A LSQR-type method provides a computationally efficient automated optimal choice of regularization parameter in diffuse optical tomography

Purpose: Developing a computationally efficient automated method for the optimal choice of regularization parameter in diffuse optical tomography. Methods: The least-squares QR (LSQR)-type method that uses Lanczos bidiagonalization is known to be computationally efficient in performing the reconstruction procedure in diffuse optical tomography. The same is effectively deployed via an optimization procedure that uses the simplex method to find the optimal regularization parameter. The proposed LSQR-type method is compared with the traditional methods such as L-curve, generalized cross-validation (GCV), and recently proposed minimal residual method (MRM)-based choice of regularization parameter using numerical and experimental phantom data. Results: The results indicate that the proposed LSQR-type and MRM-based methods performance in terms of reconstructed image quality is similar and superior compared to L-curve and GCV-based methods. The proposed method computational complexity is at least five times lower compared to MRM-based method, making it an optimal technique. Conclusions: The LSQR-type method was able to overcome the inherent limitation of computationally expensive nature of MRM-based automated way finding the optimal regularization parameter in diffuse optical tomographic imaging, making this method more suitable to be deployed in real-time. (C) 2013 American Association of Physicists in Medicine. http://dx.doi.org/10.1118/1.4792459]

Optimal parameter selection for bilateral filters using Poisson unbiased risk estimate

Bilateral filters perform edge-preserving smoothing and are widely used for image denoising. The denoising performance is sensitive to the choice of the bilateral filter parameters. We propose an optimal parameter selection for bilateral filtering of images corrupted with Poisson noise. We employ the Poisson's Unbiased Risk Estimate (PURE), which is an unbiased estimate of the Mean Squared Error (MSE). It does not require a priori knowledge of the ground truth and is useful in practical scenarios where there is no access to the original image. Experimental results show that quality of denoising obtained with PURE-optimal bilateral filters is almost indistinguishable with that of the Oracle-MSE-optimal bilateral filters.

A GIS (geographical information system)-based spatial data mining approach for optimal location and capacity planning of distributed biomass power generation facilities: A case study of Tumkur district, India

This paper primarily intends to develop a GIS (geographical information system)-based data mining approach for optimally selecting the locations and determining installed capacities for setting up distributed biomass power generation systems in the context of decentralized energy planning for rural regions. The optimal locations within a cluster of villages are obtained by matching the installed capacity needed with the demand for power, minimizing the cost of transportation of biomass from dispersed sources to power generation system, and cost of distribution of electricity from the power generation system to demand centers or villages. The methodology was validated by using it for developing an optimal plan for implementing distributed biomass-based power systems for meeting the rural electricity needs of Tumkur district in India consisting of 2700 villages. The approach uses a k-medoid clustering algorithm to divide the total region into clusters of villages and locate biomass power generation systems at the medoids. The optimal value of k is determined iteratively by running the algorithm for the entire search space for different values of k along with demand-supply matching constraints. The optimal value of the k is chosen such that it minimizes the total cost of system installation, costs of transportation of biomass, and transmission and distribution. A smaller region, consisting of 293 villages was selected to study the sensitivity of the results to varying demand and supply parameters. The results of clustering are represented on a GIS map for the region.

SEP-optimal adaptive gain and transmit power amplify-and-forward relaying

Amplify-and-forward (AF) relay based cooperation has been investigated in the literature given its simplicity and practicality. Two models for AF, namely, fixed gain and fixed power relaying, have been extensively studied. In fixed gain relaying, the relay gain is fixed but its transmit power varies as a function of the source-relay (SR) channel gain. In fixed power relaying, the relay's instantaneous transmit power is fixed, but its gain varies. We propose a general AF cooperation model in which an average transmit power constrained relay jointly adapts its gain and transmit power as a function of the channel gains. We derive the optimal AF gain policy that minimizes the fading- averaged symbol error probability (SEP) of MPSK and present insightful and tractable lower and upper bounds for it. We then analyze the SEP of the optimal policy. Our results show that the optimal scheme is up to 39.7% and 47.5% more energy-efficient than fixed power relaying and fixed gain relaying, respectively. Further, the weaker the direct source-destination link, the greater are the energy-efficiency gains.

Power-optimal scheduling for a green base station with delay constraints

We consider a power optimization problem with average delay constraint on the downlink of a Green Base-station. A Green Base-station is powered by both renewable energy such as solar or wind energy as well as conventional sources like diesel generators or the power grid. We try to minimize the energy drawn from conventional energy sources and utilize the harvested energy to the maximum extent. Each user also has an average delay constraint for its data. The optimal action consists of scheduling the users and allocating the optimal transmission rate for the chosen user. In this paper, we formulate the problem as a Markov Decision Problem and show the existence of a stationary average-cost optimal policy. We also derive some structural results for the optimal policy.

Optimal design of timer-based, distributed selection with unknown number of nodes

The timer-based selection scheme is a popular, simple, and distributed scheme that is used to select the best node from a set of available nodes. In it, each node sets a timer as a function of a local preference number called a metric, and transmits a packet when its timer expires. The scheme ensures that the timer of the best node, which has the highest metric, expires first. However, it fails to select the best node if another node transmits a packet within Delta s of the transmission by the best node. We derive the optimal timer mapping that maximizes the average success probability for the practical scenario in which the number of nodes in the system is unknown but only its probability distribution is known. We show that it has a special discrete structure, and present a recursive characterization to determine it. We benchmark its performance with ad hoc approaches proposed in the literature, and show that it delivers significant gains. New insights about the optimality of some ad hoc approaches are also developed.

Training for Antenna Selection in Time-Varying Channels: Optimal Selection, Energy Allocation, and Energy Efficiency Evaluation

Single receive antenna selection (AS) is a popular method for obtaining diversity benefits without the additional costs of multiple radio receiver chains. Since only one antenna receives at any time, the transmitter sends a pilot multiple times to enable the receiver to estimate the channel gains of its N antennas to the transmitter and select an antenna. In time-varying channels, the channel estimates of different antennas are outdated to different extents. We analyze the symbol error probability (SEP) in time-varying channels of the N-pilot and (N+1)-pilot AS training schemes. In the former, the transmitter sends one pilot for each receive antenna. In the latter, the transmitter sends one additional pilot that helps sample the channel fading process of the selected antenna twice. We present several new results about the SEP, optimal energy allocation across pilots and data, and optimal selection rule in time-varying channels for the two schemes. We show that due to the unique nature of AS, the (N+1)-pilot scheme, despite its longer training duration, is much more energy-efficient than the conventional N-pilot scheme. An extension to a practical scenario where all data symbols of a packet are received by the same antenna is also investigated.

Interplay Between Optimal Selection Scheme, Selection Criterion, and Discrete Rate Adaptation in Opportunistic Wireless Systems

An opportunistic, rate-adaptive system exploits multi-user diversity by selecting the best node, which has the highest channel power gain, and adapting the data rate to selected node's channel gain. Since channel knowledge is local to a node, we propose using a distributed, low-feedback timer backoff scheme to select the best node. It uses a mapping that maps the channel gain, or, in general, a real-valued metric, to a timer value. The mapping is such that timers of nodes with higher metrics expire earlier. Our goal is to maximize the system throughput when rate adaptation is discrete, as is the case in practice. To improve throughput, we use a pragmatic selection policy, in which even a node other than the best node can be selected. We derive several novel, insightful results about the optimal mapping and develop an algorithm to compute it. These results bring out the inter-relationship between the discrete rate adaptation rule, optimal mapping, and selection policy. We also extensively benchmark the performance of the optimal mapping with several timer and opportunistic multiple access schemes considered in the literature, and demonstrate that the developed scheme is effective in many regimes of interest.

An approximately H-1-optimal Petrov-Galerkin meshfree method: application to computation of scattered light for optical tomography

Nearly pollution-free solutions of the Helmholtz equation for k-values corresponding to visible light are demonstrated and verified through experimentally measured forward scattered intensity from an optical fiber. Numerically accurate solutions are, in particular, obtained through a novel reformulation of the H-1 optimal Petrov-Galerkin weak form of the Helmholtz equation. Specifically, within a globally smooth polynomial reproducing framework, the compact and smooth test functions are so designed that their normal derivatives are zero everywhere on the local boundaries of their compact supports. This circumvents the need for a priori knowledge of the true solution on the support boundary and relieves the weak form of any jump boundary terms. For numerical demonstration of the above formulation, we used a multimode optical fiber in an index matching liquid as the object. The scattered intensity and its normal derivative are computed from the scattered field obtained by solving the Helmholtz equation, using the new formulation and the conventional finite element method. By comparing the results with the experimentally measured scattered intensity, the stability of the solution through the new formulation is demonstrated and its closeness to the experimental measurements verified.

An integrated model for optimal reservoir operation for irrigation of multiple crops

An integratedm odel is developed,b asedo n seasonailn puts of reservoiri nflow and rainfall in the irrigated area, to determine the optimal reservoir release policies and irrigation allocationst o multiple crops.T he model is conceptuallym ade up of two modules. Module 1 is an intraseasonal allocation model to maximize the sum of relative yieldso f all crops,f or a givens tateo f the systemu, singl inear programming(L P). The module takes into account reservoir storage continuity, soil moisture balance, and crop root growthw ith time. Module 2 is a seasonaal llocationm odel to derive the steadys tate reservoiro peratingp olicyu sings tochastidc ynamicp rogramming(S DP). Reservoir storage, seasonal inflow, and seasonal rainfall are the state variables in the SDP. The objective in SDP is to maximize the expected sum of relative yields of all crops in a year.The resultso f module 1 and the transitionp robabilitieso f seasonailn flow and rainfall form the input for module 2. The use of seasonailn puts coupledw ith the LP-SDP solution strategy in the present formulation facilitates in relaxing the limitations of an earlier study,w hile affectinga dditionali mprovementsT. he model is applied to an existing reservoir in Karnataka State, India.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

Optimal incentive timing strategies for product marketing on social networks

We consider the problem of devising incentive strategies for viral marketing of a product. In particular, we assume that the seller can influence penetration of the product by offering two incentive programs: a) direct incentives to potential buyers (influence) and b) referral rewards for customers who influence potential buyers to make the purchase (exploit connections). The problem is to determine the optimal timing of these programs over a finite time horizon. In contrast to algorithmic perspective popular in the literature, we take a mean-field approach and formulate the problem as a continuous-time deterministic optimal control problem. We show that the optimal strategy for the seller has a simple structure and can take both forms, namely, influence-and-exploit and exploit-and-influence. We also show that in some cases it may optimal for the seller to deploy incentive programs mostly for low degree nodes. We support our theoretical results through numerical studies and provide practical insights by analyzing various scenarios.

Hardness results for computing optimal locally Gabriel graphs

Delaunay and Gabriel graphs are widely studied geo-metric proximity structures. Motivated by applications in wireless routing, relaxed versions of these graphs known as Locally Delaunay Graphs (LDGs) and Lo-cally Gabriel Graphs (LGGs) have been proposed. We propose another generalization of LGGs called Gener-alized Locally Gabriel Graphs (GLGGs) in the context when certain edges are forbidden in the graph. Unlike a Gabriel Graph, there is no unique LGG or GLGG for a given point set because no edge is necessarily in-cluded or excluded. This property allows us to choose an LGG/GLGG that optimizes a parameter of interest in the graph. We show that computing an edge max-imum GLGG for a given problem instance is NP-hard and also APX-hard. We also show that computing an LGG on a given point set with dilation ≤k is NP-hard. Finally, we give an algorithm to verify whether a given geometric graph G= (V, E) is a valid LGG.

Optimal synthesis of adjustable planar four-bar crank-rocker type mechanisms for approximate multi-path generation

This paper deals with an optimization based method for synthesis of adjustable planar four-bar, crank-rocker mechanisms. For multiple different and desired paths to be traced by a point on the coupler, a two stage method first determines the parameters of the possible driving dyads. Then the remaining mechanism parameters are determined in the second stage where a least-squares based circle-fitting procedure is used. Compared to existing formulations, the optimization method uses less number of design variables. Two numerical examples demonstrate the effectiveness of the proposed synthesis method. (C) 2013 Elsevier Ltd. All rights reserved.

Mechanism design for cost optimal PAC learning in the presence of strategic noisy annotators

We consider the problem of Probably Ap-proximate Correct (PAC) learning of a bi-nary classifier from noisy labeled exam-ples acquired from multiple annotators(each characterized by a respective clas-sification noise rate). First, we consider the complete information scenario, where the learner knows the noise rates of all the annotators. For this scenario, we derive sample complexity bound for the Mini-mum Disagreement Algorithm (MDA) on the number of labeled examples to be ob-tained from each annotator. Next, we consider the incomplete information sce-nario, where each annotator is strategic and holds the respective noise rate as a private information. For this scenario, we design a cost optimal procurement auc-tion mechanism along the lines of Myer-son’s optimal auction design framework in a non-trivial manner. This mechanism satisfies incentive compatibility property,thereby facilitating the learner to elicit true noise rates of all the annotators.