The quality of medical ultrasound images is limited by inherent poor resolution due to the finite temporal bandwidth of the acoustic pulse and the non-negligible width of the system point-spread function. One of the major difficulties in designing a practical and effective restoration algorithm is to develop a model for the tissue reflectivity
that can adequately capture significant image features without being
computationally prohibitive. The reflectivities of biological tissues
do not exhibit the piecewise smooth characteristics of natural images
considered in the standard image processing literature; while the
macroscopic variations in echogenicity are indeed piecewise smooth,
the presence of sub-wavelength scatterers adds a pseudo-random component
at the microscopic level. This observation leads us to propose modelling
the tissue reflectivity as the product of a piecewise smooth echogenicity
map and a unit-variance random field. The chief advantage of such
an explicit representation is that it allows us to exploit representations
for piecewise smooth functions (such as wavelet bases) in modelling
variations in echogenicity without neglecting the microscopic pseudo-random
detail. As an example of how this multiplicative model may be exploited,
we propose an expectation-maximisation (EM) restoration algorithm
that alternates between inverse filtering (to estimate the tissue
reflectivity) and logarithmic wavelet denoising (to estimate the echogenicity
map). We provide simulation and in vitro results to demonstrate
that our proposed algorithm yields solutions that enjoy higher resolution,
better contrast and greater fidelity to the tissue reflectivity compared
with the current state-of-the-art in ultrasound image restoration.
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