In this paper, a discrete model representing the pulse-tissue interaction in the medical ultrasound scanning and
imaging process is developed. The model is based on discretizing the acoustical wave equation and is in terms
of convolution between the input ultrasound pulses and the tissue mass density variation. Such a model can
provide a useful means for ultrasound echo signal processing and imaging.
Most existing models used for ultrasound imaging are based on frequency domain transform. A disadvantage
of the frequency domain transform is that it is only applicable to shift-invariant models. Thus it has ignored the
shift-variant nature of the original acoustic wave equation where the tissue compressibility and mass density distributions
are spatial-variant factors. The discretized frequency domain model also obscures the compressibility
and mass density representations of the tissue, which may mislead the physical understanding and interpretation
of the image obtained. Moreover, only the classical frequency domain filtering methods have been applied to the
frequency domain model for acquiring some tissue information from the scattered echo signals. These methods
are non-parametric and require a prior knowledge of frequency spectra of the transmitted pulses.
Our proposed model technique will lead to discrete, multidimensional, shift-variant and parametric difference or convolution equations with the transmitted pulse pressure as the input, the measurement data of the echo signals as the output, and functions of the tissue compressibility and mass density distributions as shift-variant parameters that can be readily identified from input-output measurements. The proposed model represents the entire multiple scattering process, and hence overcomes the key limitation in the current ultrasound imaging methods.
Observed medical ultrasound images are degraded representations of true tissue images. The degradation is a combination of blurring due to the finite resolution of the imaging system and the observation noise. This paper presents a new wavelet based deconvolution method for medical ultrasound imaging. We design a new orthogonal wavelet basis known as the symmetrical mirror wavelet basis that can provide more desirable frequency resolution. Our proposed ultrasound image restoration with wavelets consists of an inversion of the observed ultrasound image using the estimated two-dimensional (2-D) point spread function (PSF) followed by denoising in the designed wavelet basis. The tissue image restoration is then accomplished by modelling the tissue structures with the generalized Gaussian density (GGD) function using the Bayesian estimation. Both subjective and objective measures show that the deconvolved images are more appealing in the visualization and resolution gain.