Ultrasound tomography for simultaneous reconstruction of acoustic density, attenuation, and compressibility profiles

Abstract

A fast and efficient forward scattering solver is developed for use in ultrasound tomography. The solver is formulated so as to enable the calculation of scattering from large and relatively high-contrast objects with inhomogeneous physical properties that vary simultaneously in acoustic attenuation, compressibility, and density. It is based on the method of moments in conjunction with a novel implementation of the conjugate gradient algorithm which requires the use of the adjoints of the scattering operators. The solver takes advantage of the symmetric block Toeplitz matrix with symmetric Toeplitz blocks property of the Green's function matrix to increase efficiency and only stores the first row of this matrix to reduce memory requirements. This row is then used for the matrix-vector multiplication using the fast Fourier transform technique, thus, resulting in the computational complexity of O(n log n). The marching-on-source technique is also used to provide a good initial guess which allows the conjugate gradient technique to converge faster than initializing with an arbitrary guess. This feature is important in tomographic inversion algorithms which require that the object to be imaged be interrogated via several incident fields. Forward scattering and inversion examples, based on the Conjugate Gradient Least Squares regularized Born Iterative Method, are shown, in two-dimensions, for objects varying in all three physical properties.

Tissue-Type Classification With Uncertainty Quantification of Microwave and Ultrasound Breast Imaging: A Deep Learning Approach

“…The simulated scattered field is defined as the subtraction of the incident field (i.e., the field in the absence of the OI) from total field (i.e., the field in the presence of the OI). The simulated scattered pressure for the inhomogeneous compressibility and attenuation can be found as [9], [19], [21]…”

“…The Gauss-Newton inversion is used as the non-linear inversion algorithm to reconstruct both dielectric and ultrasonic properties of the OI [20]. It should be noted that the variation of density considered in [5], [21]…”

Redatuming of 2-D Wave Fields Measured on an Arbitrary-Shaped Closed Aperture

“…Once the coefficients c n (ω) are found, the field can be computed at any location outside D using equation (10). In this way, we can redatum the wave field measured at S to the domain S .…”

“…First, full-wave inversion is computationally expensive. Several attempts have been made to overcome this problem, varying from source encoding [9] to the application of special accelerating and memory techniques [10].…”

Acoustic beam anomalies in automated breast imaging

“…In the past decade, there has been great demand for ultrasound in the United States for breast cancer screening as a supplement of x-ray mammography, since ultrasound can detect unsuspected, mammographically occult cancer, especially in radiographically dense breasts that have a higher risk of developing breast cancer. [2][3][4] Also, several tissue acoustical properties obtained from received ultrasound signals such as speed of sound, [5][6][7][8][9][10][11][12][13] attenuation, [8][9][10]12,[14][15][16][17] density, 18 and elasticity [19][20][21] can be used for characterizing different tissue types as they tend to have different acoustic properties. The ability of ultrasonic imaging to characterize tissues, particularly the differentiation of malignant lesions from benign tissues, shows promise in decreasing the number of breast biopsies needed for adequate diagnosis.…”