An Efficient Compressive Hyperspectral Imaging Algorithm Based on Sequential Computations of Alternating Least Squares

Geunseop Lee

doi:10.3390/rs11242932

Abstract

Hyperspectral imaging is widely used to many applications as it includes both spatial and spectral distributions of a target scene. However, a compression, or a low multilinear rank approximation of hyperspectral imaging data, is required owing to the difficult manipulation of the massive amount of data. In this paper, we propose an efficient algorithm for higher order singular value decomposition that enables the decomposition of a tensor into a compressed tensor multiplied by orthogonal factor matrices. Specifically, we sequentially compute low rank factor matrices from the Tucker-1 model optimization problems via an alternating least squares approach. Experiments with real world hyperspectral imaging revealed that the proposed algorithm could compute the compressed tensor with a higher computational speed, but with no significant difference in accuracy of compression compared to the other tensor decomposition-based compression algorithms.

Highlights

Hyperspectral imaging (HSI) allows one to provide information on the spatial and spectral distributions of a target scene simultaneously by acquiring up to hundreds of narrow and adjacent spectral band images ranging from ultraviolet to far-infrared electromagnetic spectrum [1,2]
We focused on developing an efficient algorithm to compute a higher order singular value decomposition (HOSVD), which is a special case of Tucker decomposition with orthogonal constraints on the factor matrices
To compare the performances of the proposed algorithm with previous algorithms, we evaluated the relative errors and the execution times with the algorithm from higher order orthogonal iterations (HOOI), a Crank–Nicholson-like algorithm for HOSVD (CrNc henceforce) [19]; a quasi-Newton-based nonlinear least squares algorithm [17]; and a method based on block coordinate descent search [18] which is a slight modification of the algorithm described in [23] ( BCD-CD)

Summary

Introduction

Hyperspectral imaging (HSI) allows one to provide information on the spatial and spectral distributions of a target scene simultaneously by acquiring up to hundreds of narrow and adjacent spectral band images ranging from ultraviolet to far-infrared electromagnetic spectrum [1,2]. The signals captured by the imaging sensor are digitized and arranged into pixels of a two-dimensional image T = RI×λ, where I denotes the size of X-directional spatial information, and λ is the number of quantized spectra of the signals. Once the HSI data are obtained, they can be used in many applications, such as detecting and identifying objects at a distance in environmental monitoring [3] or medical image processing [4], finding anomaly in automatic visual inspection [5], or detecting and identifying targets of interest [6,7]. Efficient compression techniques must be employed as preprocessing for applications to filter out some redundancy along their adjacent spectral bands or spatial information, thereby reducing the size of T

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Conclusion