Generalized spatiotemporal joint Richardson-Lucy reconstruction for non-line-of-sight imaging with explicit IRF modeling

Time-of-flight non-line-of-sight (NLOS) imaging reconstructs hidden scenes by inverting transient photon-count measurements recorded on a relay surface. Although light-cone-transform (LCT) and wave-based f - k pipelines enable efficient propagation inversion under ideal or near-impulsive temporal-response assumptions, their performance can be degraded when the temporal response of the imaging system is no longer close to an impulse. Practical TCSPC/SPAD systems exhibit non-impulsive instrument response functions (IRFs) due to laser pulse width, electronic timing jitter, and bandwidth limits. When IRF temporal broadening becomes comparable to inter-voxel path-length separations, depth responses overlap, axial resolution degrades, and forward-model mismatch propagates as depth-dependent artifacts and elevated background residue. This paper develops a physically consistent, IRF-aware reconstruction framework within an LCT-compatible operator family. First, we explicitly embed the calibrated IRF as a temporal convolution operator in the forward model and construct an IRF-aware regularized inverse filtering baseline (Reg-Inv) as a controlled linear reference. Building on the same discretization, we derive a Poisson-likelihood spatiotemporal Richardson-Lucy update (GRL) that integrates temporal compensation and 3D voxel inversion within a single multiplicative iteration under non-negativity. The implementation enforces strictly matched forward/adjoint cascades, including resampling conventions and time-window consistency, so that the observed performance differences can be attributed to the reconstruction strategy rather than inconsistent preprocessing or operator definitions. Evaluations are conducted on Bowling and USAF resolution-target simulations under ideal, Gaussian-broadened, and calibrated measured IRF settings, planar letter simulations for boundary/topology evaluation, and real measured CH/C-with-tilted-H experiments using the calibrated system IRF. The proposed method is compared with Reg-Inv, separable RL(1D) deconvolution, LCT, f - k , and phasor-field reconstruction. Quantitative results show that GRL yields more compact target support and improved contour preservation in most cases, while providing stronger target-background separation and lower background residuals in the measured CH experiment and under several broadened-IRF simulation settings. These results demonstrate that explicitly coupling IRF compensation with volumetric reconstruction is beneficial for improving the robustness of practical photon-counting NLOS imaging systems.