Ultrasound Lesion Detectability as a Distance Between Probability Measures

Area of Science:

• Medical Imaging
• Ultrasound Technology
• Image Analysis

Background:

• Lesion detectability (LD) is crucial for assessing ultrasound imaging performance.
• Contrast-to-noise ratio (CNR) is a common LD metric but is sensitive to dynamic range changes.
• Generalized CNR (gCNR) offers a robust, histogram-based alternative.

Purpose of the Study:

• To evaluate the shortcomings of CNR and the strengths of gCNR for lesion detectability.
• To mathematically define LD using measure theory and probability measures.
• To explore the implications of measure-theoretic LD in simulations and provide practical guidance.

Main Methods:

• Formulated lesion detectability as a distance between empirical probability measures (histograms).
• Proved gCNR equals total variation distance and is related to the ideal observer's error rate.
• Conducted simulation studies to analyze histogram distances and their properties.

Main Results:

• Identified key limitations of CNR and advantages of gCNR for modern ultrasound beamformers.
• Demonstrated that gCNR is equivalent to total variation distance and linked to ideal observer performance.
• Found histogram distances are influenced by bin selection and spatial resolution, and are invariant to dynamic range transformations.

Conclusions:

• gCNR provides a more reliable measure of lesion detectability than CNR, particularly in the presence of dynamic range variations.
• Measure theory provides a robust framework for understanding lesion detectability metrics.
• Quantitative image comparisons require careful consideration of dynamic range and units; histogram matching can facilitate comparisons.