L –penalized Technique to Enhance the Spatial Resolution of Microwave Radiometer Data

Microwave remote sensing from spaceborne instruments plays a fundamental role in several remote sensing applications. A dense spatial and temporal coverage represents the peculiarity of instruments used to perform operational meso-scale earth observations (EO) monitoring. This is the case of radiometer and scatterometer, microwave instruments widely employed to obtain many EO products. Their spatial resolution, while adequate for many global applications, prevents their application in regional-scale studies. Moreover, data fusion among various sensor channels is strongly affected by the different channels spatial resolution. Further, multi-sensor data fusion techniques call for a co-registration of different dataset, e.g. in the forthcoming SMAP mission where Synthetic Aperture Radar (SAR) and radiometer data are simultaneously acquired. In all the cases, the first problem to be dealt with is the different spatial/temporal resolution of the available measurements. The simplest but ineffective approach consists of degrading the measurements at a finer resolution to a coarser one. Alternatively, the intrinsic spatial resolution is to be enhanced. Adjacent radiometer observations mostly cover the same scene features on the ground but with different contribution to the overall received signal. This overlap can be, in principle, accounted for the spatial resolution enhancement of the brightness field. In other terms, this means recovering the high frequency information attenuated (but not nulled out) by the low-pass system transfer function. It must be explicitly pointed out that, although one may think to consider an arbitrarily fine grid, the actual resolution enhancement capabilities are physically limited by the overlap of the measurements and by the sampling pattern. Therefore, a higher sampling density leads to a larger overlap in the measurements, which implies that better resolution enhancement can be achieved but at the expense of an increase in the noise level. Mathematically, the class of problem which describes the relationship between the coarse but partially correlated radiometer measurements and the temperatures to be retrieved on the high resolution grid belongs to the class of Fredholm integral equations of first kind, whose kernel depends on the antenna gain. It is a linear ill-posed inversion problem. In order to reconstruct the brightness temperature a regularization method must be accounted for. In literature some methods to enhance the intrinsic radiometer spatial resolution have been proposed. The classical regularization methods give rise to smooth (and sometimes over-smooth) solution. This represents a drawback in the practical applications, as in resolution enhancement of radiometer data. In this study, an innovative approach …