]> Filtered Backprojection

Filtered Backprojection

Invert the forward matrix using filtered backprojection with a user-supplied regularization parameter.

Function Summary

Syntax:	X = fbp(A, Y, alpha[, CD[, CI]]);
Inputs:	A	Forward matrix
	Y	The residue appropriate to A
	alpha	Regularization parameter, multiplies CI
	CD	Covariance of the data. Optional: identity of not specified
	CI	Covariance of the image. Optional: identity of not specified
Outputs:	X	The reconstructed image

Filtered backprojection applies the following operator to the experimental residue $Y$ to solve for the unknown perturbation $Δ X$

Δ X = A^{†} {(A A^{†} + α I)}^{-1} Y .

The covariance matrices CI and CD are used by analogy with Tikhonov regularization and not by a proper derivation—caveat emptor.