Sparsity Optimization Method for Slow-Moving Landslides Detection in Satellite Image Time-Series.

This paper presents a new method based on recent optimization technique to detect slow-moving landslides (<150m/year) in time series of displacement field generated by satellite images. Sparse optimization is applied simultaneously on the 3-D data set in space as well as in time. The proposed method takes into account the distinctive signal physical properties in space and time, by enforcing a sparse representation by blocks in space, but a continuing and monotonous representation in time of the landslides. As a result, we show that a mixed $\ell _{1,2}$ -norm is the most suitable norm for this detection problem, compared to pure $\ell _{1}$ -norm or $\ell _{2}$ -norm. Moreover, an outlier estimation step is included that sets apart the Gaussian noise from locally sparse processing errors in the data. The performance of this approach is tested by applying it both on synthetic data and on a time series of displacements fields over 16 dates in the Colca Valley, Peru. This detection presents commission and omission errors for landslides of 29% and 14%, respectively, using a medium resolution (10 m) data set of optical satellite images. It detects all important landslides, already known from field investigations. Moreover, it also points out other smaller or unknown landslides, increasing the existing slow-moving landslide inventory by +50%. [ABSTRACT FROM AUTHOR]