Evaluation of uncertainty for regularized deconvolution: A case study in hydrophone measurements

Area of Science:

• Dynamic Metrology
• Measurement Science
• Signal Processing

Background:

• Estimating measurands in dynamic metrology often requires deconvolution, an ill-posed inverse problem.
• Existing deconvolution methods require regularization for stable results, but evaluating measurement uncertainty remains a challenge.
• The uncertainty contribution from regularization significantly impacts estimation results.

Purpose of the Study:

• To propose a versatile approach for expressing prior knowledge in regularized deconvolution.
• To enable the derivation of uncertainty associated with regularization methods in line with metrology guidelines.
• To address the unsolved issue of measurement uncertainty evaluation in dynamic metrology.

Main Methods:

• A flexible, low-dimensional modeling approach for an upper bound on the measurand's magnitude spectrum is proposed.
• This upper bound facilitates the derivation of regularization uncertainty.
• The method is demonstrated using hydrophone measurements in medical ultrasound (up to 7.5 MHz).

Main Results:

• The proposed approach allows for the derivation of regularization uncertainty consistent with metrology guidelines.
• It offers a versatile framework applicable to various estimation methods in dynamic metrology.
• The case study demonstrates the method's effectiveness in a practical scenario.

Conclusions:

• The developed method provides a robust solution for uncertainty evaluation in regularized deconvolution.
• It enhances the reliability and accuracy of estimations in dynamic metrology.
• The approach is broadly applicable to frequency-domain estimation problems requiring regularization.