Proc. SPIE. 10233, Holography: Advances and Modern Trends V
KEYWORDS: Analytics, Holograms, Digital signal processing, Solar energy, Digital holography, Data modeling, Fourier transforms, Data conversion, Electronics engineering, Signal analyzers, Radium, Systems modeling, Digital Light Processing
The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques; however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.
The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.
This paper presents a novel low-rank and sparse decomposition (LSD) based model for anomaly detection in
hyperspectral images. In our model, a local image region is represented as a low-rank matrix plus spares noises in the
spectral space, where the background can be explained by the low-rank matrix, and the anomalies are indicated by the
sparse noises. The detection of anomalies in local image regions is formulated as a constrained LSD problem, which can
be solved efficiently and robustly with a modified “Go Decomposition” (GoDec) method. To enhance the validity of this
model, we adapts a “simple linear iterative clustering” (SLIC) superpixel algorithm to efficiently generate homogeneous
local image regions i.e. superpixels in hyperspectral imagery, thus ensures that the background in local image regions
satisfies the condition of low-rank. Experimental results on real hyperspectral data demonstrate that, compared with
several known local detectors including RX detector, kernel RX detector, and SVDD detector, the proposed model can
comfortably achieves better performance in satisfactory computation time.