Bayesian Image Superresolution Research Articles

Bayesian Image Super-Resolution With Deep Modeling of Image Statistics.

Modeling statistics of image priors is useful for image super-resolution, but little attention has been paid from the massive works of deep learning-based methods. In this work, we propose a Bayesian image restoration framework, where natural image statistics are modeled with the combination of smoothness and sparsity priors. Concretely, first we consider an ideal image as the sum of a smoothness component and a sparsity residual, and model real image degradation including blurring, downscaling, and noise corruption. Then, we develop a variational Bayesian approach to infer their posteriors. Finally, we implement the variational approach for single image super-resolution (SISR) using deep neural networks, and propose an unsupervised training strategy. The experiments on three image restoration tasks, i.e., ideal SISR, realistic SISR, and real-world SISR, demonstrate that our method has superior model generalizability against varying noise levels and degradation kernels and is effective in unsupervised SISR. The code and resulting models are released via https://zmiclab.github.io/projects.html.

Stroke width‐based directional total variation regularisation for document image super resolution

In the Bayesian image super resolution (SR), a regularisation term is minimised along with a data-fidelity term to generate a high-resolution (HR) image from input low-resolution (LR) image. The regularisation term is incorporated into the SR to fulfil a prior knowledge over the HR image. For instance, smoothness in the background and foreground regions is a prior knowledge about document images. The bilateral total variation (BTV), as a known regularisation term, uniformly smooths the image in all directions while preserving the edges. In this study, the authors present a document image SR method by introducing a new regularisation term called the stroke width-based directional total variation (SWDTV). It is a modified version of the BTV, and adaptively performs smoothing based on the local width and local direction of the character strokes. By analysing the input LR image and its interpolation, the local stroke width and local stroke direction in the output image are approximated. This information is encapsulated into the SWDTV regularisation term. By minimising the linear combination of the regularisation and data-fidelity terms, the HR image is reconstructed. The authors’ method achieves significant improvements in visual image quality and optical character recognition accuracy compared to related non-example-based document image SR methods.

Posterior-Mean Super-Resolution With a Causal Gaussian Markov Random Field Prior

We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with the line process supplies a preferable prior for natural images with edges. We improve the existing image transformation model, the compound MRF model, and its hyperparameter prior model. We also derive the optimal estimator--not the joint maximum a posteriori (MAP) or the marginalized maximum likelihood (ML) but the posterior mean (PM)--from the objective function of the L2-norm-based (mean square error) peak signal-to-noise ratio. Point estimates such as MAP and ML are generally not stable in ill-posed high-dimensional problems because of overfitting, whereas PM is a stable estimator because all the parameters in the model are evaluated as distributions. The estimator is numerically determined by using the variational Bayesian method. The variational Bayesian method is a widely used method that approximately determines a complicated posterior distribution, but it is generally hard to use because it needs the conjugate prior. We solve this problem with simple Taylor approximations. Experimental results have shown that the proposed method is more accurate or comparable to existing methods.

Application of Bayesian image superresolution to spectral reflectance estimation

Hyperspectral imaging provides us with high-dimensional, scene-independent color information but faces problems such as long image acquisition time and severe lighting and focusing conditions. To achieve efficient spectral imaging, this study presents an extended method of Bayesian image superresolution. The proposed method increases both the spatial and the wavelength resolution of input images and enables the processing of hyperspectral images to a higher resolution from easily acquired low-spatial-resolution multispectral images. In an experiment using acquired multispectral images of a Japanese traditional painting, visible and near-infrared hyperspectral images were produced, and the obvious effect of superresolution was validated.

Generative Bayesian Image Super Resolution With Natural Image Prior

We propose a new single image super resolution (SR) algorithm via Bayesian modeling with a natural image prior modeled by a high-order Markov random field (MRF). SR is one of the long-standing and active topics in image processing community. It is of great use in many practical applications, such as astronomical observation, medical imaging, and the adaptation of low-resolution contents onto high-resolution displays. One category of the conventional approaches for image SR is formulating the problem with Bayesian modeling techniques and then obtaining its maximum-a-posteriori solution, which actually boils down to a regularized regression task. Although straightforward, this approach cannot exploit the full potential offered by the probabilistic modeling, as only the posterior mode is sought. On the other hand, current Bayesian SR approaches using the posterior mean estimation typically use very simple prior models for natural images to ensure the computational tractability. In this paper, we present a Bayesian image SR approach with a flexible high-order MRF model as the prior for natural images. The minimum mean square error (MMSE) criteria are used for estimating the HR image. A Markov chain Monte Carlo-based sampling algorithm is presented for obtaining the MMSE solution. The proposed method cannot only enjoy the benefits offered by the flexible prior, but also has the advantage of making use of the probabilistic modeling to perform a posterior mean estimation, thus is less sensitive to the local minima problem as the MAP solution. Experimental results indicate that the proposed method can generate competitive or better results than state-of-the-art SR algorithms.

Bayesian image superresolution and hidden variable modeling

Superresolution is an image processing technique that estimates an original high-resolution image from its low-resolution and degraded observations. In superresolution tasks, there have been problems regarding the computational cost for the estimation of high-dimensional variables. These problems are now being overcome by the recent development of fast computers and the development of powerful computational techniques such as variational Bayesian approximation. This paper reviews a Bayesian treatment of the superresolution problem and presents its extensions based on hierarchical modeling by employing hidden variables.

Bayesian Methods for Image Super-Resolution

We present a novel method of Bayesian image super-resolution in which marginalization is carried out over latent parameters such as geometric and photometric registration and the image point-spread function. Related Bayesian super-resolution approaches marginalize over the high-resolution image, necessitating the use of an unfavourable image prior, whereas our method allows for more realistic image prior distributions, and reduces the dimension of the integral considerably, removing the main computational bottleneck of algorithms such as Tipping and Bishop's Bayesian image super-resolution. We show results on real and synthetic datasets to illustrate the efficacy of our method.