Linear Convergence of Adaptively Iterative Thresholding Algorithms for Compressed Sensing

This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the original sparse solution at a linear rate under a certain gRIP condition in the noise free case. While in the noisy case, its convergence rate is also linear until attaining a certain error bound. Moreover, as by-products, we also provide some sufficient conditions for the convergence of the AIT algorithm based on the two well-known properties, i.e., the coherence property and the restricted isometry property (RIP), respectively. It should be pointed out that such two properties are special cases of gRIP. The solid improvements on the theoretical results are demonstrated and compared with the known results. Finally, we provide a series of simulations to verify the correctness of the theoretical assertions as well as the effectiveness of the AIT algorithm.Comment: 15 pages, 5 figure

A multi-task learning CNN for image steganalysis

Convolutional neural network (CNN) based image steganalysis are increasingly popular because of their superiority in accuracy. The most straightforward way to employ CNN for image steganalysis is to learn a CNN-based classifier to distinguish whether secret messages have been embedded into an image. However, it is difficult to learn such a classifier because of the weak stego signals and the limited useful information. To address this issue, in this paper, a multi-task learning CNN is proposed. In addition to the typical use of CNN, learning a CNN-based classifier for the whole image, our multi-task CNN is learned with an auxiliary task of the pixel binary classification, estimating whether each pixel in an image has been modified due to steganography. To the best of our knowledge, we are the first to employ CNN to perform the pixel-level classification of such type. Experimental results have justified the effectiveness and efficiency of the proposed multi-task learning CNN

Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution

We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret key rate of the CV-MDI QKD protocol and should not be ignored.Comment: 9 pages, 9 figure