Browsing by Subject "Convex optimization"

Now showing 1 - 20 of 24

Open Access
Denoising images corrupted by impulsive noise using projections onto the epigraph set of the total variation function (PES-TV)
(Springer U K, 2015) Tofighi M.; Kose, K.; Çetin, A. Enis
In this article, a novel algorithm for denoising images corrupted by impulsive noise is presented. Impulsive noise generates pixels whose gray level values are not consistent with the neighboring pixels. The proposed denoising algorithm is a two-step procedure. In the first step, image denoising is formulated as a convex optimization problem, whose constraints are defined as limitations on local variations between neighboring pixels. We use Projections onto the Epigraph Set of the TV function (PES-TV) to solve this problem. Unlike other approaches in the literature, the PES-TV method does not require any prior information about the noise variance. It is only capable of utilizing local relations among pixels and does not fully take advantage of correlations between spatially distant areas of an image with similar appearance. In the second step, a Wiener filtering approach is cascaded to the PES-TV-based method to take advantage of global correlations in an image. In this step, the image is first divided into blocks and those with similar content are jointly denoised using a 3D Wiener filter. The denoising performance of the proposed two-step method was compared against three state-of-the-art denoising methods under various impulsive noise models.
Open Access
FIR filter design by convex optimization using directed iterative rank refinement algorithm
(Institute of Electrical and Electronics Engineers Inc., 2016) Dedeoğlu, M.; Alp, Y. K.; Arıkan, Orhan
The advances in convex optimization techniques have offered new formulations of design with improved control over the performance of FIR filters. By using lifting techniques, the design of a length-L FIR filter can be formulated as a convex semidefinite program (SDP) in terms of an L× L matrix that must be rank-1. Although this formulation provides means for introducing highly flexible design constraints on the magnitude and phase responses of the filter, convex solvers implementing interior point methods almost never provide a rank-1 solution matrix. To obtain a rank-1 solution, we propose a novel Directed Iterative Rank Refinement (DIRR) algorithm, where at each iteration a matrix is obtained by solving a convex optimization problem. The semidefinite cost function of that convex optimization problem favors a solution matrix whose dominant singular vector is on a direction determined in the previous iterations. Analytically it is shown that the DIRR iterations provide monotonic improvement, and the global optimum is a fixed point of the iterations. Over a set of design examples it is illustrated that the DIRR requires only a few iterations to converge to an approximately rank-1 solution matrix. The effectiveness of the proposed method and its flexibility are also demonstrated for the cases where in addition to the magnitude constraints, the constraints on the phase and group delay of filter are placed on the designed filter.
Open Access
Fir filter design by convex optimization using rank refinement
(2014) Dedeoğlu, Mehmet
Finite impulse response ﬁlters have been one of the primary topics of digital signal processing since their inception. Consequently, diverse class of design techniques including Chebyshev approximation, Fast Fourier Transform and optimization based methods had been proposed in the literature. With developments in com- putational tools, new design technique tools and formulations on ﬁlters including interior-point solvers and semideﬁnite programming (SDP), emerged. Since FIR ﬁlter design problem can be modelled as a quadratically constrained quadratic program, ﬁlter design problem can be solved via interior-point based convex op- timization methods such as semideﬁnite programming. Unfortunately, SDP for- mulation of problem is nonconvex due to positive lower limit constraint in the passband. To overcome that problem, nonconvex problem can be cast into a convex SDP using semideﬁnite relaxation, which can be solved in polynomial time. Since relaxed formulation does not guarantee rank-1 solution matrix, re- cently proposed directed iterative rank reﬁnement (DIRR) algorithm is used to impose a convex rank-1 constraint. Due to utilization of semideﬁnite relaxation and DIRR, addition of various constraints, such as phase and group delay masks, in convex manner is made possible. For feasibility type optimization formulations of ﬁlter design problem, a convergence rate improved version of DIRR is devel- oped. Proposed techniques are applied on ﬁlter design problems with diﬀerent set of constraints including phase and group delay constraints. Explicit simulations demostrate that the proposed technique is capable of solving nonlinear phase, phase constrained, and group delay constrained ﬁlter design problems.
Open Access
FIR filter design by iterative convex relaxations with rank refinement
(IEEE, 2014) Dedeoğlu, Mehmet; Alp, Yaşar Kemal; Arıkan, Orhan
Finite impulse response (FIR) filters have been a primary topic of digital signal processing since their inception. Although FIR filter design is an old problem, with the developments of fast convex solvers, convex modelling approach for FIR filter design has become an active research topic. In this work, we propose a new method based on convex programming for designing FIR filters with the desired frequency characteristics. FIR filter design problem, which is modelled as a non-convex quadratically constrained quadratic program (QCQP), is transformed to a semidefinite program (SDP). By relaxing the constraints, a convex programming problem, which we call RSDP(Relaxed Semidefinite Program), is obtained. Due to the relaxation, solution to the RSDPs fails to be rank-1. Typically used rank-1 approximations to the obtained RSDP solution does not satisfy the constraints. To overcome this issue, an iterative algorithm is proposed, which provides a sequence of solutions that converge to a rank-1 matrix. Conducted experiments and comparisons demonstrate that proposed method successfully designs FIR filters with highly flexible frequency characteristics.
Open Access
A heterogeneous memory organization with minimum energy consumption in 3D chip-multiprocessors
(IEEE, 2016-05) Asad, Arghavan; Onsori, Salman; Fathy, M.; Jahed-Motlagh, M. R.; Raahemifar, K.
Main memories play an important role in overall energy consumption of embedded systems. Using conventional memory technologies in future designs in nanoscale era cause a drastic increase in leakage power consumption and temperature-related problems. Emerging non-volatile memory (NVM) technologies offer many desirable characteristics such as near-zero leakage power, high density and non-volatility. They can significantly mitigate the issue of memory leakage power in future embedded chip-multiprocessor (eCMP) systems. However, they suffer from challenges such as limited write endurance and high write energy consumption which restrict them for adoption in modern memory systems. In this article, we propose a stacked hybrid memory system for 3D chip-multiprocessors to take advantages of both traditional and non-volatile memory technologies. For reaching this target, we present a convex optimization-based model that minimizes the system energy consumption while satisfy endurance constraint in order to design a reliable memory system. Experimental results show that the proposed method improves energy-delay product (EDP) and performance by about 44.8% and 13.8% on average respectively compared with the traditional memory design where single technology is used. © 2016 IEEE.
Open Access
High performance 3D CMP design with stacked hybrid memory architecture in the dark silicon era using a convex optimization model
(IEEE, 2016-05) Onsori, Salman; Asad, Arghavan; Raahemifar, K.; Fathy, M.
In this article, we present a convex optimization model to design a stacked hybrid memory system to improve performance and reduce energy consumption of the chip-multiprocessor (CMP). Our convex model optimizes numbers and placement of SRAM and STT-RAM memories on the memory layer, and efficiently maps applications/threads on cores in the core layer. Power consumption that is the main challenge in the dark silicon era is represented as a power constraint in this work and it is satisfied by the detailed optimization model in order to design a dark silicon aware 3D CMP. Experimental results show that the proposed architecture considerably improves the energy-delay product (EDP) and performance of the 3D CMP compared to the Baseline memory design. © 2016 IEEE.
Open Access
A high-performance hybrid memory architecture for embedded CMPs using a convex optimization model
(IEEE, 2015-11) Onsori, Salman; Asad, Arghavan; Raahemifar, K.; Fathy, M.
In this article, we present a convex optimization model to design a stacked hybrid memory system for 3D embedded chip-multiprocessors (eCMP). Our convex model optimizes numbers and placement of SRAM and STT-RAM memories on the memory layer, and maps applications/threads on cores in the core layer effectively. The detailed proposed model satisfies the power constraint which is the main challenge of dark-silicon era. Experimental results show that the proposed architecture considerably improves the energy-delay product (EDP) and performance of the 3D eCMP compared to the Baseline memory design. © 2015 IEEE.
Open Access
Hybrid stacked memory architecture for energy efficient embedded chip-multiprocessors based on compiler directed approach
(IEEE, 2015-12) Onsori, Salman; Asad, A.; Öztürk, Özcan; Fathy, M.
Energy consumption becomes the most critical limitation on the performance of nowadays embedded system designs. On-chip memories due to major contribution in overall system energy consumption are always significant issue for embedded systems. Using conventional memory technologies in future designs in nano-scale era causes a drastic increase in leakage power consumption and temperature-related problems. Emerging non-volatile memory (NVM) technologies are promising replacement for conventional memory structure in embedded systems due to its attractive characteristics such as near-zero leakage power, high density and non-volatility. Recent advantages of NVM technologies can significantly mitigate the issue of memory leakage power. However, they introduce new challenges such as limited write endurance and high write energy consumption which restrict them for adoption in modern memory systems. In this article, we propose a stacked hybrid memory system to minimize energy consumption for 3D embedded chip-multiprocessors (eCMP). For reaching this target, we present a convex optimization-based model to distribute data blocks between SRAM and NVM banks based on data access pattern derived by compiler. Our compiler-assisted hybrid memory architecture can achieve up to 51.28 times improvement in lifetime. In addition, experimental results show that our proposed method reduce energy consumption by 56% on average compared to the traditional memory design where single technology is used. © 2015 IEEE.
Open Access
Image restoration and reconstruction using projections onto epigraph set of convex cost fuchtions
(2015) Tofighi, Mohammad
This thesis focuses on image restoration and reconstruction problems. These inverse problems are solved using a convex optimization algorithm based on orthogonal Projections onto the Epigraph Set of a Convex Cost functions (PESC). In order to solve the convex minimization problem, the dimension of the problem is lifted by one and then using the epigraph concept the feasibility sets corresponding to the cost function are defined. Since the cost function is a convex function in R N , the corresponding epigraph set is also a convex set in R N+1. The convex optimization algorithm starts with an arbitrary initial estimate in R N+1 and at each step of the iterative algorithm, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The PESC algorithm provides globally optimal solutions for different functions such as total variation, `1-norm, `2-norm, and entropic cost functions. Denoising, deconvolution and compressive sensing are among the applications of PESC algorithm. The Projection onto Epigraph Set of Total Variation function (PES-TV) is used in 2-D applications and for 1-D applications Projection onto Epigraph Set of `1-norm cost function (PES-`1) is utilized. In PES-`1 algorithm, first the observation signal is decomposed using wavelet or pyramidal decomposition. Both wavelet denoising and denoising methods using the concept of sparsity are based on soft-thresholding. In sparsity-based denoising methods, it is assumed that the original signal is sparse in some transform domain such as Fourier, DCT, and/or wavelet domain and transform domain coefficients of the noisy signal are soft-thresholded to reduce noise. Here, the relationship between the standard soft-thresholding based denoising methods and sparsity-based wavelet denoising methods is described. A deterministic soft-threshold estimation method using the epigraph set of `1-norm cost function is presented. It is demonstrated that the size of the `1-ball can be determined using linear algebra. The size of the `1-ball in turn determines the soft-threshold. The PESC, PES-TV and PES-`1 algorithms, are described in detail in this thesis. Extensive simulation results are presented. PESC based inverse restoration and reconstruction algorithm is compared to the state of the art methods in the literature.
Open Access
Non-linear pricing by convex duality
(Elsevier, 2015) Pınar, M. Ç.
We consider the pricing problem of a risk-neutral monopolist who produces (at a cost) and offers an infinitely divisible good to a single potential buyer that can be of a finite number of (single dimensional) types. The buyer has a non-linear utility function that is differentiable, strictly concave and strictly increasing. Using a simple reformulation and shortest path problem duality as in Vohra (2011) we transform the initial non-convex pricing problem of the monopolist into an equivalent optimization problem yielding a closed-form pricing formula under a regularity assumption on the probability distribution of buyer types. We examine the solution of the problem when the regularity condition is relaxed in different ways, or when the production function is non-linear and convex. For arbitrary type distributions, we offer a complete solution procedure.
Open Access
On explicit solutions of a two-echelon supply chain coordination game
(Springer Verlag, 2018) Pınar, Mustafa Çelebi
A contracting game under asymmetric information specific to two-echelon supply chain coordination between a retailer of unknown type and a supplier is studied. When the parameter which is private information to the retailer (holding cost) is known up to an interval of uncertainty, a uniform discrete approximation for retailer types leads to closed-form solutions where the joint (coordinated) optimal order quantity for a modified holding cost plays a major role. Furthermore, the closed-form solutions result in increasing information rent for higher types under easy-to-verify conditions involving strict lower limits on the total holding costs of retailer and supplier and the difference between uncoordinated optimal costs of consecutive retailer types.
Open Access
Optimal and robust power allocation for visible light positioning systems under illumination constraints
(IEEE, 2019-01) Keskin, Musa Furkan; Sezer, Ahmet Dündar; Gezici, Sinan
The problem of optimal power allocation among light emitting diode (LED) transmitters in a visible light positioning system is considered for the purpose of improving localization performance of visible light communication (VLC) receivers. Specifically, the aim is to minimize the Cramér-Rao lower bound (CRLB) on the localization error of a VLC receiver by optimizing LED transmission powers in the presence of practical constraints, such as individual and total power limitations and illuminance constraints. The formulated optimization problem is shown to be convex and thus can efficiently be solved via standard tools. We also investigate the case of imperfect knowledge of localization parameters and develop robust power allocation algorithms by taking into account both overall system uncertainty and individual parameter uncertainties related to the location and orientation of the VLC receiver. In addition, we address the total power minimization problem under predefined accuracy requirements to obtain the most energy-efficient power allocation vector for a given CRLB level. Numerical results illustrate the improvements in localization performance achieved by employing the proposed optimal and robust power allocation strategies over the conventional uniform and non-robust approaches.
Open Access
Optimal pulse design for visible light positioning systems
(Elsevier BV, 2021-10-16) Yazar, Onurcan; Gezici, Sinan
The problem of optimal pulse design for light-emitting diode (LED) transmitters is investigated in an indoor visible light positioning (VLP) setup. In particular, the problem of localization performance maximization is formulated for both asynchronous and synchronous VLP systems with consideration of practical limitations related to power consumption, illumination levels, and/or effective bandwidths, while quantifying the localization accuracy via the Cramér–Rao lower bound (CRLB). In both asynchronous and synchronous scenarios, the formulated problems are shown to be convex optimization problems, and some properties of the optimal solutions are derived. In addition, the pulse design problem for minimum power consumption is formulated under a CRLB constraint along with other practical limitations; and this problem is also revealed to be a convex optimization problem. Based on the solutions of the proposed optimization problems, pulse design procedures are described to determine the parameters of optimal pulse shapes. Numerical results illustrate the benefits of the proposed optimal pulse design approach in comparison with the state-of-the-art optimal power allocation scheme in the literature. In particular, electrical power consumption can be reduced by around 45% or localization accuracy can be improved by as much as 25% via the proposed optimal pulse design approach in certain scenarios.
Open Access
Optimal signal design for visible light positioning under power and illumination constraints
(2021-11) Yazar, Onurcan
The optimal design of transmit signals for light-emitting diodes (LEDs) in a visible light positioning (VLP) system is analyzed with the objectives of im-provements in localization accuracy and power eﬃciency. Speciﬁcally, the lo-calization performance maximization problem is addressed for asynchronous and synchronous VLP systems where certain system limitations including power con-sumption, illumination, and eﬀective bandwidth are considered, and the localiza-tion performance is quantiﬁed using the Cram´er-Rao lower bound (CRLB). The formulated signal design problems are demonstrated to be convex optimization problems and some properties of the optimal signal design parameters are found. On the other hand, the signal design problem is also formulated for achieving the lowest possible power consumption while guaranteeing a certain localization ac-curacy. Then, the optimal signal design parameters resulted from the solution of these optimization problems are used to construct the optimal transmit signals in the LEDs. The advantages of the optimal signal design approach is demonstrated through the numerical experiments while also presenting a comparison with the state-of-the-art optimal power allocation method in the literature.
Open Access
OptMem: dark-silicon aware low latency hybrid memory design
(IEEE, 2016-01) Onsori, Salman; Asad, Arghavan A; Raahemifar, K.; Fathy, M.
In this article, we present a convex optimization model to design a three dimension (3D)stacked hybrid memory system to improve performance in the dark silicon era. Our convex model optimizes numbers and placement of static random access memory (SRAM) and spin-Transfer torque magnetic random-Access memory(STT-RAM) memories on the memory layer to exploit advantages of both technologies. Power consumption that is the main challenge in the dark silicon era is represented as a main constraint in this work and it is satisfied by the detailed optimization model in order to design a dark silicon aware 3D Chip-Multiprocessor (CMP). Experimental results show that the proposed architecture improves the energy consumption and performanceof the 3D CMPabout 25.8% and 12.9% on averagecompared to the Baseline memory design. © 2016 IEEE.
Open Access
Power-efficient positioning for visible light systems via chance constrained optimization
(IEEE, 2020) Yazar, Onurcan; Keskin, M. F.; Gezici, Sinan
The problem of minimizing total power consumption in light-emitting diode transmitters is investigated for achieving power efficient localization in a visible light communication and positioning system. A robust power allocation approach based on stochastic uncertainties is proposed for total power minimization in the presence of localization accuracy, power, and illumination constraints. Specifically, the power consumption minimization problem is formulated under a chance constraint on the probability of Cramér-Rao lower bound exceeding a tolerable limit, which is a computationally intractable constraint. The sphere bounding method is used to propose a safe convex approximation to this intractable constraint, which makes the resulting problem suitable for standard convex optimization tools. Numerical results demonstrate the advantages of the proposed robust solution over the nonrobust solution and uniform power allocation in the presence of stochastic uncertainty.
Open Access
Projections onto convex sets (POCS) based optimization by lifting
(IEEE, 2013) Çetin, A. Enis; Bozkurt, Alican; Günay, Osman; Habiboglu, Yusuf Hakan; Köse, K.; Onaran, İbrahim; Tofighi, Mohammad; Sevimli, Rasim Akın
A new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in RN the corresponding set which is the epigraph of the cost function is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in R N+1 and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp; p < 1 may be handled by using the supporting hyperplane concept. The new POCS based method can be used in image deblurring, restoration and compressive sensing problems. © 2013 IEEE.
Open Access
Scheduling and queue management for information freshness in multi-source status update systems
(2023-09) Gamgam, Ege Orkun
Timely delivery of information to its intended destination is essential in many ex-isting and emerging time-sensitive applications. While conventional performance metrics like delay, throughput, or loss have been extensively studied in the literature, research concerning the management of age-sensitive traffic is relatively immature. Recently, a number of information freshness metrics have been intro-duced for quantifying the timeliness of information in networked systems carrying age-sensitive traffic, primarily the Age of Information (AoI) and peak AoI (PAoI) metrics as well as their alternatives including Age of Synchronization (AoS), ver-sion age, binary freshness, etc. The focus of this thesis is the development and performance modeling of age-agnostic scheduling and queue management policies in various multi-source status update systems carrying age-sensitive traffic, using the recently introduced information freshness metrics. In this thesis, first, the exact distributions of the AoI and PAoI for the probabilistic Generate-At-Will (GAW) and Random Arrival with Single Buffer (RA-SB) servers are studied with general number of heterogeneous information sources with phase-type (PH-type) service time distributions for which an absorbing Continuous-Time Markov Chains (CTMC) based analytical modeling method, namely AMC (Absorbing Markov Chains) method, is proposed. Secondly, a homogeneous multi-source status update system with Poisson information packet arrivals and exponentially distributed service times is studied for which the server is equipped with a queue holding the freshest packet from each source referred to as Single Buffer Per-Source Queueing (SBPSQ). For this case, two SBPSQ-based scheduling policies are studied, namely First Source First Serve (FSFS) and the Earliest Served First Serve (ESFS) policies, using the AMC method, and it is shown that ESFS presents a promising scheduler for this special setting. Third, a general status update system with two heterogeneous information sources is studied, i.e., sources have different priorities and generally distributed service times, for Deterministic GAW (D-GAW) and Deterministic RA-SB (D-RA-SB) servers. The aim in both servers is to minimize the system AoI/AoS that is time-averaged and weighted across the two sources. For the D-GAW server, the optimal update policy is obtained in closed form. A packet replacement policy, referred to as Pattern-based Replacement (PR) policy, is then proposed for the D-RA-SB server based on the optimal policy structure of the D-GAW server. Finally, scheduling in a cache update system is investigated where a remote server delivers time-varying contents of multiple items with heterogeneous popularities and service times to a local cache so as to maximize the weighted sum binary freshness of the system, and the server is equipped with a queue that holds the most up-to-date content for each item. A Water-filling based Scheduling (WFS) policy and its extension, namely Extended WFS (E-WFS) policy, are proposed based on convex optimization applied to a relaxation of the original system, with low computational complexity and near optimal weighted sum binary freshness performance.
Open Access
Self-Scaled Barrier Functions on Symmetric Cones and Their Classification
(2002) Hauser, R.A.; Güler O.
Self-scaled barrier functions on self-scaled cones were axiomatically introduced by Nesterov and Todd in 1994 as a tool for the construction of primal-dual long-step interior point algorithms. This paper provides firm foundations for these objects by exhibiting their symmetry properties, their close ties with the symmetry groups of their domains of definition, and subsequently their decomposition into irreducible parts and their algebraic classification theory. In the first part we recall the characterization of the family of self-scaled cones as the set of symmetric cones and develop a primal-dual symmetric viewpoint on self-scaled barriers, results that were first discovered by the second author. We then show in a short, simple proof that any pointed, convex cone decomposes into a direct sum of irreducible components in a unique way, a result which can also be of independent interest. We then proceed to showing that any self-scaled barrier function decomposes, in an essentially unique way, into a direct sum of self-scaled barriers defined on the irreducible components of the underlying symmetric cone. Finally, we present a complete algebraic classification of self-scaled barrier functions using the correspondence between symmetric cones and Euclidean-Jordan algebras.
Open Access
Stochastic subgradient algorithms for strongly convex optimization over distributed networks
(IEEE Computer Society, 2017) Sayin, M. O.; Vanli, N. D.; Kozat, S. S.; Başar, T.
We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a different node; and a limited number of gradient oracle calls is allowed at each node. In this framework, we introduce a convex optimization algorithm based on stochastic subgradient descent (SSD) updates. We use a carefully designed time-dependent weighted averaging of the SSD iterates, which yields a convergence rate of O N ffiffiffi N p (1s)T after T gradient updates for each node on a network of N nodes, where 0 ≤ σ < 1 denotes the second largest singular value of the communication matrix. This rate of convergence matches the performance lower bound up to constant terms. Similar to the SSD algorithm, the computational complexity of the proposed algorithm also scales linearly with the dimensionality of the data. Furthermore, the communication load of the proposed method is the same as the communication load of the SSD algorithm. Thus, the proposed algorithm is highly efficient in terms of complexity and communication load. We illustrate the merits of the algorithm with respect to the state-of-art methods over benchmark real life data sets. © 2017 IEEE.