MRI reconstruction matrices from Mark Bydder, UCSD.
Note that that A is sparse and rectangular, and b is complex.
Added March, 2006.
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Excerpts of description, from email:
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Inside there is a matrix A and a RHS vector b. Usually we want to
solve Ax=b, for example x = lsqr(A,b,0,10) uses conjugate gradient
on the normal equations to give an approximate answer. The data b are
Fourier coefficients at arbitrary locations (in this case, in a spiral
trajectory) and the matrix interpolates these data onto
a regular grid suitable for FFT. So it's like non-uniform FFT.
Please let me know if you find this matrix helpful or want to try some
other (similar) matrices, eg. with radial trajectories.
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The matrix I sent derives from a technique called regridding - a process
of interpolating data at arbitrary locations onto an equally spaced grid.
Eg. we sample a function f at two points 0