Multi-Snapshot Inversion Technique for an Interferometric Earth-Observation Satellite

Antenna arrays for passive microwave remote sensing of Earth produce images contaminated by aliasing due to insufficient sampling of the u-v plane: engineering constraints often preclude the deployment of arrays with antennas spaced sufficiently close together to reconstruct, via inversion of an observation model based on the Van Cittert-Zernike theorem, a brightness temperature image free from folding artifacts. Assuming an appropriate yaw-steering correction and using a spherical model of Earth and a locally circular orbit, we use the shift-invariance of the acquisition geometry in geodetic coordinates relative to the satellite's trace to express the Van Cittert-Zernike theorem as a convolution between an observation function and an image of parameters that sparsely model the curves of each pixel's directional emissivity. We then use a ``Fourier transform trick'' to decompose a multi-snapshot inversion into a sequence of independent inversions over each along-track orbital frequency, with each frequency's inversion being more tractable than a single-snapshot inversion. This multi-snapshot inversion technique takes advantage of the fact that pixels can be observed dozens of times (at different, but correlated temperatures) across an orbit to denoise and remove aliasing artifacts of regular or irregular antenna arrays, increasing swath width. The denoising power comes from the prior knowledge we introduce : directionnal emissivity curves can be modeled sparsely.