Esteban Aguilera just sent me the following:
Dear Igor,I am grateful for your dedication to this blog and have explicitly stated that in my acknowledgements. I will be glad to send you a hard copy if you are interested.
I defended my PhD last September and have just made my thesis available online. It is entitled:
Synthetic Aperture Radar Tomography
Compressed Sensing Models and Algorithms
Although the thesis is more on application side of things, I have provided a theoretical introduction to Compressed Sensing, which many people have found very useful – let us hope a bigger audience can benefit from it, too. In addition, I have included many examples of Disciplined Convex Programming and common matrix factorizations (based on tomographic/polarimetric data).
This is the official link of the German Aerospace Center (DLR), which will include the full text very soon. For now, the thesis can be downloaded here.
I wish you a great start to 2015.
Thank you for your kind words Esteban ! I think this is the first thesis acknowledgement and hence this post goes directly in the Citing Nuit Blanche category. We have featured Esteban's work before:
- Compressive Sensing in the Skies
- A Data-Adaptive Compressed Sensing Approach to Polarimetric SAR Tomography of Forested Areas
Here is the thesis abstract:
Synthetic Aperture Radar Tomography: Compressed Sensing Models and Algorithms
A synthetic aperture radar (SAR) is an active microwave instrument capable of imaging the surface of the earth at specific wavelengths and polarizations in day/night and all-weather conditions. In its basic configuration, a small airborne/spaceborne antenna traveling along a straight-line trajectory is pointed perpendicular to the flight track in a side-looking fashion. This results in the synthesis of a virtual along-track antenna aperture that enables the formation of a high-resolution 2-D image of the illuminated area. Moreover, when multiple parallel trajectories—with cross-track and/or elevation displacements—are considered, the resulting sensing geometry enables the synthesis of two virtual antenna apertures that allow for 3-D backscatter profiling. This imaging modality is known as SAR tomography and is commonly approached by first obtaining multiple 2-D coregistered SAR images—such that each image corresponds with a parallel pass—followed by 1-D standard spectral estimation techniques. A typical application is the 3-D imaging of vegetated areas which, due to the high-penetration capabilities of radiation at long wavelengths, has proven to be of great value for the estimation of forest structure and, in turn, for the quantification of above ground biomass. In addition, with the anticipated advent of long-wavelength spaceborne radars, tomographic SAR techniques will become of considerable interest, as tomographic data sets will be available on a large scale. However, ideal sampling conditions are known to require a large number of dense regular acquisitions, which are not only limited and expensive but can also lead to temporal decorrelation. This dissertation explores the possibility of reducing the number of passes required for 3-D SAR imaging of forested areas by formulating the problem in a sparsity driven framework usually referred to as compressed sensing (CS). To this end, the aforementioned 1-D spectral estimation step—which basically yields a vertical backscatter profile—will be regarded as the process of singling out a solution to an underdeter- mined linear system. In this regard, the criterion will be based on choosing a backscatter profile such that it can be sparsely represented in an alternative domain. In particular, the use of a wavelet basis will prove to be a suitable choice. The method will be formulated for both single-channel and polarimetric sensors and will be shown to be robust to nonideal acquisitions as well as to be able to ensure physical validity. Also, these sparsity-based techniques will be evaluated as a function of sensor-to-target distance, required a priori knowledge, and computation time. Furthermore, a convex optimization approach to separation of forest scattering mechanisms will be introduced. In essence, the method aims to pre-filter tomographic data sets so that canopy and ground contributions can be separately reconstructed. Finally, a thorough validation will be provided by using polarimetric L- and P-band data acquired by the Experimental SAR (E-SAR) sensor of the German Aerospace Center (DLR).
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