Improved Poisson intensity estimation: denoising application using Poisson data

Area of Science:

• Statistics
• Computational Science

Background:

• Timmermann and Nowak developed algorithms for estimating means of independent Poisson random variables.
• These algorithms utilize a multiscale model with a beta-mixture density function.
• A simplification was made by assuming known beta parameters and estimating only one mixture parameter.

Purpose of the Study:

• To enhance the accuracy of Poisson random variable mean estimation.
• To address limitations in existing density estimation methods for Poisson data.
• To evaluate the proposed method's performance in a practical application.

Main Methods:

• Generating training data from observed Poisson data.
• Computing maximum likelihood estimates for all beta-mixture parameters.
• Applying the modified estimation technique to a Poisson data denoising task.

Main Results:

• The proposed maximum likelihood approach yields improved performance compared to existing methods.
• Accurate estimation of all beta-mixture parameters was achieved.
• Enhanced results were observed in the denoising application using Poisson data.

Conclusions:

• The developed maximum likelihood estimation method offers a more robust approach for Poisson random variable mean estimation.
• This enhancement leads to better performance in applications like signal denoising.
• The study highlights the benefits of estimating all mixture parameters for improved statistical modeling.