3.2 Iterative Reconstruction (SART/OSEM)

Iterative reconstruction (IR) is often preferred when assumptions behind analytic methods break (low-dose, sparse-view, more complex physics). It typically solves an optimization/statistical estimation problem instead of applying a closed-form inverse.

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Linear model

After discretization:

$$Af=p$$

where (A) is the system matrix/operator, (f) is the image, and (p) are measured projections.

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SART (algebraic)

SART updates the image iteratively using projection residuals, often providing better robustness for sparse-view data.

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OSEM (statistical)

For Poisson-like counts (common in emission tomography), OSEM/EM-style updates are widely used and enforce non-negativity.

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Regularization (L2 / TV)

Common objective forms:

$$\underset{f}{min}\parallel Af-p{\parallel }_2^2+\lambda R(f)$$

where (R(f)) could be L2 (Tikhonov) or TV, etc.

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Next

Deep learning reconstruction: /en/guide/ch03/03-dl-recon