Short-lag spatial coherence imaging on matrix arrays, Part 1: Beamforming methods and simulation studies

Abstract

Short-lag spatial coherence (SLSC) imaging is a beamforming technique that has demonstrated improved imaging performance compared with conventional B-mode imaging in previous studies. Thus far, the use of 1-D arrays has limited coherence measurements and SLSC imaging to a single dimension. Here, the SLSC algorithm is extended for use on 2-D matrix array transducers and applied in a simulation study examining imaging performance as a function of subaperture configuration and of incoherent channel noise. SLSC images generated with a 2-D array yielded superior contrast-to-noise ratio (CNR) and texture SNR measurements over SLSC images made on a corresponding 1-D array and over B-mode imaging. SLSC images generated with square subapertures were found to be superior to SLSC images generated with subapertures of equal surface area that spanned the whole array in one dimension. Subaperture beamforming was found to have little effect on SLSC imaging performance for subapertures up to 8 × 8 elements in size on a 64 × 64 element transducer. Additionally, the use of 8 × 8, 4 × 4, and 2 × 2 element subapertures provided 8, 4, and 2 times improvement in channel SNR along with 2640-, 328-, and 25-fold reduction in computation time, respectively. These results indicate that volumetric SLSC imaging is readily applicable to existing 2-D arrays that employ subaperture beamforming.

Short-lag spatial coherence imaging on matrix arrays, Part II: Phantom and in vivo experiments

“…Spatial coherence can be expressed as spatial correlation and further simplified to a product of two triangle functions when the diffuse scatterers are insonified with a narrowband pulse from an unapodized rectangular aperture. The spatial correlation for this case (of diffuse scatterers) has been derived in Part I [7] and is given here again: $$R_{DS}(\Delta x,\Delta y)=true(1-true\mid \frac{\Delta x}{D_x}true\mid true)true(1-true\mid \frac{\Delta y}{D_y}true\mid true),$$ In 1, Δ x and Δ y denote the distance between two points in the aperture plane, and D x and D y denote the transmit aperture size in the x and y dimensions, respectively. The spatial correlation of the pressure field can be estimated from the signals of the individual elements of a matrix array as $$\widehat{R}(i,j)=\frac{\sum _{n=n_1}^{n_2}{s}_i\left(n\right)s_j\left(n\right)}{\sqrt{\sum _{n=n_1}^{n_2}{s}_i^2\left(n\right)\sum _{n=n_1}^{n_2}{s}_j^2\left(n\right)}},$$ where i and j are two elements on the 2-D aperture, s i (n) and s j (n) are the signals sampled by those elements, n is a sample number in the time dimension, and the difference n 2 – n 1 represents the axial kernel length used to calculate interelement correlation and is typically on the order of a wavelength.…”

“…Then, to obtain a single SLSC voxel, $\widehat{R}(i,j)$ is computed (by applying equation 2 to the individual-element signals) and summed over all short-lag pairs of i and j . For a complete SLSC volume, the last step is repeated at each depth for every received individual-element data set [7]. …”

“…We presented a theoretical model for applying SLSC imaging to 2-D arrays as well as simulations showing that volumetric SLSC imaging improves lesion detectability compared to conventional 3-D delay-and-sum imaging [7]. Here, we demonstrate the feasibility of volumetric SLSC imaging in vivo on a modified commercial 3-D ultrasound system.…”

“…In a companion paper [7], we extended the use of a recently developed beamforming method, short-lag spatial coherence (SLSC) imaging [8], to volumetric data in an attempt to improve image quality in clinical 3-D ultrasound. We presented a theoretical model for applying SLSC imaging to 2-D arrays as well as simulations showing that volumetric SLSC imaging improves lesion detectability compared to conventional 3-D delay-and-sum imaging [7].…”

“…A companion paper explored the performance of the SLSC method on simulated volumetric data and showed that for small 2-D subapertures, partial beamforming within subapertures does not degrade the SLSC-image quality [7]. In the following, we demonstrate the concept of volumetric SLSC imaging using phantom and in vivo liver data from a commercial matrix array and 3-D ultrasound scanner.…”