Validation maps for bias correction in Monte Carlo denoising

A fundamental prerequisite of computer aided radiotherapy treatment is the accurate estimation of the dose distributions so as to deliver a high homogeneous dose volume to the tumor without causing unnecessary side effects for the patient. The Monte Carlo (MC) method is considered the most effective dose distribution computational technique. However, it is too slow and contaminated with noisy degradations that could affect the dose contour visibility and the estimates of dosimetric parameters. Various algorithms for denoising Monte Carlo dose distributions have been proposed. However, they all suffer from the tradeoff between variance reduction and the introduction of bias. We introduce an independent method to estimate the local smoothing bias, thereby generating ´validation maps´. These maps can be used either to tune the aggressiveness of the local smoothing parameters or to directly subtract an estimate of the bias. This technique can be applied in conjunction with any denoising method to control local smoothing parameters. Two different validation map methods were investigated: a generalized cross-validation method and a bootstrapping method. The methods estimate the mean-square-error and the bias. We tested the technique on a challenging 2-D synthetic dataset that simulates charged particle transport, 2-D/3-D phantoms and on full 3-D computed-tomography-based Monte Carlo datasets. The results are promising.