Noise behavior of Spline Mojette FBP reconstruction

摘要

The goal of this paper is to characterize the noise properties of a spline Filtered BackP reject ion (denoted as FBP) reconstruction scheme. More specifically, the paper focuses on angular and radial sampling of projection data and on assumed local properties of the function to be reconstructed. This new method is visually and quantitatively compared to standard sampling used for FBP scheme. In the second section, we recall the sampling geometry adapted to the discrete geometry of the reconstructed image. Properties of the discrete zero order Spline Ramp filter for classic angles and discrete angles generated from Farey's series reconstruction are used to generate their equivalent representations for first order Spline filters. Digital phantoms are used to assess the results and the correctness of the linearity and shift-invariantness assumption for the discrete reconstructions. The filter gain has been studied in the Mojette case since the number of projections can be very different from one angle to another. In the third section, we describe the Spline filter implementation and the continuous/discrete correspondence. In section 4, Poisson noise is added to noise-free onto the projections. The reconstructions between classic angle distribution and Mojette acquisition geometry are compared. Even if the number of bins per projections is fixed for classic FBP while it varies for the Mojette geometry (leading to very different noise behavior per bin) the results of both algorithms are very close. The discussion allows for a general comparison between classic FBP reconstruction and Mojette FBP. The very encouraging results obtained for the Mojette case conclude for the developments of future acquisition devices modeled with the Mojette geometry.