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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Ax\sim b\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mi>x</mi> <mo>∼</mo> <mi>b</mi> </mrow> </math></EquationSource> </InlineEquation> the noise can be in the data vector <i>b</i> and/or in the matrix <i>A</i>. Under certain conditions it is shown that the noise error asymptotically grows like <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(O(\sqrt{k})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msqrt> <mi>k</mi> </msqrt> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, with <i>k</i> the iteration index. For ISRA we also introduce a relaxation parameter and give conditions under which convergence is maintained.</p>

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

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  • 发表日期：

    2026年1月5日

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  • Tommy Elfving

摘要

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 \(Ax\sim b\) A x ∼ b 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 \(O(\sqrt{k})\) O ( k ) , with k the iteration index. For ISRA we also introduce a relaxation parameter and give conditions under which convergence is maintained.