Band selection (BS) algorithms are an effective means of reducing the high volume of redundant data produced by the hundreds of contiguous spectral bands of Hyperspectral images (HSI). However, BS is a feature selection optimization problem and can be a computationally intensive to solve. Compressive sensing (CS) is a new minimally lossy data reduction (DR) technique used to acquire sparse signals using global, incoherent, and random projections. This new sampling paradigm can be implemented directly in the sensor acquiring undersampled, sparse images without further compression hardware. In addition, CS can be simulated as a DR technique after an HSI has been collected. This paper proposes a new combination of CS and BS using band clustering in the compressively sensed sample domain (CSSD). The new technique exploits the incoherent CS acquisition to develop BS via a CS transform utilizing inter-band similarity matrices and hierarchical clustering. It is shown that the CS principles of the restricted isometric property (RIP) and restricted conformal property (RCP) can be exploited in the novel algorithm coined compressive sensing band clustering (CSBC) which converges to the results computed using the original data space (ODS) given a sufficient compressive sensing sampling ratio (CSSR). The experimental results show the effectiveness of CSBC over traditional BS algorithms by saving significant computational space and time while maintaining accuracy.
Hyperspectral imaging (HSI) systems have found success in a variety of applications and are continuing to grow into new applications placing an emphasis on developing more affordable systems. Compressive sensing (CS) is an enabling technology for applications requiring low cost, size, weight, and power (SWAP) HSI sensors. A typical compressed sensing system includes both sparse sampling (encoding) and sparse recovery (decoding); however, recent work has investigated the design of algorithms capable of operating directly in the compressed domain and have shown great success. Many of these works are based on a random sampling mathematical framework that explicitly models both the sparse representation basis and the sampling basis. Such a model requires the selection of a sparsifying representation basis that is seldom proven to be optimal for hyperspectral images and typically left as an open-ended question for future research. In this work, a brief review of the compressive sensing framework for Hyperspectral pixel vectors is provided and the concept of Universality is exploited to simplify the model, removing the need to specify the sparsifying basis entirely for CS applications where sparse recovery is not required. A simple experiment is constructed to demonstrate Universality in sparse reconstruction and to better illustrate the concept. The results to this experiment clearly show, that with a random sampling framework, knowledge of the sparsifying basis is only required during sparse recovery.
Unsupervised target generation for hyperspectral imagery (HSI) have generated great interest in the hyperspectral community. However, most of the current unsupervised target generation algorithms have to process large HSI data, which is acquired using the traditional Nyquist-Shannon sampling theorem, resulting in data with high band-to-band correlation. As a consequence, these algorithms end up processing redundant information, raising the demand for large memory storage, processing time, and transmission bandwidth. In the past, some efforts have been dedicated to dealing with the redundant information via data reduction (DR) or data compression post-acquisition. However, to the best of our knowledge, this challenge has been addressed outside the context of Compressive Sensing (CS). This paper applies CS data acquisition process at the sensor level so that the redundant information is removed at the early stage of the data processing chain. The main advantage of our approach is that it employs a random sensing process, and the concept of universality, to randomly sense the HSI bands and produce data containing the bare minimum information. We take advantage of CS Restricted Isometric Properties (RIP), Restricted Conformal Properties (RCP), and newly derived orthogonal sub-space projection (OSP) properties to perform automatic target generation process (ATGP) in the compressively sensed band domain (CSBD), instead of in the original data space (ODS), where the HSI data contains full spectral bands. Our experimental results show that, by working in the CSBD, we avoid processing redundant data and still maintain performance results that are comparable with the performance results obtained in the ODS.
Although hyperspectral technology has continued to improve over the years, its use is often still limited due to size, weight and power (SWaP) constraints. One of the more taxing requirements, is the need to sample a large number of very fine spectral bands. The prohibitively large size of hyperpsectral data creates challenges in both archival and processing. Compressive sensing is an enabling technology for reducing the overall processing and SWaP requirements. This paper explores the viability of performing classification on sparsely sampled hyperspectral data without the need of performing sparse reconstruction. In particular, a spatial-spectral classifier based on a Support Vector Machine (SVM) and edge-preserving filters (EPFs) is applied directly in the compressed domain. The well-known Restricted Isometry Property (RIP) and a random spectral sampling strategy are used to evaluate analytically, the error between the compressed classifier and the full band classifier. The mathematical analysis presented shows that the classification error can be expressed in terms of the Restricted Isometry Constant (RIC) and that it is indeed possible to achieve full classification performance in the compressed domain, given that sufficient sampling conditions are met. A set of experiments are performed to empirically demonstrate compressed classification. Images from both the Airborne Visible / Infrared Imaging Spectrometer (AVIRIS) and Reflective Optics System Imaging Spectrometer (ROSIS) are examined to draw inferences on the impact of scene complexity. The results presented clearly demonstrate the possibility of compressed classification and lead to several open research questions to be addressed in future work.
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