Super-Resolution Based on Fast Registration and Maximum a Posteriori Reconstruction

In this paper, we propose a maximum a posteriori framework for the super-resolution problem, i.e., reconstructing high-resolution images from shifted, rotated, low-resolution degraded observations. The main contributions of this work are two; first, the use of a new locally adaptive edge preserving prior for the super-resolution problem. Second an efficient two-step reconstruction methodology that includes first an initial registration using only the low-resolution degraded observations. This is followed by a fast iterative algorithm implemented in the discrete Fourier transform domain in which the restoration, interpolation and the registration subtasks of this problem are preformed simultaneously. We present examples with both synthetic and real data that demonstrate the advantages of the proposed framework.     

Super-resolution based on fast registration and maximum a posteriori reconstruction.

In this paper, we propose a maximum a posteriori ramework for the super-resolution problem, i.e., reconstructing high-resolution images from shifted, rotated, low-resolution degraded observations. The main contributions of this work are two; first, the use of a new locally adaptive edge preserving prior for the super-resolution problem. Second an efficient two-step reconstruction methodology that includes first an initial registration using only the low-resolution degraded observations. This is followed by a fast iterative algorithm implemented in the discrete Fourier transform domain in which the restoration, interpolation and the registration subtasks of this problem are preformed simultaneously. We present examples with both synthetic and real data that demonstrate the advantages of the proposed framework.     

Variational Bayesian Image Restoration With a Product of Spatially Weighted Total Variation Image Priors

In this paper, a new image prior is introduced and used in image restoration. This prior is based on products of spatially weighted total variations (TV). These spatial weights provide this prior with the flexibility to better capture local image features than previous TV based priors. Bayesian inference is used for image restoration with this prior via the variational approximation. The proposed restoration algorithm is fully automatic in the sense that all necessary parameters are estimated from the data and is faster than previous similar algorithms. Numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state-of-the-art restoration algorithms.      

Variational-Bayes Optical Flow

The Horn-Schunck (HS) optical flow method is widely employed to initialize many motion estimation algorithms. In this work, a variational Bayesian approach of the HS method is presented, where the motion vectors are considered to be spatially varying Student’s t-distributed unobserved random variables, i.e., the prior is a multivariate Student’s t-distribution, while the only observations available is the temporal and spatial image difference. The proposed model takes into account the residual resulting from the linearization of the brightness constancy constraint by Taylor series approximation, which is also assumed to be a spatially varying Student’s t-distributed observation noise. To infer the model variables and parameters we recur to variational inference methodology leading to an expectation-maximization (EM) framework with update equations analogous to the Horn-Schunck approach. This is accomplished in a principled probabilistic framework where all of the model parameters are estimated automatically from the data. Experimental results show the improvement obtained by the proposed model which may substitute the standard algorithm in the initialization of more sophisticated optical flow schemes.     

Bayesian restoration using a new nonstationary edge-preserving image prior.

In this paper, we propose a class of image restoration algorithms based on the Bayesian approach and a new hierarchical spatially adaptive image prior. The proposed prior has the following two desirable features. First, it models the local image discontinuities in different directions with a model which is continuous valued. Thus, it preserves edges and generalizes the on/off (binary) line process idea used in previous image priors within the context of Markov random fields (MRFs). Second, it is Gaussian in nature and provides estimates that are easy to compute. Using this new hierarchical prior, two restoration algorithms are derived. The first is based on the maximum a posteriori principle and the second on the Bayesian methodology. Numerical experiments are presented that compare the proposed algorithms among themselves and with previous stationary and non stationary MRF-based with line process algorithms. These experiments demonstrate the advantages of the proposed prior.     

Variational Bayesian Image Restoration Based on a Product of t-Distributions Image Prior

Image priors based on products have been recognized to offer many advantages because they allow simultaneous enforcement of multiple constraints. However, they are inconvenient for Bayesian inference because it is hard to find their normalization constant in closed form. In this paper, a new Bayesian algorithm is proposed for the image restoration problem that bypasses this difficulty. An image prior is defined by imposing Student-t densities on the outputs of local convolutional filters. A variational methodology, with a constrained expectation step, is used to infer the restored image. Numerical experiments are shown that compare this methodology to previous ones and demonstrate its advantages.