Extrapolation and iteration for the problem of LFOV Dr. Shuangren Zhao Research Associate Radiation Physics Department Princess Margaret Hospital.

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Presentation transcript:

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 Crop outside ROI is the image outside the ROI Projections we study are truncated

The Influence of truncated projections

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)

Extrapolations for phantom 3

Extrapolations for phantom 3 and 4

Quadratic extrapolation (ax^2+bx+c) (d) Projection should positive:

Update from quadratic extrapolation to mixed extrapolation {exp(-x/aL)(ax^2+bx+c)}

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 (ax 2 +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 extrapolations using phantom 1

Reconstructions with different extrapolations using 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 1 with 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 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= 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= 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?