Maximum likelihood, least squares, and penalized least squares for PET

Area of Science:

• Medical imaging
• Computational mathematics
• Image reconstruction

Background:

• The expectation-maximization (EM) algorithm is standard for positron emission tomography (PET) image reconstruction.
• EM algorithm maximizes log-likelihood and handles non-negativity constraints.

Purpose of the Study:

• To adapt scaled steepest descent algorithms for least squares in PET reconstruction.
• To accelerate computation using conjugate gradient methods.

Main Methods:

• Applied scaled steepest descent to least squares objective function.
• Integrated conjugate gradient approach for acceleration.
• Evaluated penalized least squares functions for smoother images.

Main Results:

• Demonstrated applicability of scaled steepest descent to least squares.
• Achieved significant computational speed-up (approx. 3x) with conjugate gradient acceleration.
• Successfully applied methods to penalized least squares for image smoothing.

Conclusions:

• Conjugate gradient acceleration offers substantial computational gains for PET image reconstruction.
• The adapted methods are effective for producing smoother PET images using penalized least squares techniques.