte Carlo scenarios shows that, under the same sampling density, SBA outperforms inverse distance weighting (IDW) and orthogonal matching pursuit (OMP) in reconstruction accuracy, stability, and source identification. Even in complex shielding scenarios, SBA achieves reconstruction errors below 20% and source identification success rates above 80% using only about 4% of the detection points. Its errors are mainly concentrated in localized regions affected by shielding and do not exhibit the wide-spread or high-magnitude deviations observed in IDW and OMP, resulting in more stable overall reconstruction.