Frank-Wolfe-type methods for a class of nonconvex inequality-constrained problems

The Frank-Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed compact convex set, has recently received much attention in the optimization and machine learning literature. In this paper, we propose a new FW-type method for minimizing a smooth function over a compact set defined as the level set of a single difference-of-convex function, based on new generalized linear-optimization oracles (LO). We show that these LOs can be computed efficiently with closed-form solutions in some important optimization models that arise in compressed sensing and machine learning. In addition, under a mild strict feasibility condition, we establish the subsequential convergence of our nonconvex FW-type method. Since the feasible region of our generalized LO typically changes from iteration to iteration, our convergence analysis is completely different from those existing works in the literature on FW-type methods that deal with fixed feasible regions among subproblems. Finally, motivated by the away steps for accelerating FW-type methods for convex problems, we further design an away-step oracle to supplement our nonconvex FW-type method, and establish subsequential convergence of this variant. Numerical results on the matrix completion problem with standard datasets are presented to demonstrate the efficiency of the proposed FW-type method and its away-step variant.Comment: We updated grant information and fixed some minor typos in Section

Robust prior-based single image super resolution under multiple Gaussian degradations

Although SISR (Single Image Super Resolution) problem can be effectively solved by deep learning based methods, the training phase often considers single degradation type such as bicubic interpolation or Gaussian blur with fixed variance. These priori hypotheses often fail and lead to reconstruction error in real scenario. In this paper, we propose an end-to-end CNN model RPSRMD to handle SR problem in multiple Gaussian degradations by extracting and using as side information a shared image prior that is consistent in different Gaussian degradations. The shared image prior is generated by an AED network RPGen with a rationally designed loss function that contains two parts: consistency loss and validity loss. These losses supervise the training of AED to guarantee that the image priors of one image with different Gaussian blurs to be very similar. Afterwards we carefully designed a SR network, which is termed as PResNet (Prior based Residual Network) in this paper, to efficiently use the image priors and generate high quality and robust SR images when unknown Gaussian blur is presented. When we applied variant Gaussian blurs to the low resolution images, the experiments prove that our proposed RPSRMD, which includes RPGen and PResNet as two core components, is superior to many state-of-the-art SR methods that were designed and trained to handle multi-degradation

CTooth+: A Large-scale Dental Cone Beam Computed Tomography Dataset and Benchmark for Tooth Volume Segmentation

Accurate tooth volume segmentation is a prerequisite for computer-aided dental analysis. Deep learning-based tooth segmentation methods have achieved satisfying performances but require a large quantity of tooth data with ground truth. The dental data publicly available is limited meaning the existing methods can not be reproduced, evaluated and applied in clinical practice. In this paper, we establish a 3D dental CBCT dataset CTooth+, with 22 fully annotated volumes and 146 unlabeled volumes. We further evaluate several state-of-the-art tooth volume segmentation strategies based on fully-supervised learning, semi-supervised learning and active learning, and define the performance principles. This work provides a new benchmark for the tooth volume segmentation task, and the experiment can serve as the baseline for future AI-based dental imaging research and clinical application development

Spectrum efficiency maximization in multiband OFDM ultra wideband cognitive radio systems

UltraWideband is a high-speed, short-range and low-power wireless technology. UWB system is overlapped with wireless systems such as WLAN, WiMax and UMTS, which limits the use of UWB. Cognitive radio technology enables the UWB system to efficiently use the overlapped spectrum without causing interference to other wireless systems. The thesis focuses on the design of the cognitive radio resource allocation algorithms for spectrum efficiency maximization in the multiband OFDM UWB system. The spectrum efficiency of a cognitive UWB system depends on the cognitive algorithms used in spectrum sensing, spectrum sharing and spectrum management. The spectrum efficiency maximization problem is formulated to a multi-dimensional knapsack problem with constraints in the transmit power of the UWB subcarriers, the average bit error rate and the interference to the primary users. New cognitive algorithms for spectrum sensing and spectrum management are developed to solve the optimization problem. The proposed low-complexity cognitive algorithms include: primary and advanced power allocation algorithm, group power allocation algorithm and spectrum sensing time optimization algorithm. In a cognitive UWB system, the primary and advanced power allocation algorithm as well as the group power allocation algorithm are used for spectrum management, while spectrum sensing time optimization algorithm is used for spectrum sensing. The spectrum sensing time optimization algorithm computes the optimal spectrum sensing period which maximizes the cognitive UWB system’s data transmission period while guaranteeing a target probability of detection/false-alarm. During the data transmission period, the primary and advanced power allocation algorithm achieves the optimal spectrum efficiency by equally allocating the transmit power and distributing the excessively allocated power to the subcarriers in a greedy manner. Also, the group power allocation algorithm can obtain the optimal spectrum efficiency by adaptively assigning the transmit power to the subcarrier groups according to the effective signal-to-noise ratio of each subcarrier group whose bandwidth is less than the coherence bandwidth of the UWB channel. For energy-limited cognitive UWB system, the proposed cognitive algorithms maximize the spectrum efficiency with lower order-of-growth than the traditional dynamic radio resource allocation algorithms

Optimal Power and Bit Allocation Schemes for Ultra Wideband Cognitive Radio Systems

An optimal power and bit allocation scheme for rate maximization in the ultra wideband (UWB) cognitive radio system is presented in this paper. The scheme generates a series of M-ary quadrature amplitude modulation (M-QAM) zones over each UWB subcarrier. Total transmit power is optimally distributed among the UWB subcarriers for the use of the M-QAM modulation with a maximum M on each subcarrier. This optimization is constrained by the probability of detection, probability of false alarm, bit error rate and the UWB transmit power spectral density mask. The performance of the scheme is analyzed over different UWB fading channels. The results show that the system data rate is significantly improved by using the proposed power and bit allocation scheme.JRC.DG.G.6-Security technology assessmen

Rate Maximization for Multiband OFDM Ultra Wideband Systems Using Adaptive Power and Bit Loading Algorithm

A new design for maximizing the data rate of the multiband orthogonal frequency division multiplexing ultra wideband systems is presented. The design is based on the generation of a series of M-ary quadrature amplitude modulation zones for each UWB subcarrier whose levels of fading depend on the UWB channel model. The available transmitted power is then optimally distributed to use the modulation scheme with the maximum M in the subcarriers. The optimization is constrained by the target bit error rate and the limitation of the UWB transmit power spectral density in each subcarrier. The rate maximization has been obtained in a three-step algorithm consisting of M-QAM zones generation, primary and advanced power and bit loading. The performance of the proposed algorithm is analyzed over UWB channel. The results show that the data rate is significantly improved by an advanced power and bit loading scheme.JRC.G.6-Security technology assessmen