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

Abstract

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.

A general sparse image prior combination in super-resolution

“…2 shows a quantitative comparison in terms of PSNR, of the restorations of the images in Fig. 1 at different noise levels, obtained using the following methods: 1) bicubic interpolation (denoted by BBC), 2) the SR method in [8] (denoted by ZMT), which is based on backprojection with median filtering, 3) the robust SR method in [9] (denoted by RSR), which is based on bilateral TV priors, 4) the variational SR method using a TV prior in [10] (denoted by TV), 5) the variational SR method in [4] based in a combination of 1 and SAR priors (denoted by L1SAR), and our proposed algorithm 1 using the filter combinations 6) NF2, 7) NF3, 8) NF4 and 9) NF5. It can be observed in Fig.…”

“…(20), are not straightforward since B(s k ) is nonlinear with respect to s k . In [4] these estimations were performed by expanding B(s k ), using its first-order Taylor series, around the mean value < s k >=s k = (θ k ,h k ,v k ) T of the distribution q(s k ). We follow here the same approach, and refer to [4], where the detailed derivation and the resulting expressions for these estimated values may be found.…”

“…Sparse image priors are known to produce good results in Bayesian image restoration, in general, and in SR, in particular (see [3], [4]). An image prior is considered as sparse when it is Super-Gaussian (SG) [5], i.e., compared to the Gaussian distribution, it has heavier tails and it is more peaked.…”

Super Resolution of PET Images using Hybrid Regularization

“…Thus, following [9] the degradation process of a HR PET image x of N 1 ×N 2 is formulated as , 1,..., ,…”

A Bayesian Data Fusion Approach to Spatio-Temporal Fusion of Remotely Sensed Images

“…The first step of our approach is to build a model to describe the relationship between the low-resolution image and the high-resolution image at the target date t 0 . We call it the observational model, which can be written in a matrix form as [48,49]:…”