Covariance Decomposition of Ultrasonic Backscatter: Application to Estimation-based Image Formation

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Medical ultrasound imaging is portable, real-time, and inexpensive, with countless applications across a range of pathologies and imaging targets. Despite these advantages, many patients suffer from suboptimal image quality, hampered by acoustic clutter which can reduce contrast and obscure targets of interest. Obesity, in particular, has been linked to increased rates of inadequate visualization and reduced diagnostic efficacy of ultrasound imaging. Rising obesity rates support the need for improved image quality in challenging imaging environments.

Advanced beamforming methods may offer an opportunity to mitigate sources of acoustic clutter and improve image quality. Many methods have been proposed in the literature, which have been shown to improve aspects of image quality over conventional delay-and-sum beamforming. However, these methods often exchange enhanced contrast for coarse speckle texture, distort the native echogenicty of the imaging target, and/or employ ad hoc approaches to image formation that lack a sound basis in physical principles.

This dissertation presents a new paradigm for image formation: an estimation-based approach to image the statistical properties of tissue. The foundation for this approach is the fundamental observation that targets in medical ultrasound consist of inherently unresolvable, diffuse scatterers. Backscattered echoes from diffuse targets can be characterized by their statistical properties, which are classically described by the van Cittert-Zernike (VCZ) theorem under a statistically stationary, spatially incoherent scattering model.

This work applies the VCZ theorem to a piecewise-stationary scattering model. This application yields a key insight: the spatial covariance of the received echo data is the linear superposition of covariances from distinct spatial regions in the imaging target. This relationship is derived from first principles and validated through simulation studies demonstrating superposition and scaling.

Under the framework of spatial covariance decomposition, a novel method to image the statistical properties of stochastic targets is derived. Multi-covariate Imaging of Sub-resolution Targets, or MIST, employs an estimation-based method to image the on-axis contributions to the echo data covariance matrix. MIST covariance models are defined based on a spatial decomposition of the theoretical transmit intensity distribution into contributions received on- and off-axis. The mathematical foundations of the MIST estimator are analytically derived, and imaging performance is evaluated in simulation, phantom, and in vivo studies, which demonstrate consistent improvements in contrast-to-noise ratio (CNR) and speckle signal-to-noise ratio (SNR) across imaging targets, while preserving target echogenicity and lateral resolution.

In a pilot clinical study, MIST image quality was evaluated in fifteen patients at the Duke Fetal Diagnostic Center, using data collected with the Verasonics Vantage 256 research scanner from a variety of fetal structures in first- and second-trimester pregnancies. Patient body habitus varied from underweight to obese (body mass indices of 17.5--58.3). Across 152 images from all patients, MIST demonstrated improved contrast (93.2% of images), CNR (99.1%) and speckle SNR (99.5%) over matched B-Mode images. Image quality improvements were consistent across patient body habitus and between fundamental and harmonic imaging modes, showing promising indications for MIST in fetal applications.

To characterize the intrinsic tradeoffs associated with MIST, the effects of varying two key parameters on image quality were explored: (1) the spatial cutoff delineating the on- from off-axis covariance models and (2) the degree of spatial averaging of the measured echo data covariance matrix. The results demonstrated a fundamental tradeoff between resolution and speckle texture. This fundamental tradeoff was compared to similar tradeoffs in spatial and frequency compounding. MIST was shown to provide greater improvements in speckle texture at a comparable resolution to each method. Across these tunable parameters, MIST also demonstrated stable performance in noise and fidelity to native contrast. These results present a framework for parameter selection in MIST to maximize speckle SNR without an appreciable loss in resolution.

Like many coherence-based imaging methods, MIST suffers from reduced image quality outside the depth of field for focused ultrasound transmissions. To extend the depth of field, synthetic aperture focusing was applied to MIST under focused, plane wave and diverging wave transmit geometries. Synthetic aperture MIST demonstrated consistent improvements in image quality over conventional dynamic receive MIST, with approximately equivalent results between transmit geometries. In an in vivo liver example, synthetic aperture MIST images demonstrated 16.8 dB and 16.6% improvements in contrast and CNR, respectively, over dynamic receive MIST images, as well as 17.4 dB and 32.3% improvements over synthetic aperture B-Mode. Simulation and experimental results indicate wide applicability of MIST to synthetic aperture focusing methods.

Lastly, MIST imaging performance in multi-dimensional arrays was evaluated through a preliminary simulation study. MIST images were formed using 1-D, 1.75-D, and 2-D transducer geometries on a number of targets with a range of native contrast values. MIST image quality was demonstrated to be stable in the presence of noise across array geometries. Preliminary results showed substantial improvements in contrast, speckle SNR, and lesion detectability metrics with only a modest increase in system complexity.

In summary, Multi-covariate Imaging of Sub-resolution Targets is a novel approach to image the statistical properties of diffuse scattering targets, based on a spatial decomposition of aperture domain covariance into on- and off-axis contributions. Simulated and experimental results indicate significant improvements of image quality over conventional methods, promising preliminary clinical data, and feasibility under modern focusing schemes and advanced hardware. This work suggests MIST may greatly benefit image quality patients in patients for whom conventional methods fail.





Morgan, Matthew Robert (2020). Covariance Decomposition of Ultrasonic Backscatter: Application to Estimation-based Image Formation. Dissertation, Duke University. Retrieved from


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