A multiscale filter for noise reduction of low-dose cone beam projections

The Poisson or compound Poisson process governs the randomness of photon fluence in cone beam computed tomography (CBCT) imaging systems. The probability density function depends on the mean (noiseless) of the fluence at a certain detector. This dependence indicates the natural requirement of multiscale filters to smooth noise while preserving structures of the imaged object on the low-dose cone beam projection. In this work, we used a Gaussian filter, exp(-x2/2σ(2)(f)) as the multiscale filter to de-noise the low-dose cone beam projections. We analytically obtained the expression of σ(f), which represents the scale of the filter, by minimizing local noise-to-signal ratio. We analytically derived the variance of residual noise from the Poisson or compound Poisson processes after Gaussian filtering. From the derived analytical form of the variance of residual noise, optimal σ(2)(f)) is proved to be proportional to the noiseless fluence and modulated by local structure strength expressed as the linear fitting error of the structure. A strategy was used to obtain the reliable linear fitting error: smoothing the projection along the longitudinal direction to calculate the linear fitting error along the lateral direction and vice versa. The performance of our multiscale filter was examined on low-dose cone beam projections of a Catphan phantom and a head-and-neck patient. After performing the filter on the Catphan phantom projections scanned with pulse time 4 ms, the number of visible line pairs was similar to that scanned with 16 ms, and the contrast-to-noise ratio of the inserts was higher than that scanned with 16 ms about 64% in average. For the simulated head-and-neck patient projections with pulse time 4 ms, the visibility of soft tissue structures in the patient was comparable to that scanned with 20 ms. The image processing took less than 0.5 s per projection with 1024   ×   768 pixels.