Sparse unmixing via variable splitting and augmented Lagrangian for vegetation and urban area classification using Landsat data

Abstract

In this paper, we explore the possibility of sparse regression, a new direction in unmixing, for vegetation and urban area classification. SUnSAL (Sparse unmixing via variable splitting and augmented Lagrangian) in both unconstrained and constrained forms (with the abundance non-negativity and abundance sum-to-one constraints) were used with a set of global endmembers (substrate, vegetation and dark objects) to unmix a set of computer simulated noise-free and noisy data (with Gaussian noise of different signal-to-noise ratio) in order to judge the robustness of the algorithm. The error in the fractional estimate was examined for varying noise power (variance): 2, 4, 8, 16, 32, 64, 128 and 256. In the second set of experiments, a spectrally diverse collection of 11 scenes of Level 1 terrain corrected, cloud free Landsat-5 TM data representing an agricultural setup in Fresno, California, USA were used. The corresponding ground data for validation were collected on the same days of satellite overpass. Finally in the third set of experiments, a clear sky Landsat-5 TM data for an area near the Golden Gate Bridge, San Francisco (an urbanized landscape), California, USA were used to assess the algorithm. The fractional estimates of the 30 m Landsat-5 TM data were compared with the fractional estimates of a high-resolution World View-2 data (2 m spatial resolution) obtained using a fully constrained least squares algorithm. The results were evaluated using descriptive statistics, correlation coefficient, RMSE, probability of success and bivariate distribution function, which showed that constrained model was better than unconstrained form.