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Wave Inversion - LFE: local frequency estimate
For a full description the methods are described fully in [1,2]. Breifly, LFE estimates the local spatial frequency of the shear wave propagation pattern, using an algorithm that combines local estimates of instantaneous frequency over several scales. These estimates are derived from filters that are a product of radial and directional components. The shear stiffness is then s = (mechanical freq., squared) / (spatial freq., squared), with the assumption that tissue density is 1.0 for all soft tissues. This approach solves the Helmholtz equation under the assumptions of local homogeneity, incompressibility, and no attenuation. The center frequencies of the six radial LFE filters are 1, 2, 4, 8, 16 and 32 waves/FOV. non-complex: he real and imaginary parts are processed separately, and the LFE results are combined (averaged); six (6) one-octave filters complex: The real and imaginary parts of the (Fourier-transformed-through-time) first harmonic phase data are processed through the LFE algorithm together as a complex image Stiffness estimates are reported in kilopascals (kPa) . References: 1. Knutsson, H., Westin, C.-F., Granlund, G., 1994. Local multiscale frequency and bandwidth estimation. Proceedings of IEEE Intl Conf on Image Processing, 36-40. 2. Manduca, A., Muthupillai, R., Rossman, P.J., Greenleaf, J.F. and Ehman, R.L., 1996. Image processing for magnetic resonance elastography. SPIE Med Img 2710, 616-623.

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