BBTools

bbfbp

This function is not yet fully documented. This is a transcript of the text-formatted help.

bbfbp  Create black-box for Filtered Back-Projection
   [BB,DIM2]=bbfbp(DIM1) creates an operator that approximately invert
   the Radon transform using Filtered Back Projection (FBP). This is
   a linear operator, and can therefore be represented as a black-box.

   The operator converts a sinogram of dimension DIM1=[SAMP,K] to an
   image of dimension DIM2. The image dimension may be specified using
   the syntax BB=bbfbp(DIM1,DIM2). The default image is DIM2=[N,N] where
   N=2*floor(SAMP/sqrt(8)).

   The angles in the projection are assumed to be THETA=(0:K-1)*(180/K).
   Options may be passed in the same way as bbradon, and the options
   'len', 'roi', and 'notol' have the same meaning.

   The FBP algorithm is based on a filter to undo the Radon transform,
   but also amplifies noise. To reduce the noise, a cut-off frequency
   may be set as bbfbp(...,'cut',D), where 0<D<=1 is normalized to
   the Nyquist frequency, i.e. the highest possible frequency allowed
   by the discretization (default: D=1).

   To alleviate the effect of the sharp cut-off, which can result in
   "ringing", the filter may also be multiplied by a window:
     'ramp':       Ramp-filter, no window (default)
                   AKA: 'ram-lak', 'rect', or 'none'
     'triangular': Triangular window (AKA 'bartlett')
     'hamming':    Hamming window
     'hanning':    Hanning window (AKA 'hann')
     'blackman':   Blackman window

   Example:
     I0=bbphantom([150,150],'restest');
     figure(1); imagesc(I0); axis image; colormap(gray);

     [bb,dim2,opt]=bbradon(size(I0),0:5:175,'notol');
     S=reshape(bb*I0(:),dim2);
     figure(2); imagesc(S); colormap(gray);

     [bbi,dim3]=bbfbp(dim2,'cut',.75,'hamming','notol');
     I1=reshape(bbi*S(:),dim3);
     figure(3); imagesc(I1); axis image; colormap(gray);

   See also bbradon, bbempoisson,  (image toolbox).

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