Optimal estimation: Prior free methods and physiological application

Martin Raphan

PhD thesis, Courant Institute of Mathematical Sciences, New York University,
New York, NY, May 2007.

Recipient of the 2008 K. O. Friedrichs prize for an outstanding dissertation in mathematics.


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    • Table of Contents:
    1. Contrast Dependent Receptive Field Size
      1. Why Contrast Dependent Receptive Field Size?
      2. Increased Receptive Field Size through Positive Feedback
      3. Mechanisms for Positive Feedback
      4. Computational Models
      5. Simulations
      6. Discussion
      7. Prelude to Prior-Free
    2. Prior-Free Estimation
      1. Bayes Least Squares (BLS) Estimators
      2. Common Formulations of BLS Estimators
      3. Prior-free reformulation of the BLS estimator
      4. Example estimators
      5. Prior-free reformulation of the mean squared error
      6. Simulations
      7. Discussion
    3. Nonparametric Denoising of Additive Gaussian Noise
      1. Prior-free formulation of BLS estimator for Additive Gaussian Noise
      2. Learning the estimator function from data
      3. Approach to ideal BLS estimator with increase in data
      4. Comparison with Empirical Bayes
      5. Image denoising example
      6. Discussion
    4. Optimal Denoising in Redundant Bases
      1. Stein's Lemma for overcomplete bases
      2. Point Estimators
      3. Optimal nonlinearity
      4. Redundancy improves performance
      5. Simulations
      6. Discussion
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