Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets

A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

COMPUTER AIDED SYSTEM FOR BREAST CANCER DIAGNOSIS USING CURVELET TRANSFORM

Breast cancer is a leading cause of death among women worldwide. Early detection is the key for improving breast cancer prognosis. Digital mammography remains one of the most suitable tools for early detection of breast cancer. Hence, there are strong needs for the development of computer aided diagnosis (CAD) systems which have the capability to help radiologists in decision making. The main goal is to increase the diagnostic accuracy rate. In this thesis we developed a computer aided system for the diagnosis and detection of breast cancer using curvelet transform. Curvelet is a multiscale transform which possess directionality and anisotropy, and it breaks some inherent limitations of wavelet in representing edges in images. We started this study by developing a diagnosis system. Five feature extraction methods were developed with curvelet and wavelet coefficients to differentiate between different breast cancer classes. The results with curvelet and wavelet were compared. The experimental results show a high performance of the proposed methods and classification accuracy rate achieved 97.30%. The thesis then provides an automatic system for breast cancer detection. An automatic thresholding algorithm was used to separate the area composed of the breast and the pectoral muscle from the background of the image. Subsequently, a region growing algorithm was used to locate the pectoral muscle and suppress it from the breast. Then, the work concentrates on the segmentation of region of interest (ROI). Two methods are suggested to accomplish the segmentation stage: an adaptive thresholding method and a pattern matching method. Once the ROI has been identified, an automatic cropping is performed to extract it from the original mammogram. Subsequently, the suggested feature extraction methods were applied to the segmented ROIs. Finally, the K-Nearest Neighbor (KNN) and Support Vector Machine (SVM) classifiers were used to determine whether the region is abnormal or normal. At this level, the study focuses on two abnormality types (mammographic masses and architectural distortion). Experimental results show that the introduced methods have very high detection accuracies. The effectiveness of the proposed methods has been tested with Mammographic Image Analysis Society (MIAS) dataset. Throughout the thesis all proposed methods and algorithms have been applied with both curvelet and wavelet for comparison and statistical tests were also performed. The overall results show that curvelet transform performs better than wavelet and the difference is statistically significant