Misspecified Cramér-Rao lower bound with Poisson statistics and its application in localization microscopy

Area of Science:

• Optics and Photonics
• Statistical Physics
• Biophysical Imaging

Background:

• Localization microscopy (LM) uses statistical models to estimate emitter locations and theoretical accuracy bounds.
• The Cramér-Rao lower bound (CRLB) is a standard performance metric, assuming perfect model-data agreement.
• Experimental uncertainties frequently cause model-data mismatch, invalidating CRLB accuracy.

Purpose of the Study:

• To derive and analyze the Misspecified Cramér-Rao Bound (MCRB) for localization microscopy.
• To quantify the impact of experimental imperfections on localization accuracy limits.
• To provide a framework for understanding performance bounds under model mismatch.

Main Methods:

• Derivation of the MCRB for various LM configurations.
• Analysis of MCRB behavior under different Poisson statistics.
• Quantitative assessment of experimental uncertainty effects on localization precision.

Main Results:

• The MCRB provides a more accurate lower bound on localization error than CRLB when models are misspecified.
• Experimental imperfections significantly affect achievable localization accuracy.
• The derived MCRB framework elucidates the impact of aberrations, calibration errors, and misalignment.

Conclusions:

• The MCRB is essential for realistic performance evaluation in localization microscopy.
• Understanding model-data mismatch is critical for advancing LM precision.
• This work offers a quantitative tool for optimizing LM experimental designs and data analysis.