2009 GUI Interaction E - Inverse Problem Solving

GOAL: Solve inverse problem using Standard Diffusion and Monte Carlo Models.

I. Impact of Optical Properties on Spatially-Resolved Reflectance

  1. On the "Inverse" Panel select: (a) Forward Model Engine: Scaled Monte Carlo (g=0.8), Inverse Model Engine: Standard Diffusion (Analytic - Point Source) and (c) Solution Domain: Steady State(R(ρ)).
  2. Select start and stop locations to 0.5 and 9.5 mm, respectively with 10 points (every 1 mm).
  3. Set Optimization Parameters to: μa and μ's.
  4. Simulate measured data: set Forward Simulation Optical Properties to: μa = 1 mm-1, μ's = 1 mm-1, g = 0.8 and n = 1.4 and 2% noise.
  5. Plot Measured Data and make sure "Hold On" is checked.
  6. Set Initial Guess Optical Properties to: μa = 0.05 mm-1, μ's = 1.5 mm-1, g = 0.8 and n = 1.4.
  7. Plot Initial Guess.
  8. Press "Run Inverse Solver".
  1. To what optical property values did the inverse solver converge? (Scroll to the bottom of the page to see the output).
  2. Why are the converged values not exactly the forward simulation optical properties?
  3. Perform the same analysis with 0% noise added to the simulated measured data. How accurate are the converged properties now?

II. Change Inverse Model Engine

  1. Perform the same analysis changing the Inverse Model Engine to Monte Carlo.
  2. Which Model Engine produced the more accurate converged values?

III. Change number of detectors

  1. Repeat II using only 2 detectors. Can you strategically place the two detectors to obtain the same accuracy in the converged values as you obtained with 10 detectors?
  2. Use the analysis plots of ∂R/∂μa and ∂R/∂μ's to help guide their placement.