Synchronously separating the area and crop condition of mixed pixel using ICA

Independent component analysis (ICA) is a powerful new method that use information contained in higher order cross-moments of multivariate data to find a linear representation of non-Gaussian data, so that the components are statistically independent. As the perpendicular vegetation index (PVI) of mixed pixel can be expressed by the linear summation of the PVI value of components, we can use remotely sensed time series of PVI to retrieve the area proportion and crop condition of components in mixed pixel by ICA. In this paper an ICA based approach is proposed for quantitatively separating the area and crop condition of mixed pixel and solving uncertainty of ICA. Because the area proportion of components is fixed during the growing period, and the sum of area proportion of components in pixel is equal to 1, the uncertainty of ICA, therefore is solved perfectly. The numerical simulation shows the area of soil and wheat and the multi-temporal perpendicular vegetation index of the wheat can be quantitatively retrieved synchronously by ICA. Three components: rape, wheat and soil in mixed pixel can also be separated exactly. Even the difference of crop condition among pixels can be retrieved exactly. The retrieval error of area proportion and PVI value of crop is less than 5 %, when no input error is added. As adding 20% input error, the retrieval error can also be restricted within 10%. In order to make the method in use, we try to inverse the area proportion and crop condition of components in mixed pixels using MODIS reflectivity product. The study area lies in Hebei Province. The main crop in the period is wheat. The area and PVI value calculated by ETM image validated the retrieval result