Salvador Villena

Bayesian combination of sparse and non-sparse priors in image super resolution

In this paper the application of image prior combinations to the Bayesian Super Resolution (SR) image registration and reconstruction problem is studied. Two sparse image priors, a Total Variation (TV) prior and a prior based on the @?1 norm of horizontal and vertical first-order differences (f.o.d.), are combined with a non-sparse Simultaneous Auto Regressive (SAR) prior. Since, for a given observation model, each prior produces a different posterior distribution of the underlying High Resolution (HR) image, the use of variational approximation will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the HR image given the observations that minimizes a linear convex combination of Kullback-Leibler (KL) divergences. We find this distribution in closed form. The estimated HR images are compared with the ones obtained by other SR reconstruction methods.

Bayesian Super-Resolution image reconstruction using an ℓ1 prior

This paper deals with the problem of high-resolution (HR) image reconstruction, from a set of degraded, under-sampled, shifted and rotated images, under the Bayesian paradigm, utilizing a variational approximation. Bayesian methods rely on image models that encapsulate prior image knowledge and avoid the ill-posedness of the image restoration problems. In this paper a new prior based on the lscr1 norm of vertical and horizontal first order differences of image pixel values is introduced and its parameters are estimated. The estimated HR images are compared with images provided by other HR reconstruction methods.

Using the Kullback-Leibler divergence to combine image priors in Super-Resolution image reconstruction

This paper is devoted to the combination of image priors in Super Resolution (SR) image reconstruction. Taking into account that each combination of a given observation model and a prior model produces a different posterior distribution of the underlying High Resolution (HR) image, the use of variational posterior distribution approximation on each posterior will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the HR image given the observations that minimizes a linear convex combination of the Kullback-Leibler divergences associated with each posterior distribution. We find this distribution in closed form and also relate the proposed approach to other prior combination methods in the literature. The estimated HR images are compared with images provided by other SR reconstruction methods.

Bayesian super-resolution of text image sequences from low resolution observations

This paper deals with the problem of reconstructing high-resolution text images from an incomplete set of under-sampled, blurred, and noisy images shifted with subpixel displacement. We derive mathematical expressions for the calculation of the maximum a posteriori estimate of the high resolution image and the estimation of the parameters involved in the model. The method is tested on real text images and car plates, examining the impact of blurring and the number of available low resolution images on the final estimate.

A non-stationary image prior combination in super-resolution

A new Bayesian Super-Resolution (SR) image registration and reconstruction method is proposed. The new method utilizes a prior distribution based on a general combination of spatially adaptive, or non-stationary, image filters, which includes an adaptive local strength parameter able to preserve both image edges and textures. With the application of variational techniques, the proposed method allows for the automatic estimation of all problem unknowns. An experimental comparison between state of the art methods and the proposed SR approach has been performed on both synthetic and real images.

Compressive sensing super resolution from multiple observations with application to passive millimeter wave images

In this work we propose a novel framework to obtain high resolution images from compressed sensing imaging systems capturing multiple low resolution images of the same scene. The proposed approach of Compressed Sensing Super Resolution (CSSR), combines existing compressed sensing reconstruction algorithms with a low-resolution to high-resolution approach based on the use of a super Gaussian regularization term. The reconstruction alternates between compressed sensing reconstruction and super resolution reconstruction, including registration parameter estimation. The image estimation subproblem is solved using majorization-minimization while the compressed sensing reconstruction becomes an l 1 -minimization subject to a quadratic constraint. The performed experiments on grayscale and synthetically compressed real millimeter wave images, demonstrate the capability of the proposed framework to provide very good quality super resolved images from multiple low resolution compressed acquisitions.

Image prior combination in super-resolution image registration & reconstruction

In this paper the application of image prior combinations to the Bayesian Super Resolution (SR) image registration and reconstruction problem is studied. A sparse image prior based on the horizontal and vertical first order differences is combined with a non-sparse SAR prior. Since, for a given observation model, each prior produces a different posterior distribution of the underlying High Resolution (HR) image, the use of variational posterior distribution approximation on each posterior will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the HR image given the observations that minimize a linear convex combination of the Kullback-Leibler (KL) divergences associated with each posterior distribution. We find this distribution in closed form. The estimated HR images are compared with images provided by other SR reconstruction methods.

Estimation of High Resolution Images and Registration Parameters from Low Resolution Observations

In this paper we consider the problem of reconstructing a high resolution image from a set of undersampled and degraded frames, all of them obtained from high resolution images with unknown shifting displacements between them. We derive an iterative method to estimate the unknown shifts and the high resolution image given the low resolution observations. Finally, the proposed method is tested on real images.

PMMW image super resolution from compressed sensing observations

In this paper we propose a novel optimization framework to obtain High Resolution (HR) Passive Millimeter Wave (P-MMW) images from multiple Low Resolution (LR) observations captured using a simulated Compressed Sensing (CS) imaging system. The proposed CS Super Resolution (CSS-R) approach combines existing CS reconstruction algorithms with the use of Super Gaussian (SG) regularization terms on the image to be reconstructed, smoothness constraints on the registration parameters to be estimated and the use of the Alternate Direction Methods of Multipliers (ADMM) to link the CS and SR problems. The image estimation subproblem is solved using Majorization-Minimization (MM), registration is tackled minimizing a quadratic function and CS reconstruction is approached as an l1-minimization problem subject to a quadratic constraint. The performed experiments, on simulated and real PMMW observations, validate the used approach.

Parameter estimation in bayesian super-resolution image reconstruction from low resolution rotated and translated images

This paper deals with the problem of high-resolution (HR) image reconstruction, from a set of degraded, under-sampled, shifted and rotated images, utilizing the variational approximation within the Bayesian paradigm. The proposed inference procedure requires the calculation of the covariance matrix of the HR image given the LR observations and the unknown hyperparameters of the probabilistic model. Unfortunately the size and complexity of such matrix renders its calculation impossible, and we propose and compare three alternative approximations. The estimated HR images are compared with images provided by other HR reconstruction methods.