iradon_d2d_mstage

3D and 4D filtered backprojection image reconstruction from 1D projections. Sequential 2D reconstructions (multi-stage) are employed.

Syntax:

image = iradon_d2d_mstage(Pela, radon_pars, recon_pars)

Description:

3D and 4D filtered backprojection image reconstruction from 1D projections. Sequential 2D reconstructions (multi-stage) are employed. Equal angular projection scheme is required. Definition of angles is shown in the figure below.
Θ and φ are spatial angles. α is spectral angle discussed in Iradon toolbox.
Pela - equal linear angle sampled projections (float) for 3D: size(Pela)=[points_in_projection, 1, N_Θ, N_φ] for 4D: size(Pela)=[points_in_projection, N_Θ, N_φ, N_α] radon_pars - projection parameters (structure) ~.ELA - equal angle gradient scheme parameters (structure) ~.imtype - Image type (int, 1 for 4D, 14 for 3D) ~.nPolar - Number of polar (N_Θ) angles (int) ~.nAz - Number of azimuthal (N_φ) angles (int) ~.nSpec - Number of spectral (N_α) angles (int) ~.size - length of the spacial projection (float, in cm) recon_pars - reconstruction parameters (structure) ~.nBins - Image size in all dimensions (int, in voxels) ~.Filter - (string, 'ram-lak'/'shepp-logan'/'cosine'/'hamming'/'hann') ~.FilterCutOff - Filter cut off, part of full bandwidth (float, 0 to 1) ~.InterpFactor - Projection interpolation factor, (int, 1/2/4/etc) ~.Interpolation - Inerpolation method, (string, 'none'/'sinc'/'spline'/'linear') ~.CodeFlag - Reconstruction code (string, 'C'/'MATLAB'/'FORTRAN') ~.zeropadding - zeropadding factor (int, >= 1) image - reconstructed object Number of bins in reconstructed matrix in all dimensions is equal to the number of points in projections

Example:

% Generate equal solid angle layout of projections fbp_struct.nAz = 36; fbp_struct.nPolar = 36; fbp_struct.imtype = iradon_GetFBPImageType('XYZ'); fbp_struct.MaxGradient = 1; % maximum gradient (G/cm) fbp_struct.angle_sampling = 'UNIFORM_SPATIAL_FLIP'; pars = iradon_FBPGradTable(fbp_struct); % Radon transformation parameters radon_pars.un = pars.G; % unit vectors of the gradients radon_pars.size = 5; % projection spatial support (cm) radon_pars.nBins = 64; % length of the projection spatial support % Phantom parameters phantom.r = 2.2; % radius of the sphere (cm) phantom.offset = [0.1,-0.1,0]; % offset of the sphere (cm) % use radon_c2d_sphere to generate analytic projections P = radon_c2d_sphere(phantom, radon_pars); % convert serial projection layout into iradon_d2d_mstage layout PP = zeros(size(P,1), fbp_struct.nAz*fbp_struct.nPolar); PP(:,pars.gidx) = P; Pela = reshape(PP, [size(P,1), 1, fbp_struct.nAz, fbp_struct.nPolar]); % Interpolate projections to the uniform angular scheme switch fbp_struct.angle_sampling case {'UNIFORM_SPATIAL_FLIP', 'UNIFORM_SPATIAL'} Pela=iradon_InterpToUniformAngle(Pela, 'imgData'); end radon_pars.ELA = fbp_struct; recon_pars.size = 5; % ignored, radon_pars.size is used instead recon_pars.nBins = 128; % ignored, radon_pars.nBins is used instead recon_pars.Filter = 'ram-lak'; recon_pars.FilterCutOff = 1.0; recon_pars.Interpolation = 'spline'; recon_pars.InterpFactor = 2; recon_pars.CodeFlag = 'C'; recon_pars.zeropadding = 2; % any number >= 1 % call the reconstruction program and display result image = iradon_d2d_mstage(Pela, radon_pars, recon_pars); ibGUI(image);

Legend: EPR-IT functions; MATLAB functions; comments.

[1] K.H. Ahn, H.J. Halpern, Spatially uniform sampling in 4-D EPR spectral-spatial imaging, J. Magn. Reson., 185 (2007) 152-158 DOI 10.1016/j.jmr.2006.12.007.
[2] K.H. Ahn, H.J. Halpern, Simulation of 4D spectral-spatial EPR images, J. Magn. Reson., 187 (2007) 1-9 DOI 10.1016/j.jmr.2007.02.013.
[3] K.H. Ahn, H.J. Halpern, Comparison of local and global angular interpolation applied to spectral-spatial EPR image reconstruction, Medical Physics, 34 (2007) 1047-1052 Doi 10.1118/1.2514090.

See also:

radon_c2d_sphere, iradon_InterpToUniformAngle