Cosmic ray muons enable non-invasive imaging of dense structures through multipleCoulomb scattering (MCS), with scattering angles dependent on atomic number (Z). Traditional algorithms like Point of Closest Approach (PoCA) assume single scattering, limiting accuracy. This work presents the μTRec algorithm, which models muon paths using a Bayesian approach with Gaussian approximations, accounting for MCS and energy loss. μTRec is applied to simulate muon imaging of dry storage casks (DSCs) used for spent nuclear fuel, with four loading configurations: fully loaded, one row missing, one assembly missing, and half assembly missing. The results demonstrate improved accuracy and resolution in identifying missing assemblies compared to conventional methods. It is observed that the μTRec algorithm exhibits markedly superior performance over the classical PoCA method achieving respective improvements of 122% in signal-to-noise ratio (SNR), 35% in contrast-to-noise ratio (CNR), and 201% in detection power (DP) for the case of one missing fuel assembly with a muon flux of 106 and a voxel size of 5 cm. Furthermore, {\mu}TRec supports high-resolution reconstruction with voxel sizes as small as 1 cm which enables the accurate localization of structural components such as the 2.5 cm thick steel canister. Notably, μTRec is also capable of reliably detecting a single missing fuel assembly at a muon flux as low as 105, a task that remains infeasible using PoCA under the same conditions.