Computational Imaging for Compressive Synthetic Aperture Interferometric Radiometer

Recent work proved the effectiveness of a new concept, namely compressive synthetic aperture interferometric radiometer, which aims to reduce the number of RF chains of an interferometric radiometer by means of a passive microwave component. The device is used for coding <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> antenna signals into <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$N~\ll ~M$ </tex-math></inline-formula>) measured waveforms. Thereafter, a decoding process is applied to retrieve the antenna signals necessary to compute the basic observables of an interferometer, namely complex visibilities. Initially, a Fourier algorithm was applied to reconstruct the images, and nonetheless, this kind of imaging algorithm ignores the visibility observation errors, which cause blurring and distortion effects in the images. Herein, a generalized visibility equation is given while considering <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> antennas associated with <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> receivers. Then, a linear relationship between these visibility samples and the noise source brightness temperature is established, and a regularization method is applied to compute the source image. Furthermore, the impact of the device on the reconstructed images is studied by means of numerical analysis as well as by experiment measurements performed in the <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>-band (2–4 GHz). The results confirm that the computational approach provides accurate reconstructed images compared with those obtained with the Fourier algorithm.

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