Direct-current biased optical orthogonal frequency division multiplexing (DCO-OFDM) exhibits a high peak-to-average power ratio (PAPR), which leads to nonlinear distortion in the system. In response to the above, the study proposes a scheme that combines direct-current biased optical orthogonal frequency division multiplexing with index modulation (DCO-OFDM-IM) and convex optimization algorithms. The proposed scheme utilizes partially activated subcarriers of the system to transmit constellation modulated symbol information, and transmits additional symbol information of the system through the combination of activated carrier index. Additionally, a dither signal is added to the system’s idle subcarriers, and the convex optimization algorithm is applied to solve for the optimal values of this dither signal. Therefore, by ensuring the system’s peak power remains unchanged, the scheme enhances the system’s average transmission power and thus achieves a reduction in the PAPR. Experimental results indicate that at a system’s complementary cumulative distribution function (CCDF) of 10-4, the proposed scheme reduces the PAPR by approximately 3.5 dB compared to the conventional DCO-OFDM system. Moreover, at a bit error rate (BER) of 10-3, the proposed scheme can lower the signal-to-noise ratio (SNR) by about 1 dB relative to the traditional DCO-OFDM system. Therefore, the proposed scheme enables a more substantial reduction in PAPR and improvement in BER performance compared to the conventional DCO-OFDM approach.

In this paper, we consider a distributed stochastic nonconvex optimization problem for multiagent systems. We propose a distributed stochastic gradient-tracking method with event-triggered communication. A group of agents cooperatively finds a critical point of the sum of local cost functions, which are smooth but not necessarily convex. We show that the proposed algorithm achieves a sublinear convergence rate by appropriately tuning the step size and the trigger threshold. Moreover, we show that agents can effectively solve a nonconvex optimization problem by the proposed event-triggered algorithm with less communication than by the existing time-triggered gradient-tracking algorithm. We confirm the validity of the proposed method by numerical experiments.

Compressed sensing is a rapidly growing research field in signal and image processing, machine learning, statistics, and systems control. In this survey paper, we provide a review of the theoretical foundations of compressed sensing and present state-of-the-art algorithms for solving the corresponding optimization problems. Additionally, we discuss several practical applications of compressed sensing, such as group testing, sparse system identification, and sparse feedback gain design, and demonstrate their effectiveness through Python programs. This survey paper aims to contribute to the advancement of compressed sensing research and its practical applications in various scientific disciplines.

This paper presents a quantized gradient descent algorithm for distributed nonconvex optimization in multiagent systems that takes into account the bandwidth limitation of communication channels. Each agent encodes its estimation variable using a zoom-in parameter and sends the quantized intermediate variable to the neighboring agents. Then, each agent updates the estimation by decoding the received information. In this paper, we show that all agents achieve consensus and their estimated variables converge to a critical point in the optimization problem. A numerical example of a nonconvex logistic regression shows that there is a trade-off between the convergence rate of the estimation and the communication bandwidth.

The mean, median, and mode are usually calculated from univariate observations as the most basic representative values of a random variable. To measure the spread of the distribution, the standard deviation, interquartile range, and modal interval are also calculated. When we analyze continuous relations between a pair of random variables from bivariate observations, regression analysis is often used. By minimizing appropriate costs evaluating regression errors, we estimate the conditional mean, median, and mode. The conditional standard deviation can be estimated if the bivariate observations are obtained from a Gaussian process. Moreover, the conditional interquartile range can be calculated for various distributions by the quantile regression that estimates any conditional quantile (percentile). Meanwhile, the study of the modal interval regression is relatively new, and spline regression models, known as flexible models having the optimality on the smoothness for bivariate data, are not yet used. In this paper, we propose a modal interval regression method based on spline quantile regression. The proposed method consists of two steps. In the first step, we divide the bivariate observations into bins for one random variable, then detect the modal interval for the other random variable as the lower and upper quantiles in each bin. In the second step, we estimate the conditional modal interval by constructing both lower and upper quantile curves as spline functions. By using the spline quantile regression, the proposed method is widely applicable to various distributions and formulated as a convex optimization problem on the coefficient vectors of the lower and upper spline functions. Extensive experiments, including settings of the bin width, the smoothing parameter and weights in the cost function, show the effectiveness of the proposed modal interval regression in terms of accuracy and visual shape for synthetic data generated from various distributions. Experiments for real-world meteorological data also demonstrate a good performance of the proposed method.

With the popularity of smart devices, mobile crowdsensing, in which the crowdsensing platform gathers useful data from users of smart devices, e.g., smartphones, has become a prevalent paradigm. Various incentive mechanisms have been extensively adopted for the crowdsensing platform to incentivize users of smart devices to offer sensing data. Existing works have concentrated on rewarding smart-device users for their short term effort to provide data without considering the long-term factors of smart-device users and the quality of data. Our previous work has considered the quality of data of smart-device users by incorporating the long-term reputation of smart-device users. However, our previous work only considered a quality maximization problem with budget constraints on one location. In this paper, multiple locations are considered. Stackelberg game is utilized to solve a two-stage optimization problem. In the first stage, the crowdsensing platform allocates the budget to different locations and sets price as incentives for users to maximize the total data quality. In the second stage, the users make efforts to provide data to maximize its utility. Extensive numerical simulations are conducted to evaluate proposed algorithm.

The multi-category support vector machine (MC-SVM) is one of the most popular machine learning algorithms. There are numerous MC-SVM variants, although different optimization algorithms were developed for diverse learning machines. In this study, we developed a new optimization algorithm that can be applied to several MC-SVM variants. The algorithm is based on the Frank-Wolfe framework that requires two subproblems, direction-finding and line search, in each iteration. The contribution of this study is the discovery that both subproblems have a closed form solution if the Frank-Wolfe framework is applied to the dual problem. Additionally, the closed form solutions on both the direction-finding and line search exist even for the Moreau envelopes of the loss functions. We used several large datasets to demonstrate that the proposed optimization algorithm rapidly converges and thereby improves the pattern recognition performance.

We propose a useful formulation for ill-posed inverse problems in Hilbert spaces with nonlinear clipping effects. Ill-posed inverse problems are often formulated as optimization problems, and nonlinear clipping effects may cause nonconvexity or nondifferentiability of the objective functions in the case of commonly used regularized least squares. To overcome these difficulties, we present a tractable formulation in which the objective function is convex and differentiable with respect to optimization variables, on the basis of the Bregman divergence associated with the primitive function of the clipping function. By using this formulation in combination with the representer theorem, we need only to deal with a finite-dimensional, convex, and differentiable optimization problem, which can be solved by well-established algorithms. We also show two practical examples of inverse problems where our theory can be applied, estimation of band-limited signals and time-harmonic acoustic fields, and evaluate the validity of our theory by numerical simulations.

This paper considers a distributed subgradient method for online optimization with event-triggered communication over multi-agent networks. At each step, each agent obtains a time-varying private convex cost function. To cooperatively minimize the global cost function, these agents need to communicate each other. The communication with neighbor agents is conducted by the event-triggered method that can reduce the number of communications. We demonstrate that the proposed online algorithm achieves a sublinear regret bound in a dynamic environment with slow dynamics.

Currently, the top-k error ratio is one of the primary methods to measure the accuracy of multi-category classification. Top-k multiclass SVM was designed to minimize the empirical risk based on the top-k error ratio. Two SDCA-based algorithms exist for learning the top-k SVM, both of which have several desirable properties for achieving optimization. However, both algorithms suffer from a serious disadvantage, that is, they cannot attain the optimal convergence in most cases owing to their theoretical imperfections. As demonstrated through numerical simulations, if the modified SDCA algorithm is employed, optimal convergence is always achieved, in contrast to the failure of the two existing SDCA-based algorithms. Finally, our analytical results are presented to clarify the significance of these existing algorithms.

This paper proposes a consensus-based subgradient method under a common constraint set with switching undirected graphs. In the proposed method, each agent has a state and an auxiliary variable as the estimates of an optimal solution and accumulated information of past gradients of neighbor agents. We show that the states of all agents asymptotically converge to one of the optimal solutions of the convex optimization problem. The simulation results show that the proposed consensus-based algorithm with accumulated subgradient information achieves faster convergence than the standard subgradient algorithm.

A free-viewpoint application has been developed that yields an immersive user experience. One of the simple free-viewpoint approaches called “billboard methods” is suitable for displaying a synthesized 3D view in a mobile device, but it suffers from the limitation that a billboard should be positioned in only one position in the world. This fact gives users an unacceptable impression in the case where an object being shot is situated at multiple points. To solve this problem, we propose optimal deformation of the billboard. The deformation is designed as a mapping of grid points in the input billboard silhouette to produce an optimal silhouette from an accurate voxel model of the object. We formulate and solve this procedure as a nonlinear optimization problem based on a grid-point constraint and some a priori information. Our results show that the proposed method generates a synthesized virtual image having a natural appearance and better objective score in terms of the silhouette and structural similarity.

In this paper, we study simultaneous wireless information and power transfer (SWIPT) in two-way relay channels where two users exchange information with each other via a multi-antenna relay node. The signals forwarded by the relay node are also used to supply the power to two users. We formulate a max-min optimization problem aiming to maximize the minimum harvested energy between two users to achieve fairness. We jointly optimize the relay beamforming matrix and allocating powers at the two users subject to the quality of service (QoS) constraints. To be specific, we consider the amplify-and-forward (AF) relay strategy and the time splitting SWIPT strategy. To this end, we propose two different time splitting protocols to enable relay to supply power to two users. To solve the non-convex joint optimization problem, we propose to split the original optimization problem into two subproblems and solving them iteratively to obtain the final solution. It is shown that the first subproblem dealing with the beamforming matrix can be optimally solved by using the technique of relaxed semidefinite programming (SDR), and the second subproblem, which deals with the power allocation, can be solved via linear programming. The performance comparison of two schemes as well as the one-way relaying scheme are provided and the effectiveness of the proposed schemes is verified.

This paper proposes the mesh-topology based wireless-powered communication network (MT-WPCN), which consists of a hybrid-access point (H-AP) and nodes. The H-AP broadcasts energy to all nodes by wireless, and the nodes harvest the energy and then communicate with other nodes including the H-AP. For the communication in the MT-WPCN, we propose the harvest-then-transceive protocol to ensure that the nodes can harvest energy from the H-AP and transmit information selectively to the H-AP or other nodes, which is not supported in most protocols proposed for the conventional WPCN. In the proposed protocol, we consider that the energy harvesting can be interrupted at nodes, since the nodes cannot harvest energy during transmission or reception. We also consider that the harvested energy is consumed by the reception of information from other nodes. In addition, the energy reservation model is required to guarantee the QoS, which reserves the infimum energy to receive information reliably by the transmission power control. Under these considerations, first, we design the half harvest-then-transceive protocol, which indicates that a node transmits information only to other nodes which do not transmit information yet, for investing the effect of the energy harvesting interruption. Secondly, we also design the full harvest-then-transceive protocol for the information exchange among nodes and compatibility with the conventional star-topology based WPCN, which indicates that a node can transmit information to any network unit, i.e., the H-AP and all nodes. We study the sum-throughput maximization in the MT-WPCN based on the half and full harvest-then-transceive protocols, respectively. Furthermore, the amount of harvested energy is analytically compared according to the energy harvesting interruption in the protocols. Simulation results show that the proposed MT-WPCN outperforms the conventional star-topology based WPCN in terms of the sum-throughput maximization, when wireless information transmission among nodes occurs frequently.

Existing image deblurring methods with a blurred/noisy image pair take a two-step approach: blur kernel estimation and image restoration. They can achieve better and much more stable blur kernel estimation than single image deblurring methods. On the other hand, in the image restoration step, they do not exploit the information on the noisy image, or they require ad hoc tuning of interdependent parameters. This paper focuses on the image restoration step and proposes a new restoration method of using a blurred/noisy image pair. In our method, the image restoration problem is formulated as a constrained convex optimization problem, where data-fidelity to a blurred image and that to a noisy image is properly taken into account as multiple hard constraints. This offers (i) high quality restoration when the blurred image also contains noise; (ii) robustness to the estimation error of the blur kernel; and (iii) easy parameter setting. We also provide an efficient algorithm for solving our optimization problem based on the so-called alternating direction method of multipliers (ADMM). Experimental results support our claims.

For a multiuser multi-input multi-output (MU-MIMO) multicell network, the Han-Kobayashi strategy aims to improve the achievable rate region by splitting the data information intended to a serviced user (UE) into a common message and a private message. The common message is decodable by this UE and another UE from an adjacent cell so that the corresponding intercell interference is cancelled off. This work aims to design optimal precoders for both common and private messages to maximize the network sum-rate, which is a highly nonlinear and nonsmooth function in the precoder matrix variables. Existing approaches are unable to address this difficult problem. In this paper, we develop a successive convex quadratic programming algorithm that generates a sequence of improved points. We prove that the proposed algorithm converges to at least a local optimum of the considered problem. Numerical results confirm the advantages of our proposed algorithm over conventional coordinated precoding approaches where the intercell interference is treated as noise.

In this paper, we propose an algorithm that enhances the number of pixels for high-speed imaging. High-speed cameras have a principle problem that the number of pixels reduces when the number of frames per second (fps) increases. To enhance the number of pixels, we suppose an optical structure that block-randomly selects some percent of pixels in an image. Then, we need to reconstruct the entire image. For this, a state-of-the-art method takes three-dimensional reconstruction strategy, which requires a heavy computational cost in terms of time. To reduce the cost, the proposed method reconstructs the entire image frame-by-frame using a new cost function exploiting two types of sparsity. One is within each frame and the other is induced from the similarity between adjacent frames. The latter further means not only in the image domain, but also in a sparsifying transformed domain. Since the cost function we define is convex, we can find the optimal solution using a convex optimization technique with small computational cost. We conducted simulations using grayscale image sequences. The results show that the proposed method produces a sequence, mostly the same quality as the state-of-the-art method, with dramatically less computational time.

In recent years, covariance descriptors have received considerable attention as a strong representation of a set of points. In this research, we propose a new metric learning algorithm for covariance descriptors based on the Dykstra algorithm, in which the current solution is projected onto a half-space at each iteration, and which runs in O(n3) time. We empirically demonstrate that randomizing the order of half-spaces in the proposed Dykstra-based algorithm significantly accelerates convergence to the optimal solution. Furthermore, we show that the proposed approach yields promising experimental results for pattern recognition tasks.

Recovery of low-rank matrices has seen significant activity in many areas of science and engineering, motivated by theoretical results for exact reconstruction guarantees and interesting practical applications. Recently, numerous methods incorporated the nuclear norm to pursue the convexity of the optimization. However, this greatly restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings. This paper studies a generalized non-convex low-rank approximation, where the singular values are in lp-heuristic. Then specific results are derived for image restoration, including denoising and deblurring. Extensive experimental results on natural images demonstrate the improvement of the proposed method over the recent image restoration methods.

This paper considers the beamforming design for energy efficiency transmission over multiple-input and single-output (MISO) channels. The energy efficiency maximization problem is non-convex due to the fractional form in its objective function. In this paper, we propose an efficient method to transform the objective function in fractional form into the difference of two concave functions (DC) form, which can be solved by the successive convex approximation (SCA) algorithm. Then we apply the proposed transformation and pricing mechanism to develop a distributed beamforming optimization for multiuser MISO interference channels, where each user solves its optimization problem independently and only limited information exchange is needed. Numerical results show the effectiveness of our proposed algorithm.