The influence of data-errors in two algorithms for emission CT

Abstract We study the influence of noise in the EM algorithm and ISRA. Both methods have been used for emission computed tomography. In the underlying linear model $$Ax\sim b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>x</mml:mi> <mml:mo>∼</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> </mml:math> the noise can be in the data vector b and/or in the matrix A . Under certain conditions it is shown that the noise error asymptotically grows like $$O(\sqrt{k})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msqrt> <mml:mi>k</mml:mi> </mml:msqrt> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , with k the iteration index. For ISRA we also introduce a relaxation parameter and give conditions under which convergence is maintained.