Politecnico Di Milano

Tele-Rilevamento Europa- T.r.e. S.r.l.

Tre Altamira S.r.l.

Alessandro Ferretti

Fabio Rocca

Claudio Maria Prati

Alfio Fumagalli

Fabrizio Novali

Francesco De Zan

Alessio Rucci

Stefano Tebaldini

Roberto Locatelli

A process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, comprising the following steps: a) acquiring a series of N radar images (Al . . . AN) by means of a SAR sensor on a same area with acquisition geometries such as to allow re-sampling of the data on a common grid; b) after re-sampling on a common grid, selecting a pixel from the common grid; c) calculating the coherence matrix of the selected pixel, that is estimating the complex coherence values for each possible pair of available images; d) maximizing, with respect of the source vector &#x3b8;, here an unknown element, the functional: (formula) being R the operator which extracts the real part of a complex number, &#x3b3;the modulus of the element (n,m) of the coherence matrix, k a positive real number, &#x3c6;the phase of the element (n,m) of the coherence matrix, &#x3b8;n and &#x3b8;m the elements n and m of the unknown vector &#x3b8;. Given that only phase differences appear in the functional T, the values of the unknown factor are estimated less an additive constant, which can be fixed by setting for example &#x3b8;=0, and the phase values &#x3b8;thus obtained constitute the vector of the filtered phase values. 

Process for filtering interferograms obtained from SAR images acquired on the same area

A process includes acquiring radar images on the same area, calculating a vector of n amplitude or intensity values relating to a sample pixel in the n images available, identifying the vector as a sample vector, and defining an estimation window for the sample pixel for identifying a set of pixels around the sample pixel. Additionally, calculating vectors of N amplitude or intensity values for each pixel contained in the estimation window, comparing each vector with the sample vector, identifying pixels associated with the vectors that have passed a statistical test and identifying pixels associated with the vectors that have not passed the statistical test, eliminating the pixels contained in the estimation window that are not connected to the sample pixel, and identifying the set of pixels that are statistically homogeneous with the sample pixel.

Process for identifying statistically homogeneous pixels in SAR images acquired on the same area

Process for radar measurements of movements of city areas and landsliding zones, characterised in that permanent scatterers are identified through the analysis of N&minus;1 differential interferograms with respect to the same image (master), using a reference digital elevation model (DEM) with vertical precision better that 50 meters. For every pixel of the image selected on the satistical properties of the modulus of the reflectivity, a temporal series of the interferometric phases is generated. Then, differences among temporal series that belong to neighboring pixels are formed (differential temporal series). For every differential temporal series, the linear phase components are calculated in relation to the baseline and the phase components connected to the displacement model, already known, in relation to the time. The relative error between the precise elevation of the pixel and that supplied from the reference DEM is associated with the linear phase component of the differential temporal series in relation to the baseline.

Process for radar measurements of the movement of city areas and landsliding zones

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Milan, Italy

Alessandro Ferretti