Performing MLEM with Response Matrix for 4pi Imager and 1x3 Vector Input

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SUMMARY

The discussion focuses on implementing the Maximum Likelihood Expectation Maximization (MLEM) algorithm using a response matrix for a 4pi imager with dimensions (16 x 16 x 18) x (72 x 36). The user seeks guidance on how to perform MLEM iterations with a 1x3 vector input consisting of two detector values and an angle, despite literature indicating a need for a 1 x (72 x 36) vector format. Clarification on the definitions of MLEM and 4pi kinematic imaging is also requested to aid understanding.

PREREQUISITES
  • Understanding of Maximum Likelihood Expectation Maximization (MLEM) algorithm
  • Familiarity with response matrices in imaging systems
  • Knowledge of 4pi kinematic imaging techniques
  • Basic proficiency in vector mathematics and dimensional analysis
NEXT STEPS
  • Research the implementation of MLEM in imaging systems
  • Study the structure and application of response matrices in 4pi imaging
  • Learn about vectorized image formats and their role in MLEM
  • Explore the theoretical foundations of 4pi kinematic imaging
USEFUL FOR

Researchers and practitioners in imaging science, particularly those working with 4pi imaging systems and MLEM algorithms, as well as students seeking to deepen their understanding of advanced imaging techniques.

a.glick
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TL;DR
I am studying 4pi kinematic imaging with a neutron scatter camera and want to perform MLEM given det1, det2, and theta values for my cones.
I have a response matrix for my 4pi imager to perform MLEM that has dimensions:

(16 x 16 x 18) x (72 x 36) which is Observation Bins x Source Bins.

I'm told that I can use MLEM to create an image by feeding in a 1x3 vector of

det1, det2, theta

into the MLEM algorithm. Where det1, det2 are the 2 detectors a particle interacts with in the kinematic imaging and theta is the opening angle of a cone of probability for the particle's incident direction. However every paper I've read says I need a vectorized image (or simple backprojection) that has a 1 x (72 x 36) dimensional form. How can I do the MLEM iteration in my case?
 
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You'll have a much better chance of getting answers to your questions if you provide more information.
  • What is MLEM? We shouldn't need to do a search to find what this algorithm is. A link to a description of this algorithm would be helpful.
  • What is 4pi kinematic imaging?
 
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