A Markov random field-based approach to speckle reduction.

摘要

One of the major factors plaguing the performance of any coherent imaging system in general, and synthetic-aperture-radar (SAR) and ultrasound-medical-imaging systems in particular, is the presence of signal-dependent speckle noise. Grainy in appearance, speckle noise is primarily due to the phase fluctuations of the electromagnetic returned signals. Existing multiplicative models for speckle noise do not possess the level of generality required to capture and exploit the inherent spatial-correlation characteristics of speckle noise. The capability of Markov random fields (MRFs) to model spatially correlated and signal-dependent phenomena makes them an excellent choice for modeling speckled images without the need to adopt a multiplicative-noise model. In addition, a MRF framework can lend itself to many image-processing strategies that are not predicated on any multiplicative- or additive-noise assumptions. We propose a new mathematical framework for modeling and mitigating speckle noise that combines the flexibility and generality of a MRF with the physical properties of speckle noise drawn from the statistical optics principles. In particular, Goodman's conditional probability density function (cpdf) of the intensity of any two points in the speckled image and the associated correlation function are used to derive the cpdf of any center pixel intensity given its four neighbors. An important parameter of the cpdf, the coherence factor, characterizes the spatial correlation between two given pixels. For the first-order MRF model used in this dissertation, the coherence factor is restricted to only one value, which is estimated from the data using a pseudo-likelihood method. Equipped with the cpdf, the Hammersley-Clifford theorem is utilized to derive a convex Gibbs energy function that characterizes the MRF. Based on the proposed model, we introduce two speckle-reduction algorithms. The first algorithm, termed the simulated-annealing-MRF (SAMRF), is based on minimizing the Gibbs energy function associated with the image, and hence reducing noise. The second algorithm, termed the MRF-based conditional-expectation approach (MRFCEA), is the main contribution of this dissertation. It provides a novel method for computing the estimate of the true pixel using the conditional expectation of the pixel given its four noisy neighbors. Both SAMRF and MRFCEA offer superior performance over existing methods by reducing speckle noise without compromising the spatial resolution of the processed imagery. In addition, MRFCEA is autonomous, contrary to other existing methods such as the enhanced-Frost or the modified-Lee, which require user's input. Our MRF-based approach is also applied to real speckled ultrasound medical imagery, showing good performance in reducing speckle noise. Finally, a novel segmentation approach, based on the proposed MRF model, is successfully developed and applied to real SAR imagery.