Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

A Linear-Centric Simulation Framework for Parametric Fluctuations

Abstract: The relative tolerances for interconnect and device parameter variations have not scaled with feature sizes which have brought about significant performance variability. As we scale toward 10 nm technologies, this problem will only worsen. New circuit families and design methodologies will emerge to facilitate construction of reliable systems from unreliable nanometer scale components. Such methodologies require new models of performance which accurately capture the manufacturing realities. Recently, one step toward this goal was made via a new variational reduced order interconnect model that efficiently captures large scale fluctuations in global parameter values. Using variational calculus the linear interconnect systems are represented by analytical models that include the global variational parameters explicitly. In this work we present a framework which extends the previous work to a linear-centric simulation methodology with accurate nonlinear device models and their fluctuations. The framework is applied to generate path delay distributions under nonlinear and linear parameter fluctuations.

A mapping approach to rate-distortion computation and analysis

Abstract: In rate-distortion theory, results are often derived and stated in terms of the optimizing density over the reproduction space. In this paper, the problem is reformulated in terms of the optimal mapping from the unit interval with Lebesgue measure that would induce the desired reproduction probability density. This results in optimality conditions that are "random relatives" of the known Lloyd (1982) optimality conditions for deterministic quantizers. The validity of the mapping approach is assured by fundamental isomorphism theorems for measure spaces. We show that for the squared error distortion, the optimal reproduction random variable is purely discrete at supercritical distortion (where the Shannon (1948) lower bound is not tight). The Gaussian source is thus the only source that produces continuous reproduction variables for the entire range of positive rate. To analyze the evolution of the optimal reproduction distribution, we use the mapping formulation and establish an analogy to statistical mechanics. The solutions are given by the distribution at isothermal statistical equilibrium, and are parameterized by the temperature in direct correspondence to the parametric solution of the variational equations in rate-distortion theory. The analysis of an annealing process shows how the number of "symbols" grows as the system undergoes phase transitions. Thus, an algorithm based on the mapping approach often needs but a few variables to find the exact solution, while the Blahut (1972) algorithm would only approach it at the limit of infinite resolution. Finally, a quick "deterministic annealing" algorithm to generate the rate-distortion curve is suggested. The resulting curve is exact as long as continuous phase transitions in the process are accurately followed. >

Blind Deconvolution of Medical Ultrasound Images: A Parametric Inverse Filtering Approach

Abstract: The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.

Applications of parametric maxflow in computer vision

Abstract: The maximum flow algorithm for minimizing energy functions of binary variables has become a standard tool in computer vision. In many cases, unary costs of the energy depend linearly on parameter lambda. In this paper we study vision applications for which it is important to solve the maxflow problem for different lambda's. An example is a weighting between data and regularization terms in image segmentation or stereo: it is desirable to vary it both during training (to learn lambda from ground truth data) and testing (to select best lambda using high-knowledge constraints, e.g. user input). We review algorithmic aspects of this parametric maximum flow problem previously unknown in vision, such as the ability to compute all breakpoints of lambda and corresponding optimal configurations infinite time. These results allow, in particular, to minimize the ratio of some geometric functional, such as flux of a vector field over length (or area). Previously, such functional were tackled with shortest path techniques applicable only in 2D. We give theoretical improvements for "PDE cuts" [5]. We present experimental results for image segmentation, 3D reconstruction, and the cosegmentation problem.

Fault detection for robot manipulators with parametric uncertainty: a prediction error based approach

Abstract: In this paper, we introduce a new approach to fault detection for robot manipulators. The technique, which is based on the isolation of fault signatures via filtered torque prediction error estimates, does not require measurements or estimates of manipulator acceleration as is the case with some previously suggested methods. The method is formally demonstrated to be robust under uncertainty in the robot parameters. Furthermore, an adaptive version of the algorithm is introduced, and shown to both improve coverage and significantly reduce detection times. The effectiveness of the approach is demonstrated by experiments with a two-joint manipulator system.