Multisource data fusion for bandlimited signals: a Bayesian perspective

Abstract

Abstract. We consider data fusion as the reconstruction of a single model from multiple data sources. The model is to be inferred from a number of blurred and noisy observations, possibly from different sensors under various conditions. It is all about recovering a compound object, signal+uncertainties, that best relates to the observations and contains all the useful information from the initial data set.We wish to provide a flexible framework for bandlimited signal reconstruction from multiple data. In this paper, we focus on a general approach involving forward modeling (prior model, data acquisition) and Bayesian inference. The proposed method is valid for n-D objects (signals, images or volumes) with multidimensional spatial elements. For the sake of clarity, both formalism and test results will be shown in 1D for single band signals. The main originality lies in seeking an object with a prescribed bandwidth, hence our choice of a B-Spline representation. This ensures an optimal sampling in both signal and frequency spaces, and allows for a shift invariant processing.The model resolution, the geometric distortions, the blur and the regularity of the sampling grid can be arbitrary for each sensor. The method is designed to handle realistic Gauss+Poisson noise.We obtained promising results in reconstructing a super-resolved signal from two blurred and noisy shifted observations, using a Gaussian Markov chain as a prior. Practical applications are under development within the SpaceFusion project. For instance, in astronomical imaging, we aim at a sharp, well-sampled, noise-free and possibly super-resolved image. Virtual Observatories could benefit from such a way to combine large numbers of multispectral images from various sources. In planetary imaging or remote sensing, a 3D image formation model is needed; nevertheless, this can be addressed within the same framework.

Multi-source data fusion and super-resolution from astronomical images

“…The proposed formalism could be applied to signals [11], such as spectra recorded with various spectrographs, to help improve accuracy and faint source detection.…”

“…The general formalism for ndimensional signals was first introduced in [11]. Here we focus on images recorded by matrixlike detectors within optical telescopes.…”

“…Here we assume that both prior and observation parameters are well calibrated (automatic calibration is under investigation [11]). Therefore we aim at the conditional pdf P(X | {Y n , θ n }, ω).…”