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1 imposes the condition that the sampling lattice L be such that the translated sets K0 (ϑ, b) + η, η ∈ L⊥ are disjoint. In terms of the lattice parameters d, N and P these conditions are as follows: For the standard lattice N = 0, and the reciprocal lattice L⊥ equals L⊥ = {(P k1 , 2πk2 /d), k1 , k2 ∈ ZZ}. For reasons of efficiency as discussed above we let P = 2p be even. The translated sets K0 (ϑ, b) + η, η ∈ L⊥ are disjoint if and only if d < π/b, p > b/ϑ, P = 2p. (58) For the interlaced lattice we again let K = K0 (ϑ, b) as in (56).
M. Lewitt, Reconstruction algorithms: transform methods, Proc. IEEE, 71 (1983), pp. 390-408. [50] R. M. Lewitt, R. H. T. Bates, and T. M. Peters, Image reconstruction from projections: II: Modified back-projection methods, Optik, 50 (1978), pp. 85-109. [51] B. F. Logan, The uncertainty principle in reconstructing functions from projections, Duke Math. , 42 (1975), pp. 661-706. [52] A. K. Louis, Nonuniqueness in inverse Radon problems: the frequency distribution of the ghosts, Math. Z. 185 (1984), pp.
07,roi,P). m %Parallel-beam filtered backprojection algorithm % for the standard lattice % Last revision: August 29, 2001 %specify input parameters here p=200; %number of view angles between 0 and pi q=64; %q=1/d, d = detector spacing MX=128; MY = 128; %matrix dimensions roi=[-1 1 -1 1]; %roi=[xmin xmax ymin ymax] %region of interest where %reconstruction is computed circle = 1; % If circle = 1 image computed only inside % circle inscribed in roi. %Specify parameters of ellipses for mathematical phantom.