Adaptive Iterative Reconstruction

It is well known that, in CT reconstruction, Maximum A Posteriori (MAP) reconstruction based on a Poisson noise model can be well approximated by Penalized Weighted Least Square (PWLS) minimization based on a data dependent Gaussian noise model. We study minimization of the PWLS objective function using the Gradient Descent (GD) method, and show that if an exact inverse of the forward projector exists, the PWLS GD update equation can be translated into an update equation which entirely operates in the image domain In case of non-linear regularization and arbitrary noise model this means that a non-linear image filter must exist which solves the optimization problem. In the general case of non-linear regularization and arbitrary noise model, the analytical computation is not trivial and might lead to image filters which are computationally very expensive. We introduce a new iteration scheme in image space, based on a regularization filter with an anisotropic noise model. Basically, this approximates the statistical data weighting and regularization in PWLS reconstruction. If needed, e.g. for compensation of the non-exactness of backprojector, the image-based regularization loop can be preceded by a raw data based loop without regularization and statistical data weighting. We call this combined iterative reconstruction scheme Adaptive Iterative Reconstruction (AIR). It will be shown that in terms of low-contrast visibility, sharpness-to-noise and contrast-to-noise ratio, PWLS and AIR reconstruction are similar to a high degree of accuracy. In clinical images the noise texture of AIR is also superior to the more artificial texture of PWLS.