Giannis K. Chantas

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.

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

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.

t

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.

-Distributions Image Prior

In this paper we present new detectors for additive watermarks when the power of the watermark is unknown. These detectors are based on modeling the image using student-t statistics. As a result, due to the generative properties of the student-t density function, such models are spatially adaptive and the Expectation-Maximization algorithm can be used to obtain maximum likelihood estimates of their parameters. Using these image models detectors based on the generalized likelihood ratio and Rao tests are derived for this problem. Numerical experiments are presented that demonstrate the properties of these detectors and compared them with previously proposed detectors.

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

In this paper we propose a new hierarchical non stationary image prior for image restoration. This prior captures the directional edges using a continuous model and regularizes accordingly the restored images. In addition, the corresponding generative graphical model does not contain cycles, thus learning this model is easy and fast. Based on this prior image model, a maximum a posteriori (MAP) estimation algorithm is derived. Numerical experiments are provided that demonstrate the advantages of the proposed non stationary model as compared with algorithms that use stationary models.

New Detectors for Watermarks with Unknown Power Based on Student-t Image Priors

We propose a new iterative Bayesian non stationary image restoration algorithm. The main novelty of this approach is the introduction of a hierarchical non stationary image prior. Based on this prior and the generative graphical model for the observations, Bayesian inference is performed integrating out the hidden variables. An interesting byproduct of this approach is the justification, using a Bayesian framework, of previous non stationary image restoration formulations that were based on heuristic arguments. Numerical experiments are provided that demonstrate the advantages of the proposed non stationary approach as compared with the stationary approaches.

Maximum a posteriori image restoration based on a new directional continuous edge image prior

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 algorithm is fully automatic in the sense that all necessary parameters are estimated from the data. Numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state-of-the-art restoration algorithms.