A Fractal Multi-Dimensional Ultrasound Scatterer Distribution Model

Abstract

This paper presents a multi-dimensional point scatterer distribution model for the context of ultrasound image simulation. The model has a simple parameterisation, has low computational requirements and is flexible enough to model spatial organisation of scatterers ranging from highly clustered to nearly regular. The model extends an existing 1D model by mapping 1D scatterer positions to a Hilbert space-filling curve. The flexibility of the heuristic model is illustrated through experiments where common statistical models of ultrasonic speckle are fitted to simulated data. The results agree with theoretical predictions. Index terms: acoustic imaging, simulation, fractals, statistics, speckle BACKGROUNDAn ultrasound (US) image simulator is a useful validation platform for image processing applications where ground truth pertaining to image content or acquisition conditions is needed but not available from US data without additional equipment. It also serves as a test platform during application software development when data acquisition is impossible or awkward. Typical simulators take a list of point scatterers with their strength and position as input along with US transducer specifications and simulate the resulting backscattered signal.The density and spatial organisation of scatterers are two of many factors which determine the appearance and statistics of US speckle. In order to validate image processing applications or study image properties across different tissue types, it is useful to be able to generate random lists of point scatterers with varying density and spatial organisation, ranging from highly clustered to random to nearly regular. There is currently a lack of models displaying such flexibility along with computational efficiency and simple parameterisation.The Neyman-Scott point process model has been used for studying the effect of blood cell aggregation on ultrasonic signals [1]. The model creates random cluster centers and spawns daughter points surrounding them. It is not appropriate for generating quasi-periodic patterns. Such patterns can Catherine Laporte is funded by a doctoral scholarship from the Natural Science and Engineering Research Council of Canada.be generated with varying regularity by perturbing a regular point lattice [2], but this approach cannot generate clustered point patterns. An alternative is a Gibbs-Markov area interaction process which imposes pairwise repulsive and attractive constraints between points. This model was used to study US backscattering from aggregates of non-overlapping blood cells [3]. This type of model is computationally demanding and fails to produce a broad enough variety of clustered patterns when no repulsive constraints are used to maintain a minimal distance between points [4]. In short, previous attempts to parameterise variation in the spatial organisation of scatterers have been geared towards specific applications and have not modeled the full continuum of spatial organisations ranging from clustered to regular. One notable excep...

Assessment of Homodyned K Distribution Modeling Ultrasonic Speckles from Scatterers with Varying Spatial Organizations

“…In order to quantitatively assess the parameter characterization and goodness of fit, Table 1 lists the mean and standard deviation of the estimated parameters and maximum likelihood values of the fitted distributions with different shape α and density ρ values. To obtain a more reasonable comparison for distributions having different numbers of free parameters, the “best-fitting” value was calculated using the likelihood value based on minimized Schwarz's Bayes information criterion (BIC) [ 33 ]: where L l is the value of the maximum log-likelihood, as well as n and m are the numbers of data samples and parameters in the model, respectively.. The likelihood values based on BIC of the fitted distributions by the HK, OKRR-based K, Rayleigh, and Rician are denoted as L HK , L K , L RA , and L RI , respectively.…”

Generalized poisson 3-D scatterer distributions

“…as a result of applying a Hilbert curve mapping to the output of the 1-d generalized Poisson point process, a set of m-d points is obtained whose spatial organization displays similar characteristics to that of the original 1-d points, as supported by empirical evidence of the preservation of local scatterer count statistics [7].…”

“…The lack of systematic positive interference effects in the multidimensional model used here is due to the isotropy of the Hilbert curve mapping. While the model preserves regularity, there is absolutely no guarantee that this regularity will be aligned with a particular direction although, as shown by some of the 2-d results in [7], this may occur. For positive interference effects to invariably occur, the scatterers must be placed quasi-periodically in the direction of wave propagation, at multiples of the transmitted wavelength.…”

“…This paper demonstrates the power and flexibility of a general method, first introduced in [7], for generating lists of multidimensional scatterer positions with variable strength, density, and spatial organization ranging from tightly clustered to nearly regular to mimic a broad range of tissue types. The method extends a previous 1-d scatterer distribution model [8], [9] by mapping its output to a multidimensional space filling curve.…”

Fast simulation of ultrasound images from a CT volume

“…In the other simulators, these micro-inhomogeneities are generally simulated by randomly placed scatterers (see [10] for example). More recently, Laporte et al [12] suggested to use the 1D marked regularity model of Cramblitt and Parker [7] and to extend it to higher dimensions. This model is based on the following scatterer function adapted to the 1D space domain:…”