Computes the Square Root of the Hessian Row Sum of the objective function. More...
Namespaces | |
| stir | |
| Namespace for the STIR library (and some/most of its applications) | |
Functions | |
| int | main (int argc, char *argv[]) |
Detailed Description
Computes the Square Root of the Hessian Row Sum of the objective function.
- Usage
compute_sqrt_Hessian_row_sum compute_sqrt_Hessian_row_sum.par
This can be used to compute a spatially variant penalty strength (kappa) image. This utility uses methods proposed by: Tsai, Y.-J., Schramm, G., Ahn, S., Bousse, A., Arridge, S., Nuyts, J., Hutton, B. F., Stearns, C. W., & Thielemans, K. (2020). Benefits of Using a Spatially-Variant Penalty Strength With Anatomical Priors in PET Reconstruction. IEEE Transactions on Medical Imaging, 39(1), 11-22. https://doi.org/10.1109/TMI.2019.2913889
Based upon the value of "use approximate hessian" in the parameter file, either of two methods can be used to compute the spatially variant penalty strength, a.k.a. kappa. Both of the methods compute the square root of the Hessian row sum of the objective / likelihood function.
, or![\[ \hat\kappa = \sqrt{ P^T \bigg( \frac{y}{ (P\lambda+a)^2 } \bigg) P1 } \]](form_152.png)
![\[ \tilde\kappa = \sqrt{ P^T \bigg( \frac{1}{y} \bigg)P1 } \]](form_153.png)
This utility may be used to generate the spatially variant penalty strength (kappa) images.
