Alexey Castrodad

Learning Discriminative Sparse Representations for Modeling, Source Separation, and Mapping of Hyperspectral Imagery

A method is presented for subpixel modeling, mapping, and classification in hyperspectral imagery using learned block-structured discriminative dictionaries, where each block is adapted and optimized to represent a material in a compact and sparse manner. The spectral pixels are modeled by linear combinations of subspaces defined by the learned dictionary atoms, allowing for linear mixture analysis. This model provides flexibility in source representation and selection, thus accounting for spectral variability, small-magnitude errors, and noise. A spatial-spectral coherence regularizer in the optimization allows pixel classification to be influenced by similar neighbors. We extend the proposed approach for cases for which there is no knowledge of the materials in the scene, unsupervised classification, and provide experiments and comparisons with simulated and real data. We also present results when the data have been significantly undersampled and then reconstructed, still retaining high-performance classification, showing the potential role of compressive sensing and sparse modeling techniques in efficient acquisition/transmission missions for hyperspectral imagery.

Sparse Modeling of Human Actions from Motion Imagery

An efficient sparse modeling pipeline for the classification of human actions from video is here developed. Spatio-temporal features that characterize local changes in the image are first extracted. This is followed by the learning of a class-structured dictionary encoding the individual actions of interest. Classification is then based on reconstruction, where the label assigned to each video comes from the optimal sparse linear combination of the learned basis vectors (action primitives) representing the actions. A low computational cost deep-layer model learning the inter-class correlations of the data is added for increasing discriminative power. In spite of its simplicity and low computational cost, the method outperforms previously reported results for virtually all standard datasets.

Discriminative sparse representations in hyperspectral imagery

Recent advances in sparse modeling and dictionary learning for discriminative applications show high potential for numerous classification tasks. In this paper, we show that highly accurate material classification from hyperspectral imagery (HSI) can be obtained with these models, even when the data is reconstructed from a very small percentage of the original image samples. The proposed supervised HSI classification is performed using a measure that accounts for both reconstruction errors and sparsity levels for sparse representations based on class-dependent learned dictionaries. Combining the dictionaries learned for the different materials, a linear mixing model is derived for sub-pixel classification. Results with real hyperspectral data cubes are shown both for urban and non-urban terrain.

Sparse modeling for hyperspectral imagery with LiDAR data fusion for subpixel mapping

Several studies suggest that the use of geometric features along with spectral information improves the classification and visualization quality of hyperspectral imagery. These studies normally make use of spatial neighborhoods of hyperspectral pixels for extracting these geometric features. In this work, we merge point cloud Light Detection and Ranging (LiDAR) data and hyperspectral imagery (HSI) into a single sparse modeling pipeline for subpixel mapping and classification. The model accounts for material variability and noise by using learned dictionaries that act as spectral endmembers. Additionally, the estimated abundances are influenced by the LiDAR point cloud density, particularly helpful in spectral mixtures involving partial occlusions and illumination changes caused by elevation differences. We demonstrate the advantages of the proposed algorithm with co-registered LiDAR-HSI data.

Point Cloud Denoising via Moving RPCA

We present an algorithm for the restoration of noisy point cloud data, termed Moving Robust Principal Components Analysis (MRPCA). We model the point cloud as a collection of overlapping two‐dimensional subspaces, and propose a model that encourages collaboration between overlapping neighbourhoods. Similar to state‐of‐the‐art sparse modelling‐based image denoising, the estimated point positions are computed by local averaging. In addition, the proposed approach models grossly corrupted observations explicitly, does not require oriented normals, and takes into account both local and global structure. Sharp features are preserved via a weighted ℓ1 minimization, where the weights measure the similarity between normal vectors in a local neighbourhood. The proposed algorithm is compared against existing point cloud denoising methods, obtaining competitive results.

Multiscale and multidirectional tight frames for image analysis

There are many models for analyzing and synthesizing 2D data at a variety of different scales and directions. Characterizing directional information in data is significant since it provides information on the location of key objects in the data. These locations in turn are used to describe where these objects are relative to each other. However, often these models only account for a given set of directions, and, furthermore, they tend to be computationally intensive. For example, the theoretical developments described in the large number of published articles on wavelet transforms provides for data exploitation along horizontal, vertical, and diagonal directions as well as multiple scales. However, several techniques have been devised to model and exploit 2D data along multiple directions.1 Other state-of-the-art methods in sparse directional representations include contourlets,2 curvelets,3 shearlets,4 and multidirectional wavelets.5 These methods have been extensively analyzed, and their success in providing near optimal geometric decompositions of signals has been established.2–5 As mentioned, these models are often difficult to implement, and their high-dimensional analogs are still not well understood. We propose a computationally efficient model for analyzing 1D and 2D multiscale and multidirectional data. The model is based on a mathematical concept known as tight frames. Redundancy is a desirable property for many applications, including signal denoising,6 classification,7 sparse representations of signals,8, 9 and compressive sensing.10 It is in relation to the last two applications that we see the biggest potential of frames in creating representation models that can be optimized for a specific application. The proposed models are an extension of earlier reported research.11, 12 That work demonstrated that by using the proper choice of functions, the models can remove directional smooth content in 2D data and at the same time Figure 1. Radial lines varying in intensity and originating from the origin at 0, 14.03, 26.51, 36.86, 45, 53.13, 63.43, 75.96 and 90.

Robust categorization of point cloud data

We present a low rank and sparse modeling framework and a computationally efficient algorithm for extracting Digital Terrain Models (DTMs) and foreground objects from Point Cloud Data (PCD). The model decomposes an input point cloud into three main components: bare-earth, spatially structured objects, and spatially unstructured objects or other spurious data, generating a richer output than standard bare-earth estimation algorithms. We test the proposed method using real Light Detection And Ranging (LiDAR) data.