10_221o - Estimation of spectrum from speckled SAR images

The multiplicative model can be used to describe SAR image formation. In this context, the effect and nature of coherent speckling on the spectrum of SAR images is investigated. A method for estimate the spectrum of the backscatter image, based on estimates of the spectra of the speckled image and noise is developed. 1 Introduction Images and signals produced by coherent systems are subject to the phenomena of speckle. This kind of noise appears due to interference phenomena between the incident and reflected signals. The result makes visual and automatic interpretation a difficult task, thought it may carry some important information. Usually, images suffering from speckle noise should not be treated with the usual additive-noise derived tools (Wiener filter, for instance), since speckle corrupts the signal in the multiplicative manner and in the amplitude and intensity formats it is non-gaussian [Goodman (1976), Tur et al.(1982)]. Other schemes have been proposed to deal with it, such multilook processing (incoherent average), or various types of linear and adaptative filters. These efforts have generally been directed toward improvement of the signal in the image domain. However, application exist in which the spectrum of the output is of primary interest, [ Beal (1980)], but even in linear filtering aimed at image improvement, it would be useful to have a good estimate of the underlying image spectrum rather than work from a priori assumption such as is often done. This paper extends one-dimensional results on the problem of estimating the spectrum for speckled data [ Goldfinger (1982)]. We first discuss the effects of speckle in SAR images and the mathematical framework used to explain the statistical behaviour of this kind of data. Then we prove that, as long as the output Z is stationary, the power spectral density of Z will be a convolution of the power spectral densities of the backscatter X and the speckle Y in the intensity format. In view of that, we consider three special cases. These cases are uniform target, white uncorrelated speckle and nearest neighbour correlation. The last section presents an estimate of the underlying spectrum based on classical estimates of the return and noise spectrum. We shall study the performance of that estimate based on the performance of the other estimates involved in making it.