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16 March 2006 An iterative wavelet-based deconvolution algorithm for the restoration of ultrasound images in an EM framework
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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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J. K. H. Ng, R. W. Prager, N. G. Kingsbury, G. M. Treece, and A. H. Gee "An iterative wavelet-based deconvolution algorithm for the restoration of ultrasound images in an EM framework", Proc. SPIE 6147, Medical Imaging 2006: Ultrasonic Imaging and Signal Processing, 614709 (16 March 2006);

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