Analytic estimation of subsample spatial shift using the phases of multidimensional analytic signals

Area of Science:

• Signal Processing
• Image Analysis
• Multidimensional Systems

Background:

• Traditional subsample spatial shift estimation methods often rely on complex cross-correlation functions or cross-spectra.
• Existing techniques can suffer from reduced accuracy with low-sampled signals or complex signal components.

Discussion:

• This work proposes an analytic subsample spatial shift estimation method leveraging the linear phases of n analytic signals derived via the multidimensional Hilbert transform.
• The method provides an analytic solution for n-D shift estimation, circumventing the need for complex cross-correlation or cross-spectra processing.
• Performance is validated against classical estimators, demonstrating superior accuracy in subsample shift estimation, particularly for low-sampled signals.

Key Insights:

• The proposed estimator maintains accuracy with low-sampled signals, a significant advantage over many existing methods.
• It offers an analytical solution to translation estimation problems within block-based motion estimation frameworks.
• The method is successfully applied to motion tracking in ultrasound images, showcasing its practical utility.

Outlook:

• Further exploration of the method's applicability in other imaging modalities and complex signal processing tasks.
• Potential for integration into real-time motion tracking systems for enhanced diagnostic capabilities in ultrasound.
• Development of adaptive algorithms based on this analytic framework for dynamic environments.