Abstract:
Speckle noise is an inherent phenomenon in medical ultrasound images. Since it degrades an ultrasound image quality and reduces its diagnostic value, reduction of speckle noise is a very important pre-processing step in ultrasound image processing. For this purpose, the knowledge of the statistics of speckle noise is necessary; especially in the multi-resolution transform domain due to their sparse and efficient representation of images and henceforth their widespread application in developing efficient speckle reduction methods. In this thesis, the statistics of log-transformed speckle noise in various multi-resolution transform domains is investigated. The reason for considering the log-transformed noise is the prevalence of homomorphic approaches for speckle reduction in the literature where the multiplicative speckle noise is converted to an additive one by log-transformation and subsequently reduced by applying additive noise reduction techniques. In this thesis, a Bessel K-Form (BKF) probability density function (pdf) is proposed as a highly suitable prior for modeling the log-transformed speckle noise in the well-known discrete wavelet transform (DWT), curvelet transform, dual-tree complex wavelet transform (DT-CWT) and contourlet transform domains. The motivations for using the BKF pdf are the heavy-tailed nature of the log-transformed speckle noise, and the effectiveness of the BKF pdf in capturing the statistics of heavy-tailed , reported in several research works in the literature. Maximum likelihood- based methods are presented for estimating the parameters of the BKF pdf. The appropriateness of the BKF pdf in modeling the speckle noise is extensively explored for the case of simulated noise of different levels as well as real medical ultrasound images in various transform domains that include the DWT, curvelet transform, DT-CWT and contourlet transform. It is shown that, in general the BKF can model the statistics of the various transform coefficients corresponding to log-transformed speckle better than the traditional Gaussian and normal inverse Gaussian (NIG) pdfs. It is expected that the findings of this thesis would encourage researchers in developing effective and improved multi-resolution transform-based algorithms for reducing the speckle noise from medical ultrasound images.
