A non-local regularization-based fractional-order total variational compressive sensing algorithm for effective recovery of Geiger-mode avalanche photodiode LiDAR images

To address the challenge of low accuracy of the range image recovery of Geiger-mode avalanche photodiode (GM-APD) LiDAR in low signal-to-background ratios (SBRs), this paper proposes a non-local regularization-based fractional-order total variational compressive sensing (CS) algorithm for recovering GM-APD LiDAR images. First, the kurtosis factor peak method was utilized to obtain the target range image at low SBRs. Subsequently, a non-local regularization-based fractional-order total variational CS model for GM-APD LiDAR image recovery is proposed, leveraging the sparse and constrained isometric properties of CS as well as the memorability of fractional-order calculus. This model aims to compress and sample high-dimensional range images while performing a sparse representation. Finally, an augmented Lagrange algorithm was employed to precisely recover the target range image. The results of the experiments demonstrate that the proposed method can enhance the degree of target recovery by a minimum of 4.29% and increase the peak signal-to-noise ratio by at least 9.29% under conditions of a 60% sampling rate, identical SBR, and statistical frame number.