Reconstruction of compressed samples in shift-invariant space base on matrix factorization

According to the model of compressed sampling in shift-invariant space, the over-complete dictionary is usually a function matrix, which increases the complexity of reconstructing samples. In order to reduce the complexity of reconstructing samples, this paper proposes a reconstruction method based on matrix factorization. The method transforms over-complete dictionary into the multiplication of a reversible function matrix and a constant matrix using least squares error, and converts the samples reconstruction into the computing of constant matrix, which reduces the complexity of samples reconstruction. Meanwhile, the feasibility and convergence of method is analyzed in theory. Finally, the convergence and reconstruction error of the method is validated by simulation; and it is shown that the method is effective.     

A variational approach to recovering depth from defocused images

In this paper, we propose a regularized solution to the depth from defocus (DFD) problem using the space-frequency representation (SFR) framework. A smoothness constraint is imposed on the estimates of the blur parameter, and a variational approach to the DFD problem is developed. Among the numerous SFRs, we study the applicability of the complex spectrogram and the Wigner distribution, in particular, for depth recovery. The performance of the proposed variational method is tested on both synthetic and real images. The method yields good results, and the quality of the estimates is significantly better than that obtained without the smoothness constraint on the blur parameter     

A variational approach to vesicle membrane reconstruction from fluorescence imaging

Biological applications like vesicle membrane analysis involve the precise segmentation of 3D structures in noisy volumetric data, obtained by techniques like magnetic resonance imaging (MRI) or laser scanning microscopy (LSM). Dealing with such data is a challenging task and requires robust and accurate segmentation methods. In this article, we propose a novel energy model for 3D segmentation fusing various cues like regional intensity subdivision, edge alignment and orientation information. The uniqueness of the approach consists in the definition of a new anisotropic regularizer, which accounts for the unbalanced slicing of the measured volume data, and the generalization of an efficient numerical scheme for solving the arising minimization problem, based on linearization and fixed-point iteration. We show how the proposed energy model can be optimized globally by making use of recent continuous convex relaxation techniques. The accuracy and robustness of the presented approach are demonstrated by evaluating it on multiple real data sets and comparing it to alternative segmentation methods based on level sets. Although the proposed model is designed with focus on the particular application at hand, it is general enough to be applied to a variety of different segmentation tasks.     

A robust direct variational approach for generation of quadrangular and triangular grids on planar domains

We consider the problem of the quadrangular and triangular grid generation. The algorithm proposed for the solution of this problem is based on a generalization of the so called variational method. In particular, this generalization takes into account a combination of length and area functionals for a given triangular grid related to the quadrangular grid under consideration. As a consequence of this generalization high quality triangular grids of a given domain are obtained in a straightforward way from the quadrangular grids computed by this algorithm. We test the proposed algorithm on standard numerical examples.     

A direct algorithm for constrained variational problems in several dimensions

We introduce a heuristic, practical procedure to take into account, in an easy-to-implement way, point-wise constraints in a variational problem in several dimensions. In addition to showing a convergence result under suitable assumptions, we emphasize the flexibility of the method by using it for an optimal design problem either in conductivity or elasticity, where an optimal mixture of two materials is to be found in a given design domain, under pointwise constraints. We illustrate the performance of the algorithm with some simple test examples.     

A variational approach to monocular hand-pose estimation

In this paper, we propose a model-based approach to recover 3D hand pose from 2D images. To this end, we describe the hand structure using a compact 3D articulated model and reformulate pose estimation as a binary image segmentation problem aiming to separate the hand from the background. We propose generative models for hand and background pixels leading to a log-likelihood objective function which aims to enclose hand-like pixels within the projected silhouette of the 3D model while excluding background-like pixels. Segmentation and hand-pose estimation are jointly addressed through the minimization of a single likelihood function. Pose is determined through gradient descent in the hand parameter space of such an area-based objective function. Furthermore, we propose a new constrained variable metric gradient descent to speed up convergence and finally the so called smart particle filter to deal with occlusions and local minima through multiple hypotheses. Promising experimental results demonstrate the potentials of our approach.     

Root-mean-square gains of switched linear systems: A variational approach

We consider the problem of computing the root-mean-square (RMS) gain of switched linear systems. We develop a new approach which is based on an attempt to characterize the “worst-case” switching law (WCSL), that is, the switching law that yields the maximal possible gain. Our main result provides a sufficient condition guaranteeing that the WCSL can be characterized explicitly using the differential Riccati equations (DREs) corresponding to the linear subsystems. This condition automatically holds for first-order SISO systems, so we obtain a complete solution to the RMS gain problem in this case.     

Nonlinear relaxed cocoercive variational inclusions involving (A, η)-accretive mappings in banach spaces

In this paper, we introduce a new concept of (A, η)-accretive mappings, which generalizes the existing monotone or accretive operators. We study some properties of (A, η)-accretive mappings and define resolvent operators associated with (A, η)-accretive mappings. By using the new resolvent operator technique, we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed Cocoercive variational inclusions involving (A, η)-accretive mappings and study applications of (A, η)-accretive mappings to the approximation-solvability of this class of nonlinear relaxed Cocoercive variational inclusions in q-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works.     

A variational approach to a problem in boiler control

The paper describes work done in examining a particular problem of boiler control. The overall approach is the consideration of the boiler as a unit in the frequency control of an electrical power system.

The possibilities of including frequency control within the economic scheduling program are limited by the ability of the individual set to follow large amplitude load demands fast. This limitation is real and has arisen due to the previous empirical methods of control system design for this system. The scope of the problem outlined demands a broad approach.

One section describes the derivation of a large analytic non-linear computer model of a natural circulation, non-reheat, boiler. Conclusions are drawn as to the relative importance of various factors, design parameters and existing controls, to the dynamic characteristics of this system.

From these results, an even simpler model structure can be derived. A deterministic criterion, reflecting, for a single set, the regulating requirement of the system is desired and the resulting variational problem in two controls and two state variables is solved.

Similarly a one control problem is solved and by programming the open loop “optimal” control strategy, as input to the large analytic computer model, the effects of model simplification are demonstrated.     

Pan-sharpening:a fast variational fusion approach

A fast variational fusion model based on partial differential equations (PDEs) is presented for pansharpening. The functional framework consists of several energy terms. The gradient energy term is created by calculating the gradient vector field of the panchromatic image and the geometry of the pan is injected into the multi-spectral bands. The radiometric reduction energy term and the channel correlation energy term are defined to decrease the radiometric distortion and preserve the correlation of multi-spectral channels while enforcing the inter-bands coherence. Inspired by the shock-filtering model, an inverse diffusion term for image enhancement is put to PDEs which are deduced by minimizing the energy functional. In comparison with the state-of-the-art fusion approaches based on `a trous wavelet and non-sampled contourlet, our model can obtain the fused image with a high spatial or spectral quality by adjusting the weight coefficients of the energy terms. It can also achieve a rather good trade-off between the spatial resolution improvement and the spectral quality preserving. Our model’s computational complexity for one time step is only O(N).     

A variational approach to multi-sensor fusion of images

Past research into multi-modality sensor data fusion has given rise to approaches that are generally heuristic and ad hoc. In this paper we utilize the calculus of variations as the underlying framework for fusing registered images of different modalities when models relating these modalities are available. The result is a mathematically rigorous method for improving the accuracy with which parameters can be estimated. Using both dense and sparse simulated range and intensity data, the proposed approach is demonstrated on the problem of estimating the surface representing the three dimensional structure of a scene. The results indicate that a four to five-fold increase in surface estimation accuracy with respect to the original input data can be realized. Furthermore, an 8%–250% increase in accuracy over surface estimation from each sensing modality alone (i.e., via shape from shading or surface reconstruction) can be realized.H. Pien is supported by Draper Laboratory under IR&D No. 451; J. Gauch is partially supported by the National Science Foundation under Grant IRI-9109431.     

A variational approach to optimum distributed parameter systems

The problem of designing an optimum distributed parameter system is considered. The canonical equations which are the necessary conditions for optimality are derived by applying the calculus of variation. For systems with a quadratic performance index and with its dynamics described by the diffusion, wave, or biharmonic equation, a method for solving the canonical equations is discussed.     

A new system of variational inclusions with (H, η)-monotone operators in hilbert spaces

In this paper, we introduce and study a new system of variational inclusions involving (H, η)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, η)-monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.     

A variational inequality approach for marketable pollution permits

In this paper, we present a variational inequality framework for the modeling, qualitative analysis, and computation of equilibria in markets in pollution permits. The models developed herein allow for different modes of competitive behavior, including oligopolistic behavior, while taking into account the cost of polluting plus the prices of the licenses to pollute at different receptor points. The models deal explicitly with spatial differentiation and also ensure that the imposed environmental quality standards are met through the initial allocation of licenses. An algorithm is proposed, along with convergence results, to compute the profit-maximized quantities of the firms' products and quantities of emissions, as well as the equilibrium allocation of licenses and their prices. Numerical examples are included to illustrate the approach. This is the first time that this methodology is utilized in environmental economics.     

A variational approach to problems in calibration of multiple cameras

This paper addresses the problem of calibrating camera parameters using variational methods. One problem addressed is the severe lens distortion in low-cost cameras. For many computer vision algorithms aiming at reconstructing reliable representations of 3D scenes, the camera distortion effects will lead to inaccurate 3D reconstructions and geometrical measurements if not accounted for. A second problem is the color calibration problem caused by variations in camera responses that result in different color measurements and affects the algorithms that depend on these measurements. We also address the extrinsic camera calibration that estimates relative poses and orientations of multiple cameras in the system and the intrinsic camera calibration that estimates focal lengths and the skew parameters of the cameras. To address these calibration problems, we present multiview stereo techniques based on variational methods that utilize partial and ordinary differential equations. Our approach can also be considered as a coordinated refinement of camera calibration parameters. To reduce computational complexity of such algorithms, we utilize prior knowledge on the calibration object, making a piecewise smooth surface assumption, and evolve the pose, orientation, and scale parameters of such a 3D model object without requiring a 2D feature extraction from camera views. We derive the evolution equations for the distortion coefficients, the color calibration parameters, the extrinsic and intrinsic parameters of the cameras, and present experimental results.     

A sequential Bayesian approach to color constancy using non-uniform filters

This paper introduces a non-uniform filter formulation into the Brainard and Freeman Bayesian color constancy technique. The formulation comprises sensor measurements taken through a non-uniform filter, of spatially-varying spectral sensitivity, placed on the camera lens. The main goal of this paper is twofold. First, it presents a framework in which sensor measurements obtained through a non-uniform filter can be sequentially incorporated into the Bayesian probabilistic formulation. Second, it shows that such additional measurements obtained reduce the effect of the prior in Bayesian color constancy. For the purposes of testing the proposed framework, we use a filter formulation of two portions of different spectral sensitivities. We show through experiments on real data that improvement in the parameter estimation can be obtained inexpensively by sequentially incorporating additional information obtained from the sensor through the different portions of a filter by Bayesian chaining. We also show that our approach outperforms previous approaches in the literature.     

A scalable, high-precision, and low-noise detector of shift-invariant image locations

A scalable, high-precision, and low-noise detector of shift invariant locations in grayscale images is presented. It leads to a wide range of novel image-to-‘data structures’ processing algorithms. Experiments with a single algorithm of this range prove that (i) the output structures convey great amount of semantically relevant information about the original image; (ii) this information can be successfully extracted and used in subsequent applications.     

A gametheoretic approach for non-uniform pole shifting and pole homothety

This paper investigates the problems of non-uniform pole shifting or pole homothety in multivariable linear systems by using a gametheoretic approach and more specifically a particular Nash strategy with an open-loop information structure for a game including a time preference rate in the quadratic criteria. Such a result is possible due to properties of non-symmetric Algebraic Riccati equations associated with an open-loop Nash strategy. Numerical examples allow to illustrate the efficiency of the proposed approach.     

A variational approach to path planning for hyper-redundant manipulators

Motion planning for hyper-redundant manipulators in a complicated and cluttered workspace is a challenging problem. Many of the path planning algorithms, based on cell decomposition or potential field, fail due to the high dimensionality and complex nature of the C-space. Probabilistic roadmap methods (PRM) which have been proven to be successful in high dimensional C-spaces suffer from the drawback of generating paths which involve a lot of redundant motion. In this paper, we propose a path optimizing method to improve a given path in terms of path length and the safety against the collisions, using a variational approach. The capability of variational calculus to optimize a path is demonstrated on a variety of examples. The approach succeeds in providing a good quality path even in high dimensional C-spaces.