Toward Optimal Computation of Ultrasound Image Reconstruction Using CPU and GPU

An ultrasound image is reconstructed from echo signals received by array elements of a transducer. The time of flight of the echo depends on the distance between the focus to the array elements. The received echo signals have to be delayed to make their wave fronts and phase coherent before summing the signals. In digital beamforming, the delays are not always located at the sampled points. Generally, the values of the delayed signals are estimated by the values of the nearest samples. This method is fast and easy, however inaccurate. There are other methods available for increasing the accuracy of the delayed signals and, consequently, the quality of the beamformed signals; for example, the in-phase (I)/quadrature (Q) interpolation, which is more time consuming but provides more accurate values than the nearest samples. This paper compares the signals after dynamic receive beamforming, in which the echo signals are delayed using two methods, the nearest sample method and the I/Q interpolation method. The comparisons of the visual qualities of the reconstructed images and the qualities of the beamformed signals are reported. Moreover, the computational speeds of these methods are also optimized by reorganizing the data processing flow and by applying the graphics processing unit (GPU). The use of single and double precision floating-point formats of the intermediate data is also considered. The speeds with and without these optimizations are also compared

Noise analysis and improvement of displacement vector estimation from angular displacements

Elastography or elasticity imaging techniques typically image local strains or Young’s modulus variations along the insonification direction. Recently, techniques that utilize angular displacement estimates obtained from multiple angular insonification of tissue have been reported. Angular displacement estimates obtained along different angular insonification directions have been utilized for spatial-angular compounding to reduce noise artifacts in axial-strain elastograms, and for estimating the axial and lateral components of the displacement vector and the corresponding strain tensors. However, these angular strain estimation techniques were based on the assumption that noise artifacts in the displacement estimates were independent and identically distributed and that the displacement estimates could be modeled using a zero-mean normal probability density function. Independent and identically distributed random variables refer to a collection of variables that have the same probability distribution and are mutually independent. In this article, a modified least-squares approach is presented that does not make any assumption regarding the noise in the angular displacement estimates and incorporates displacement noise artifacts into the strain estimation process using a cross-correlation matrix of the displacement noise artifacts. Two methods for estimating noise artifacts from the displacement images are described. Improvements in the strain tensor (axial and lateral) estimation performance are illustrated utilizing both simulation data obtained using finite-element analysis and experimental data obtained from a tissue-mimicking phantom. Improvements in the strain estimation performance are quantified in terms of the elastographic signal-to-noise and contrast-to-noise ratios obtained with and without the incorporation of the displacement noise artifacts into the least-squares strain estimator