High-quality image restoration is typically challenging due to low signal–to–background ratios (SBRs) and limited statistics frames. To address these challenges, this paper devised a method based on fractional-order total variation (FOTV) regularization for recovering Geiger-mode avalanche photodiode (GM-APD) light detection and ranging (lidar) depth images. First, the spatial differential peak-picking method was used to extract the target depth image from low SBR and limited frames. FOTV regularization was introduced based on the total variation regularization recovery model, which incorporates the fractional-order differential operator, in order to realize FOTV-regularization-based depth image recovery. These frameworks were used to establish an algorithm for GM-APD depth image recovery based on FOTV. The simulation and experimental results demonstrate that the devised FOTV-recovery algorithm improved the target reduction degree, peak signal–to–noise ratio, and structural similarity index measurement by 76.6%, 3.5%, and 6.9% more than the TV, respectively, in the same SBR and statistic frame conditions. Thus, the devised approach is able to effectively recover GM-APD lidar depth images in low SBR and limited statistic frame conditions.

A Geiger-mode avalanche photodiode (GM-APD) laser radar range image has much noise when the signal-to-background ratios (SBRs) are low, making it difficult to recover the real target scene. In this paper, based on the GM-APD lidar denoising model of fractional-order total variation (FOTV), the spatial relationship and similarity relationship between pixels are obtained by using a spatial kernel function and range kernel function to optimize the fractional differential operator, and a new FOTV GM-APD lidar range-image denoising algorithm is designed. The lost information and range anomalous noise are suppressed while the target details and contour information are preserved. The Monte Carlo simulation and experimental results show that, under the same SBRs and statistical frame number, the proposed algorithm improves the target restoration degree by at least 5.11% and the peak signal-to-noise ratio (PSNR) by at least 24.6%. The proposed approach can accomplish the denoising of GM-APD lidar range images when SBRs are low.

Trajectory prediction is critical for safe robot navigation, yet standard deep learning models predominantly rely on the Mean Squared Error (MSE) criterion. While effective under ideal conditions, MSE-based optimization is inherently fragile to non-Gaussian impulsive noise—such as sensor glitches and occlusions—common in real-world deployment. To address this limitation, this paper proposes MEE-LSTM, a robust forecasting framework that integrates Long Short-Term Memory networks with the Minimum Error Entropy (MEE) criterion. By minimizing Renyi’s quadratic entropy of the prediction error, our loss function introduces an intrinsic “gradient clipping” mechanism that effectively suppresses the influence of outliers. Furthermore, to overcome the convergence challenges of fixed-kernel information theoretic learning, we introduce a Silverman-based Adaptive Annealing (SAA) strategy that dynamically regulates the kernel bandwidth. Extensive evaluations on the ETH and UCY datasets demonstrate that MEE-LSTM maintains competitive accuracy on clean benchmarks while exhibiting superior resilience in degraded sensing environments. Notably, we identify a “Scissor Plot” phenomenon under stress testing: in the presence of 20% impulsive noise, the proposed model maintains a stable Average Displacement Error (ADE “≈” 0.51 m), whereas MSE baselines suffer catastrophic degradation (ADE > 2.1 m), representing a 75.7% improvement in robustness. This work provides a statistically grounded paradigm for reliable causal inference in hostile robotic perception.

To address the challenge of accurately reconstructing multi-depth targets using single-photon Light Detection and Ranging (LiDAR) under few-frame conditions in high-precision applications such as autonomous driving perception, remote sensing, and military reconnaissance, this paper proposes a computational imaging method named the Jensen–Shannon Divergence Weighted Pixel Fusion Constant False Alarm Rate (JSWPF-CFAR) approach. First, the proposed method utilizes the Jensen–Shannon (JS) divergence to characterize the statistical similarity between adjacent pixels, thereby constructing adaptive weights to achieve the effective fusion of echo signals. The key innovation lies in the formulation of a JS divergence-based weighting factor, which fully exploits the inherent spatial correlation within 3D target structures to optimize the pixel fusion process and enhance the signal statistics of target echoes. Subsequently, a CFAR detection model tailored for Geiger-mode Avalanche Photodiode (GM-APD) multi-depth echo signals is constructed to estimate the noise photon count within a local sliding window; this estimate is then used to calculate a photon counting threshold for identifying and extracting high-confidence target intervals. Finally, a peak-picking method is employed to perform the 3D reconstruction of multi-depth targets. Compared with existing techniques such as matched filtering and Reversible Jump Markov Chain Monte Carlo (RJMCMC), the proposed method exhibits superior reconstruction quality under few-frame and low Signal-to-Background Ratio (SBR) conditions. The experimental results demonstrate that the proposed method achieves an improvement in target restoration degree (RD) of at least 21.16% and a relative variance (Var) optimization of at least 62.90% over the matched filtering and RJMCMC baselines. These results indicate that the proposed approach effectively enhances the multi-depth estimation performance of single-photon LiDAR in complex scenes.

As a key task in LiDAR data processing, point cloud classification directly determines the accuracy and reliability of downstream applications such as autonomous driving and robot navigation. However, in practical scenarios, point cloud sparsity is easily affected by various factors, leading to a decrease in classification accuracy. To address this issue, this paper proposes a sparse point cloud classification method based on the MSE-Mamba neural network. By combining the efficient sequence processing advantages of the MSE-Mamba module with the global modeling capability of the global attention Transformer module, high-precision classification of sparse point clouds is achieved. Extensive experimental results on ModelNet40, ScanObjectNN, and self-built 3D imaging LiDAR point cloud datasets show that the proposed method exhibits excellent point cloud classification performance in various scenarios, with overall accuracy improved compared to current mainstream methods. It provides a new approach for high-precision classification of sparse point clouds and is of great significance for promoting the practical application of LiDAR technology in complex scenes.

To address the issue of the Geiger-mode Avalanche Photodiode (GM-APD) LiDAR’s echo being easily overwhelmed by strong noise under low signal-to-background ratio conditions, leading to degraded performance in range parameter estimation and low target restoration accuracy, this paper proposes a range parameter estimation method based on multi-scale tracking differentiator. This method eliminates the reliance on complex statistical models and spatial prior information and uses a nonlinear dynamic tracking mechanism to extract target information. Firstly, a dual-scale tracking differentiator system is constructed, where the large-scale factor captures the transient mutation characteristics of the echo signal, and the small-scale factor estimates the overall evolution trend of the signal. Secondly, the difference between the dual-scale outputs is obtained to acquire the residual signal, and nonlinear mapping enhancement is performed in combination with the photon trigger probability characteristics to deeply suppress noise and highlight the target peak. Finally, the peak threshold method is used to complete the range calculation. Simulation results show that when the SBR = 0.06, compared with typical methods such as the neighborhood kernel density method, the method in this paper is more robust, the root mean square error of the range estimation is reduced by at least 38.35%, and the target restoration degree is improved by at least 19.99%, which provides a highly efficient way for high-fidelity single-photon three-dimensional imaging and target detection under strong noise.