Advances in Hyperspectral Image Processing Techniques

7Restricted Entropy and Spectrum Properties for Hyperspectral Imaging

Chein‐I Chang^1,2 and Bernard Lampe¹

¹Remote Sensing Signal and Image Processing Laboratory, Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD, USA

²Center for Hyperspectral Imaging in Remote Sensing (CHIRS), Information and Technology College, Dalian Maritime University, Dalian, China

7.1 Introduction

Restricted isometry property (RIP) plays a key role in developing the field of compressive sensing (CS) [1–3]. Concisely, when a matrix satisfies the RIP condition for a certain integer sparsity level k, the information of any signal vector with k or fewer nonzero components transformed by the matrix will be preserved for nearly lossless recovery using nonlinear optimization [2]. Using RIP, the theory of CS has shown that using incoherent matrices allows for under‐sampling sparse signals while preserving the sensed signal energy [4]. As a consequence, nonlinear reconstruction algorithms can be used to recover signals via CS [5–7]. Another property derived from RIP, known as restricted conformal property (RCP), states that the angle between two incoherently sensed sparse signals is preserved [8, 9]. Generally speaking, any signal vector can be completely specified by the length of the signal which corresponds to the total energy in terms of RIP and the angle between the signal vector and the representation basis in the sense of RCP. A hyperspectral ...