The projection sequence of Hadamard speckle patterns directly influences the image reconstruction quality and efficiency of computational ghost imaging under undersampled conditions. Optimizing the speckle sorting strategy is an effective approach to achieving high-quality imaging at low sampling rates.

This study aims to address the oscillation of quality metrics observed during the sampling process of traditional sorting strategies and to further enhance the signal-to-noise ratio and convergence stability within the low-sampling-rate regime.

A recursive cross (RC) sorting strategy based on the Hadamard basis is proposed. By inversely deconstructing hierarchical subspaces and utilizing an even-index mapping mechanism, this method interleaves and reorganizes speckles with orthogonal texture features, thereby disrupting the continuous accumulation of unidirectional features in the sampling sequence. Numerical simulations under both ideal and Gaussian noise environments, along with optical experiments, were conducted to validate the proposed method.

Simulation results demonstrate that the RC strategy effectively eliminates the oscillation of evaluation metrics observed in Russian Dolls sorting as the sampling rate increases across the full 0–100% range, achieving a smooth evolution and robust convergence of imaging quality. Particularly in the low-sampling-rate range of 0–10%, the peak signal-to-noise ratio of the reconstructed images shows a maximum improvement of approximately 101.7% compared to Hadamard natural sorting and 11.4% compared to laser model speckle sorting, with a maximum gain of about 3.4 dB.

By optimizing the sampling path of spectral energy, the RC sorting strategy improves the data acquisition efficiency of ghost imaging, potentially offering an effective technical pathway for realizing rapid and real-time ghost imaging applications.