Fast numerical calculation of the offset linear canonical transform.

The offset linear canonical transform (OLCT) is an important research topic in many fields, and it has a more universal and elastic performance due to its extra parameters. However, although much work has been done concerning the OLCT, its fast algorithms are rarely addressed. In this paper, an O(N log⁡N) fast OLCT (FOLCT) algorithm that can significantly reduce the amount of calculation and improve accuracy is proposed. First, the discrete form of the OLCT is provided, and several important properties of its kernel are advanced. Next, the FOLCT based on the fast Fourier transform (FT) is derived for its numerical implementation. Then, the numerical results indicate that the FOLCT is a serviceable tool for signal analysis; additionally, the FOLCT algorithm can be used for the FT, fractional FT, linear canonical transform, and other transforms. Finally, its application to the detection of linear frequency modulated signals and optical image encryption, which is a basic case in signal processing, is discussed. The FOLCT can be effectively applied for the fast numerical calculation of the OLCT with valid and accurate results.

Segmented fast linear canonical transform.

Investigation of the discrete and fast linear canonical transforms is becoming one of the hottest research topics in modern signal processing and optics. How to handle and obtain the linear canonical frequency spectrum of very large input data based on equipment with limited memory space is one of the key problems. To focus on this problem, a new kind of segmented fast linear canonical transform has been proposed in this paper. First, the large data is segmented into short data. Thereby, the proposed algorithms can calculate very large input data and simultaneously keep the ideal frequency resolution. Second, the complexity of the derived algorithms has been analyzed in detail for different kinds of signals. Their performance with regard to resolution and precision are compared with the existing fast linear canonical transforms. Finally, experimental results are presented to verify the correctness of the results obtained.

A Novel Active Contour Model for Noisy Image Segmentation based on Adaptive Fractional Order Differentiation.

The images used in various practices are often disturbed by noise, such as Gaussian noise, speckled noise, and salt and pepper noise. Images with noise are one of the challenges for segmentation, since the noise may cause inaccurate segmented results. To cope with the effect of noise on images during segmentation, a novel active contour model is proposed in this paper. The newly proposed model consists of fitting term, regularization term and penalty term. The fitting term is designed using a Gaussian kernel function and fractional order differentiation with an adaptively defined fractional order, which applies different orders to different pixels. The regularization term is applied to maintain the smoothness of curves. In order to ensure stable evolution of curves, a penalty term is added into the proposed model. Comparison experiments are conducted to show the effectiveness and efficiency of the proposed model.