Bayesian approach for sensor super-resolution
Bayesian super-resolution techniques fuse multiple low resolution images (possibly from multiple bands) to infer a higher resolution image. The super-resolution and fusion concepts are portable to a wide variety of sensors and environmental models. The procedure is model-based inference of super-resolved information. In this approach, both the point spread function of the sub-sampling process and the multi-frame registration parameters are optimized simultaneously in order to infer an optimal estimate of the super-resolved imagery. The procedure involves a significant number of improvements, among them, more accurate likelihood estimates and a more accurate, efficient, and stable optimization procedure.
1. A computer implemented method of deriving a high resolution image from a plurality of low resolution images, comprising the steps of:
initializing one or more alignment parameters to one or more likely values;
determining the marginal likelihood of the low resolution images using the one or more alignment parameters, in which the marginal likelihood is a function ƒ of the alignment parameters where:
ƒ= lg|Σ|+μ T Σ −1 μ,
and μ is the mean and Σ is the variance of the posterior distribution over the high resolution image given the plurality of low resolution images;
adjusting the alignment parameters so as to optimize the marginal likelihood determination; and
determining the high resolution image using the adjusted alignment parameters.
2. A computer implemented method of deriving a high resolution image from a plurality of low resolution images, comprising the steps of:
(a) sampling multiple portions of the low resolution images;
(b) generating alignment parameters for the low resolution images using the sampled portions of the low resolution images comprising the steps of:
(1) initializing one or more alignment parameters to one or more likely values;
(2) determining the marginal likelihood of the low resolution images using the one or more alignment parameters, in which the marginal likelihood is a function ƒ of the alignment parameters, where:
ƒ= lg|Σ|+μ T Σ −1 μ,
and μ is the mean and Σ is the variance of the posterior distribution over the high resolution image given the plurality of low resolution images; and
(3) adjusting the alignment parameters so as to optimize the marginal likelihood determination; and
(c) deriving the high resolution image from the adjusted alignment parameters and the low resolution images.
3. The method of claim 2 , in which the sampled multiple portions of the low resolution images are spatially separated.
4. The method of claim 3 , in which the sampling step selects portions of the low resolution images based on information content in the selected portions of the low resolution images.
5. The method of claim 4 , in which the sampled low resolution image portions are regions of great detail or high frequency content.