The MIDAS instrument used for the SMOS mission is presented in the course as an example of interferometric remote-sensing device using a hexagonal sampling grid. The instrument aims to measure the earth’s brightness temperature for environmental applications, but these measurements are sometimes polluted by radio-frequency interferences (RFI) produced by illegal emitters on the reserved L-band.
As shown in course, by exploiting the different sparsity patterns of RFIs (sparse spikes) and brightness temperatures (sparse edges), it is possible to separate RFI outliers from the brightness temperature map [1]. However this technique assumes that outliers lie exactly on the sampling grid. In order to better model and estimate the subpixel localization of these outliers we could use models and restoration methods based on finite rate of innovation, originally proposed in [2] and further developed in [3].
The aim of this work is to study the work of Candes on subpixel localization of spikes [3], and to find out how such a model can be adapted to the problem of separating RFIs from brightness temperatures with subpixel localization of the detected spikes. No programming is strictly required, but a thorough theoretical understanding of both problems and their relationships is expected.
Supervision
Andrés Almansa
References
[1] Preciozzi, Almansa, Musé, Durand, Khazaal, Rougé (2014), A sparsity-based variational approach for the restoration of SMOS images from L1A data, Preprint
[2] Vetterli, M., Marziliano, P., & Blu, T. (2002). Sampling signals with finite rate of innovation. IEEE Transactions on Signal Processing, 50(6), 1417–1428. doi:10.1109/TSP.2002.1003065
[3] Candès, E. J., & Fernandez-Granda, C. (2014). Towards a Mathematical Theory of Super-resolution. Communications on Pure and Applied Mathematics, 67(6), 906–956. doi:10.1002/cpa.21455