extrapolation and iteration for the problem of lfov
DESCRIPTION
Extrapolation and iteration for the problem of LFOV. Dr. Shuangren Zhao Research Associate Radiation Physics Department Princess Margaret Hospital. What is LFOV and ROI. LFOV is “Limited field of view” ROI is region of interest Crop is the image inside the ROI - PowerPoint PPT PresentationTRANSCRIPT
Extrapolation and iteration for the problem of LFOV
Dr. Shuangren Zhao
Research Associate
Radiation Physics Department
Princess Margaret Hospital
What is LFOV and ROILFOV is “Limited field of view”
ROI is region of interest
Crop is the image inside the ROI
Crop outside ROI is the image outside the ROI
Projections we study are truncated
The Influence of truncated projections
Phantoms1. Shepp-Logan head phantom2. Body phantom
3. Modified Shepp-Logan head phantom4. Strong Modified Shepp-Logan head phantom5. further Modified Shepp-Logan head phantom 6. crops for the ROI
Truncated projectionsand 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)
Extrapolations for phantom 3
Extrapolations for phantom 3 and 4
Quadratic extrapolation(ax^2+bx+c) (d)
Projection should positive:
0 5 10 15 20 25 30 35-100
-50
0
50
100
150
200
250
0 5 10 15 20 25 30 350
50
100
150
200
250
Update from quadratic extrapolation to mixed extrapolation {exp(-x/aL)(ax^2+bx+c)}
500 550 600 650 700 750
-50
0
50
100
150
500 550 600 650 700
-40
-20
0
20
40
60
80
100
120
140
160
Different fits for the boundary values:1. The values of projections 2. The differential values of the projections
Update for fitting boundary values
Update for the mixed extrapolation of (ax2+bx+c)exp(-x/αL)
Update for the mixed extrapolation of (ax2+bx+c)exp(-x/αL)
The distances of reconstructed images to the image of phantom
ideal distance: reconstruction with non-truncated projections.
Reconstructions with different extrapolationsusing phantom 1
Reconstructions with different extrapolationsusing phantom 2
Reconstructions with different extrapolations using phantom 3
Reconstructions with different extrapolations using phantom 4
Reconstructions with different extrapolations using phantom 5
Iterative reconstruction algorithm:
Projections filter (for phantom 2)
Iterative reconstruction results for the phantom 1with exp(-(x/αL)^2) extrapolation α=0.5
Iterative reconstruction results for the phantom 2 with exp(-(x/αL)^2) extrapolation α =0.5
Iterative reconstruction results for the phantom 3 with exp(-(x/αL)^2) extrapolation α =0.5
Iteration results for phantom 5 with exp(-(x/αL)^2)(ax^2+bx+c) and exp(-(x/αL)^2)
extrapolation α=0.5
Further find the optimal parameters for for phantom 5
The stability of the parameters
Further find the optimal parameters for for phantom 4
Further find the optimal parameters for for phantom 5
The stability of the parameters
Find the optimal parameters for for phantom 4
Reconstruction with …menthod
Errors of iterative reconstruction without truncation
Phantom 5Iterative reconstructionwithout truncation
Crop of Phantom
iterative Reconstructionwith truncation
Reconstruction without truncation
Errors reconstruction without truncation
Errors of iterative reconstruction with truncation
Number of Projections=180
Distance=0.0253Distance=0.0221Distance=0.0348Distance=0
Reconstruction with …menthod
Phantom 5
Crop of Phantom
Reconstruction without truncation
Iterative reconstructionwithout truncation
Errors reconstruction without truncation
Errors of iterative reconstruction without truncation
iterative Reconstructionwith 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=0 Distance=0.0167 Distance=0.0145 Distance=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?