Wavelet and Curvelet Transforms for Biomedical Image Processing

This chapter introduces two mathematical transforms—wavelet and curvelet—in the field of biomedical imaging. Presenting the theoretical background with relevant properties, the applications of the two transforms are presented. The biomedical applications include heart sound analysis, electrocardiography (ECG) characterization, positron emission tomography (PET) image analysis, medical image compression, mammogram enhancement, magnetic resonance imaging (MRI) and computer tomography (CT) image denoising, diabetic retinopathy detection. The applications emphasize the development of algorithms to diagnose human diseases, thereby rendering fast and reliable support to the medical personnel. The transforms—one classical (wavelet) and another contemporary (curvelet)—are selected to focus the difference in architecture, limitation, evolution, and application of individual transform. Two joint applications are addressed to compare their performance. This survey is also supplemented by a case study: mammogram denoising using wavelet and curvelet transforms with the underlying algorithms.

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