Phantoms 1. Shepp-Logan head phantom 2. Body phantom 3. Modified Shepp-Logan head phantom 4. Strong Modified Shepp-Logan head phantom 5. further Modified Shepp-Logan head phantom 6. crops for the ROI
Truncated projections and their direct reconstruction
Extrapolations Zero extrapolation *0 (a) Constant extrapolation *c (b) Linear extrapolation *(bx+c) Exponential extrapolation *exp(-x/αL) Exponential extrapolation *exp(-(x/αL)^2) (c) Cos extrapolation *cos(x) Quadratic extrapolation *(ax^2+bx+c) (d) Mixed extrapolation *(ax^2+bx+c)exp(-x/α) (e) Mixed extrapolation *(ax^2+bx+c)exp(-(x/α)^2) (f) Original projection without extrapolation (g)
Reconstruction with …menthod Errors of iterative reconstruction without truncation Phantom 5 Iterative reconstruction without truncation Crop of Phantom iterative Reconstruction with truncation Reconstruction without truncation Errors reconstruction without truncation Errors of iterative reconstruction with truncation Number of Projections=180 Distance=0.0253Distance=0.0221 Distance=0.0348Distance=0
Reconstruction with …menthod Phantom 5 Crop of Phantom Reconstruction without truncation Iterative reconstruction without truncation Errors reconstruction without truncation Errors of iterative reconstruction without truncation iterative Reconstruction with truncation Errors of iterative reconstruction with truncation Projections:360, 1st=mix 2, 2ed=exp 2, α1=0.65, α2=0.068,k=-1.04 Distance=0Distance=0.0167 Distance=0.0145Distance=0.0191
Contradiction Our shield (extrapolation) is the best shield, it can resist all spears in the world. Our spear (iteration) is the best spear, it can destroy all shields in the world. Which one would you like to buy? The extrapolation or the iteration?