An homomorphic filtering and expectation maximization approach for the point spread function estimation in ultrasound imaging

In modern ultrasound imaging systems, the spatial resolution is severely limited due to the effects of both the finite aperture and overall bandwidth of ultrasound transducers and the non-negligible width of the transmitted ultrasound beams. This low spatial resolution remains the major limiting factor in the clinical usefulness of medical ultrasound images. In order to recover clinically important image details, which are often masked due to this resolution limitation, an image restoration procedure should be applied. To this end, an estimation of the Point Spread Function (PSF) of the ultrasound imaging system is required. This paper introduces a novel, original, reliable, and fast Maximum Likelihood (ML) approach for recovering the PSF of an ultrasound imaging system. This new PSF estimation method assumes as a constraint that the PSF is of known parametric form. Under this constraint, the parameter values of its associated Modulation Transfer Function (MTF) are then efficiently estimated using a homomorphic filter, a denoising step, and an expectation-maximization (EM) based clustering algorithm. Given this PSF estimate, a deconvolution can then be efficiently used in order to improve the spatial resolution of an ultrasound image and to obtain an estimate (independent of the properties of the imaging system) of the true tissue reflectivity function. The experiments reported in this paper demonstrate the efficiency and illustrate all the potential of this new estimation and blind deconvolution approach.