Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis

Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a generic wavelet frame based image restoration model, called the "general model", which includes most of the existing wavelet frame based models as special cases. Moreover, the general model also includes examples that are new to the literature. Motivated by our earlier studies [1-3], We provide an asymptotic analysis of the general model as image resolution goes to infinity, which establishes a connection between the general model in discrete setting and a new variatonal model in continuum setting. The variational model also includes some of the existing variational models as special cases, such as the total generalized variational model proposed by [4]. In the end, we introduce an algorithm solving the general model and present one numerical simulation as an example

WAVELET PACKET FRAME-BASED IMAGE RESTORATION MODELS AND THEIR ASYMPTOTIC ANALYSIS

Ph.DDOCTOR OF PHILOSOPH

International Transmission of the People's Bank of China's Balance Sheet Expansion

The People's Bank of China's (PBoC) balance sheet expanded more dramatically than any of its major international counterparts during the past decade. The main contribution to this expansion was the rapid accumulation of the central bank's foreign assets