Adaptive Sparse Subpixel Mapping With a Total Variation Model for Remote Sensing Imagery

Subpixel mapping, which is a promising technique based on the assumption of spatial dependence, enhances the spatial resolution of images by dividing a mixed pixel into several subpixels and assigning each subpixel to a single land-cover class. The traditional subpixel mapping methods usually utilize the fractional abundance images obtained by a spectral unmixing technique as input and consider the spatial correlation information among pixels and subpixels. However, most of these algorithms treat subpixels separately and locally while ignoring the rationality of global patterns. In this paper, a novel subpixel mapping model based on sparse representation theory, namely, adaptive sparse subpixel mapping with a total variation model (ASSM-TV), is proposed to explore the possible spatial distribution patterns of subpixels by considering these subpixels as an integral patch. In this way, the proposed method can obtain the optimal subpixel mapping result by determining the most appropriate subpixel spatial pattern. However, the number of possible spatial configurations of subpixels can increase sharply with large-scale factors, and therefore, in ASSM-TV, the subpixel mapping is considered as a sparse representation problem. A preconstructed discrete cosine transform dictionary, which consists of piecewise smooth subpixel patches and textured patches, is utilized to express the original subpixel mapping observation in a sparse representation pattern. The total variation prior model is designed as a spatial regularization constraint to characterize the relationship between a subpixel and its neighboring subpixels. In addition, a joint maximum a posteriori model is proposed to adaptively select the regularization parameters. Compared with the other traditional and state-of-the-art subpixel mapping approaches, the experimental results using a simulated image, three synthetic hyperspectral remote sensing images, and two real remote sensing images demonstrate that the proposed algorithm can obtain better results, in both visual and quantitative evaluations.