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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]

In real hyperspectral images, there exist variations within spectra of materials. The inherent spectral variability is one of the major obstacles for the successful hyperspectral image target detection. Although several hyperspectral image target detection algorithms have been proposed, there are few algorithms considering the spectral variability. Under such circumstances, in this paper, we propose a hyperspectral image target detection algorithm that is robust to the target spectral variability. The proposed algorithm utilizes an inequality constraint to guarantee that the outputs of target spectra, which vary in a certain set, are larger than one, so that these target spectra could be detected. The proposed algorithm transforms the target detection to a convex optimization problem and uses a kind of interior point method named barrier method to solve the formulated optimization problem effectively. Two synthetic hyperspectral images and two real hyperspectral images are used to conduct experiments. The experimental results demonstrate the proposed algorithm is robust to the target spectral variability and performs better than other classical algorithms. [ABSTRACT FROM AUTHOR]