Implementation of an Optimal First-Order Method for Strongly Convex Total Variation Regularization

We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to $\mu$-strongly convex objective functions with $L$-Lipschitz continuous gradient. In the framework of Nesterov both $\mu$ and $L$ are assumed known -- an assumption that is seldom satisfied in practice. We propose to incorporate mechanisms to estimate locally sufficient $\mu$ and $L$ during the iterations. The mechanisms also allow for the application to non-strongly convex functions. We discuss the iteration complexity of several first-order methods, including the proposed algorithm, and we use a 3D tomography problem to compare the performance of these methods. The results show that for ill-conditioned problems solved to high accuracy, the proposed method significantly outperforms state-of-the-art first-order methods, as also suggested by theoretical results.Comment: 23 pages, 4 figure

Assessment of the masking effects of birdsong on the road traffic noise environment

This study aims to explore how the soundscape quality of traffic noise environments can be improved by the masking effects of birdsong in terms of four soundscape characteristics, i.e., Perceived Loudness, Naturalness, Annoyance and Pleasantness. Four factors that may influence the masking effects of birdsong (i.e., distance of the receiver from a sound source, loudness of masker, occurrence frequencies of masker, and visibility of sound sources) were examined by listening tests. The results show that the masking effects are more significant in the road traffic noise environments with lower sound levels (e.g. 19 m). Adding birdsong can indeed increase the Naturalness and Pleasantness of the traffic noise environment at different distances of the receiver from a road. Naturalness, Annoyance and Pleasantness, but not Perceived Loudness, can be altered by increasing the birdsong loudness (i.e., from 37.5 to 52.5 dBA in this study). The Pleasantness of traffic noise environments increases significantly from 2.7 to 6.7, when the occurrence of birdsong over a period of 30 s is increased from 2 to 6 times. The visibility of the sound source also influences the masking effects, but its effect is not as significant as the effects of the three other factors

Minimization Algorithms Based On Supervisor and Searcher Co-operation

In the present work, we explore a general framework for the design of new minimization algorithms with desirable characteristics, namely, supervisor-searcher cooperation. We propose a class of algorithms within this framework and examine a gradient algorithm in the class. Global convergence is established for the deterministic case in the absence of noise and the convergence rate is studied. Both theoretical analysis and numerical tests show that the algorithm is efficient for the deterministic case. Furthermore, the fact that there is no line search procedure incorporated in the algorithm seems to strengthen its robustness so that it tackles effectively test problems with stronger stochastic noises. The numerical results for both deterministic and stochastic test problems illustrate the appealing attributes of the algorithm