The main focus of this thesis is the modeling and classification of high dimensional data using
structured sparsity. Sparse models, where data is assumed to be well represented as a linear
combination of a few elements from a dictionary, have gained considerable attention in recent
years, and its use has led to state-of-the-art results in many signal and image processing tasks.
The success of sparse modeling is highly due to its ability to efficiently use the redundancy
of the data and find its underlying structure. On a classification setting, we capitalize on this
advantage to properly model and separate the structure of the classes.
We design and validate modeling solutions to challenging problems arising in computer
vision and remote sensing. We propose both supervised and unsupervised schemes for the
modeling of human actions from motion imagery under a wide variety of acquisition conditions.
In the supervised case, the main goal is to classify the human actions in the video given
a predefined set of actions to learn from. In the unsupervised case, the main goal is to analyze
the spatio-temporal dynamics of the individuals in the scene without having any prior
information on the actions themselves. We also propose a model for remotely sensed hysperspectral
imagery, where the main goal is to perform automatic spectral source separation and
mapping at the subpixel level. Finally, we present a sparse model for sensor fusion to exploit
the common structure and enforce collaboration of hyperspectral with LiDAR data for better
mapping capabilities. In all these scenarios, we demonstrate that these data can be expressed as
a combination of atoms from a class-structured dictionary. These data representation becomes
essentially a “mixture of classes,” and by directly exploiting the sparse codes, one can attain
highly accurate classification performance with relatively unsophisticated classifiers.