Bruder Herbert, Abstract Co-Author: Employee, Siemens AG

Rainer Raupach PhD, Abstract Co-Author: Employee, Siemens AG, Forchheim, Germany

Johann Sunnegardh, Abstract Co-Author: Employee, Siemens AG

Karl Stierstorfer PhD, Abstract Co-Author: Employee, Siemens AG

Thomas G. Flohr PhD, Presenter: Employee, Siemens AG

We demonstrate that statistical iterative reconstruction (IR) can be translated to non-linear image processing in case of data dependent Gaussian noise.

Statistical iterative reconstruction is known to produce images with better signal-to-noise ratio compared to conventional FBP-type reconstruction. Originally based on the Poisson noise model, it can be simplified to a data dependent Gaussian noise model for large numbers of quanta, manifesting as a signal weighting of sinogram data according to their statistical reliability. Based on the update equation of Iterative Filtered Backprojection reconstruction (IFBP), we introduce the signal weighting operator (method A) and show that, even in case of non-linear regularization, under certain conditions the update equation can be formulated as an iterative reconstruction in image space. We also derive an approximation of iterative reconstruction in image space based on a non-isotropic noise model (method B) which basically establishes the same image characteristics as method A.

The results show that, in the case of a linear regularisation term, the final image can be expressed as the result of a linear operator in image space applied to the original image. Moreover, in case of nonlinear regularization it is demonstrated that method A and method B are equivalent regarding noise characteristic and spatial resolution. For non-symmetric objects, non-isotropic image noise can be substantially reduced, revealing previously invisible low contrast details. Image sharpness of objects with contrast beyond the noise level is maintained.

We prove that statistical iterative reconstruction with data dependent Gaussian noise and noise weighted IFBP are equivalent. Under certain conditions, it can even be translated into a non-linear image processing. If iterative reconstruction is to be used for the reduction of artifacts due to the non-exactness of the reconstruction, a few IFBP iterations can be applied prior to image space processing.

Statistical iterative reconstruction with a data dependent Gaussian noise model can be translated into non-linear image processing, substantially speeding up IR without compromising image quality.

Herbert, B, Raupach, R, Sunnegardh, J, Stierstorfer, K, Flohr, T, Translation of Statistical Iterative Reconstruction into Non-linear Image Processing.  Radiological Society of North America 2010 Scientific Assembly and Annual Meeting, November 28 - December 3, 2010 ,Chicago IL. http://archive.rsna.org/2010/9014878.html