Modelling of Heterogeneous SAR Clutter for Speckle Suppression using MAP Estimation

Abstract

Synthetic Aperture Radar (SAR) is an active high resolution imaging system that has been used intensively in diverse applications such as surveillance, environmental monitoring, urban planning, agriculture assessment etc. However, coherent nature of the SAR imaging system makes it highly susceptible to a multiplicative granular effect known as ‘Speckle’. The inherent presence of such speckle results in significant loss of relevant information (local mean of backscatter, point targets, texture etc.) which in turn makes interpretation and processing of SAR data difficult to human interpreters as well as systems devised for computer vision. Moreover, the accuracy of most of the SAR image processing applications such as segmentation, classification, detection and recognition is also severely effected by such granular speckle. Consequently, speckle suppression (despeckling) is regarded as a crucial preprocessing step in various SAR imaging applications. Therefore, development of efficient despeckling filters has become the focal point of exploration for the researchers from radar community in recent years.

A multitude of despeckling approaches has been developed so far, amongst which maximum-a-posteriori (MAP) based despeckling has earned utmost importance, since its simplicity in structure and practicability of implementation are found attractive apart from its accuracy in speckle suppression. However, the state-of-the-art MAP filters are inefficient in simultaneous mean preservation and speckle suppression from clutter data with varying degree of heterogeneity. Such inefficacy is due to (i) inability of corresponding clutter models in portraying statistics of both moderately heterogeneous and extremely heterogeneous areas, (ii) inaccurate estimation of clutter model parameters, (iii) mathematically intractable expression for the clutter probability density function (pdf) and/or its associated parameter estimates. Therefore, this dissertation deals with the investigations on various mathematical distributions, their parameters estimation strategies for efficiently characterising SAR clutter statistics and application of such clutter models in the formulation of MAP based despeckling filters. The major contributions of this dissertation are threefold.

Firstly, parametric clutter distributions such as K1/2 and W1/2 are presented to characterise SAR clutter amplitude data from multiplicative modelling perspective. Also,we propose to employ method of log-cumulants (MoLC) strategy for estimation of K1/2 and W1/2 clutter model parameters. Considering Γ, symmetric β distributions as clutter texture prior densities, Γ-MAP and β-MAP filters are then formulated to obtain amplitude texture estimate from K1/2 and W1/2 distributed moderately heterogeneous clutter amplitude data. Quantitative results on despeckling 1-look real and 3-look synthetic clutter data are presented for these amplitude texture estimators to assess the effectiveness in comparison with respective texture estimators. Furthermore, we consider reparametrised inverse Gamma distribution for SAR texture and formulate corresponding G0 clutter pdf to characterise statistics of extremely heterogeneous areas accurately. The reparametrised inverse Gamma distribution is then utilised as clutter texture prior in devising a MAP filter named as ‘G0-MAP’ for efficient speckle suppression in such clutter. Experimental results are
presented to illustrate the effectiveness of G0-MAP filter compared to state-of-the-art despeckling filters in preserving mean while suppressing speckle from heterogeneous clutter data. However, it is difficult to achieve improved performance in simultaneous mean
preservation and speckle suppression from clutter with varying degree of heterogeneity through MAP based despeckling using state-of-the-art parametric clutter texture models as prior densities.

In order to overcome such limitation, semiparametric modelling is also introduced in this dissertation for SAR texture by employing a binary mixture of Gamma and inverse Gamma (ΓIΓ) distribution as an approximation to generalised inverse Gaussian (GIG) model which
can efficiently capture the statistics of diverse kind of areas. An expectation-maximisation (EM) based strategy is proposed to obtain the maximum likelihood (ML) estimates of the ΓIΓ model parameters. Cramer-Rao bounds (CRBs) for the parameters of the above mixture model are given and used for evaluating the effectiveness of EM based ML
estimation through numerical examples. Monte-Carlo simulation results are also presented to validate the effectiveness of ΓIΓ model in approximating GIG distribution. Quantitative measurements on goodness-of-fit are then provided for experimental data over textured areas to illustrate the suitability and applicability of the mixture model in characterising clutter texture from areas of diverse kind. Furthermore, we devise a MAP based despeckling filter named as ‘ΓIΓ-MAP’ by considering the above mixture model as clutter texture prior density. Experimental results on despeckling clutter data are presented for the ΓIΓ-MAP filter to illustrate its superiority over state-of-the-art filters in simultaneous mean preservation and speckle suppression from both moderately and extremely heterogeneous clutter. However, the use of iterative EM algorithm in estimation of ΓIΓ model parameters makes the same computationally inferior.

Therefore, a mathematically tractable generalised model, called Burr Type-XII (BXII) distribution along with computationally efficient estimation strategy for its parameters are introduced in the dissertation for accurate modelling of heterogeneous SAR clutter. We
propose MoLC estimator by employing Mellin transform and second-kind statistics to obtain the parameters of this model. CRBs are derived for the BXII distribution parameter estimates and used for assessing effectiveness of the proposed estimation strategies applied to real and synthetic data. The analytical conditions for applicability of MoLC are given to assess effectiveness and flexibility of BXII clutter model. Experimental assessment on goodness-of-fit and computational burden is also provided for the proposed BXII model and compared the same with the state-of-the-art clutter distributions, which illustrates the validity and applicability of the model.