Multiscale NMF based on intra-pixel and inter-pixel structure adjustment for spectral unmixing

Abstract

Various improved nonnegative matrix factorization (NMF) methods have been widely used in spectral unmixing (SU), including nonlinear versions to counter for the lower spatial resolution and interaction between materials. But the obtained abundances are still not satisfactory, especially in the boundary region. To resolve this issue, this paper develops a multiscale NMF algorithm based on intra-pixel and inter-pixel structure adjustment (ISAMNMF) for SU, which implements SU from both coarse and fine perspectives. The spatial structure of subpixel abundances is redefined to improve abundance estimation and then further corrects endmember extraction by establishing the mapping relations between superpixel scale, original pixel scale and subpixel scale. Firstly, the mapping relationship from original abundances to subpixel abundances is established, to refine the intra-pixel and inter-pixel spatial structure. Then, the subpixel abundances are divided into multiple superpixel regions to optimize similar subpixel abundances in each superpixel region, respectively. A subpixel structure-guided matrix is built according to all subpixel abundances in the superpixel region. With the structure-guided matrix, the subpixel abundances are rearranged and changed, to adaptively ensure similarities in homogeneous regions and promote differences beside the boundary. Consequently, the original abundances are corrected. Finally, considering the stronger sparse distribution of materials at subpixel level, the guided matrix is forced to ensure the sparsity of subpixel abundances. Most importantly, with the refined structure adjustment and sparsity constraints of subpixel abundances, the endmember estimation in subpixel space is optimized together via NMF. Experimental results on synthetic and real data prove that the proposed ISAMNMF can achieve better unmixing results, with higher robustness.

Keywords

• Nonnegative matrix factorization (NMF)
• Spectral unmixing
• Subpixel unmixing
• Multiple scales
• Sparse unmixing
• Structure adjustment