Multichannel stochastic image models: Theory, applications, and implementations

The restoration and enhancement of multichannel data, including multispectral images and video sequences, is now feasible, due to recent advances in computing technology. Within each channel, an assumption of stationarity is reasonable. However, spectral and temporal correlations are nonstationary, so that a simple extension of single channel estimation algorithms to multichannel data will not give the best results.; Bayesian maximum a posteriori (MAP) estimation requires a model for the data to regularize ill-posed inverse problems such as image restoration and reconstruction. Quite often, an assumption of global smoothness is made for the data, which can be modeled by a Gaussian prior. If noise corrupting the data is Gaussian as well, this results in linear Bayesian estimates containing smooth edges. A non-Gaussian prior is presented in this dissertation which models piece-wise smooth data, and thus discontinuities are more likely to appear in the resulting nonlinear estimate.; A number of topics involving Bayesian image restoration are investigated in this dissertation. A window-based Bayesian estimator is developed for use in image noise removal, constraining the amount of data used in estimating each pixel. Restorations using the window-based estimator have the same quantitative and visual quality as Bayesian estimates computed using all observed image data, even for small window sizes. The stochastic image prior is extended to model multispectral data, featuring spectral Markov random field clique functions which incorporate cross-channel correlations between frequency bands. Estimates from the corresponding Bayesian color image restoration algorithm are improved over independent channel estimates of the red, green, and blue color planes. A maximum likelihood technique for automatically estimating non-Gaussian signal and image model parameters directly from noisy and blurred observations is proposed. Numerical simulations confirm that the estimated parameters result in high quality signal reconstructions. Finally, an observation model for low-resolution video sequence data is presented, which accounts for the motion between frames. A Bayesian interpolation algorithm which extracts a high-resolution frame given several frames from a low-resolution video sequence is then described, with significant improvement over single frame interpolation methods.