Edge directed statistical inference and its applications to image processing

The performance of signal processing algorithms closely relies on the accuracy of the employed model to characterize the source. However, there still lacks accurate model for natural-image source. The effectiveness of prediction, interpolation and filtering for image signals often suffers from the mismatch between the source model and the actual observation. This thesis uses the Least-Square method to improve the modeling of natural-image source from statistical inference point of view. By exploiting important properties of images such as geometric constraint of edges, we have developed several novel and efficient image processing algorithms.; First we study the sequential prediction problem for image coding. The Least-Square method is employed to drive the predictive model to match an arbitrarily-oriented edge in the spatial domain. We also extend the application of the Least-Square method to wavelet-based lossy image coding. In order to improve the modeling of a wavelet coefficient around an edge, its biased mean is estimated from the quantized causal neighbors using the Least-Square method. Our new image coders have achieved better performance than current state-of-art coders with acceptable complexity.; The second problem benefiting from the Least-Square method is adaptive image interpolation. Our goal is to develop an orientation adaptive scheme to interpolate along the edge orientation but not across it. We have studied two important cases: resolution enhancement and error concealment. For resolution enhancement, we adapt the interpolation at high resolution with only low-resolution image available, based on the resolution invariant property of edge orientation. For error concealment, we introduce a new framework of sequential estimation to alleviate the modeling complexity.; We also investigate the problem of image denoising from the viewpoint of statistical inference. For impulse noise, we present an innovative estimation-based denoising scheme based on the Least-Square method. The performance of noise detection and noise suppression is simultaneously enhanced by exploiting geometric constraint of edges. For AWGN case, we have developed a novel denoising algorithm under overcomplete expansion in the wavelet domain. We make a systematic study of signal and noise characteristics to improve the accuracy of statistical modeling of wavelet coefficients.