A mathematical perspective of ultrasound image representations and image quality criteria

• Published in: The Journal of the Acoustical Society of America 2022-10, Vol.152 (4), p.A183-A183
• Main Author: Hyun, Dongwoon
• Format: Article
• Language: English
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/10.0015967

What is an ultrasound “image”? Where an engineer or physicist may see a quantitative map of physical properties, a physician may see qualitative anatomical features and pathologies. In the past, each image type was evaluated appropriately within its respective context: quantitative image quality was measured with criteria like the contrast-to-noise ratio (CNR), and qualitative images underwent dynamic range transformations to optimize human perception of contrast. Recent non-linear beamforming methods have blurred this line: the produced images are transformed like qualitative images but evaluated with quantitative criteria like CNR. Here, we identify the mathematical flaws in reasoning and suggest rigorous alternatives.An image assigns values to spatial coordinates. Let X denote the set of all possible image values. The mathematical structure endowed on X determines the set of equivalence-preserving transformations. For instance, qualitative images treat X as a general topological space, where images are equivalent under homeomorphisms of X (dynamic range transformations). Quantitative images treat X as a metric space and have fewer equivalence-preserving transformations. These structures determine when criteria like contrast, CNR, generalized CNR, and spatial resolution can be used. To extrapolate these criteria to other contexts, one must use relevant structure-preserving isomorphisms (e.g., histogram matching to preserve information content).