Abstract 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.

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.

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.

We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelength dependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering the potential to significantly reduce the quantity of data that need be measured. To achieve this objective, the imagery is divided into contiguous three-dimensional (3D) spatio-spectral blocks of spatial dimension much less than the image dimension. It is assumed that each such 3D block may be represented as a linear combination of dictionary elements of the same dimension, plus noise, and the dictionary elements are learned in situ based on the observed data (no a priori training). The number of dictionary elements needed for representation of any particular block is typically small relative to the block dimensions, and all the image blocks are processed jointly (“collaboratively") to infer the underlying dictionary. We address dictionary learning from a Bayesian perspective, considering two distinct means of imposing sparse dictionary usage. These models allow inference of the number of dictionary elements needed as well as the underlying wavelength-dependent noise statistics. It is demonstrated that drawing the dictionary elements from a Gaussian process prior, imposing structure on the wavelength dependence of the dictionary elements, yields significant advantages, relative to the more conventional approach of using an independent and identically distributed Gaussian prior for the dictionary elements; this advantage is particularly evident in the presence of noise. The framework is demonstrated by processing hyperspectral imagery with a significant number of voxels missing uniformly at random, with imagery at specific wavelengths missing entirely, and in the presence of substantial additive noise.

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.

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.