Dynamic Tomography Reconstruction by Projection-Domain Separable Modeling

In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant. Instead, the objective is to reconstruct a spatio-temporal representation of the object, which can be displayed as a movie. We analyze conditions for unique and stable solution of this ill-posed inverse problem, and present a recovery algorithm, validating it experimentally. We compare our approach to one based on the recently proposed GMLR variation on deep prior for video, demonstrating the advantages of the proposed approach

Level Dependence in Volatility in Linear-Rational Term Structure Models

The degree of level dependence in interest rate volatility is analysed in the linearrational term structure model. The linear-rational square-root (LRSQ) model, where level dependence is set a priori, is compared to a specification where the factor process follows CEV-type dynamics which allows a more flexible degree of level dependence. Parameters are estimated using an unscented Kalman filter in conjunction with quasi-maximum likelihood. An extended specification for the state price density process is required to ensure reliable parameter estimates. The empirical analysis indicates that the LRSQ model generally overestimates level dependence. Although the CEV specification captures the degree of level dependence in volatility more accurately, it has a trade-off with analytical tractability. The optimal specification, therefore, depends on the type of model implementation and general economic conditions

Mcmc Estimation Of Lévy Jump Models Using Stock And Option Prices

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136259/1/j.1467-9965.2010.00439.x.pd

Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github

Appearance modeling under geometric context for object recognition in videos

Object recognition is a very important high-level task in surveillance applications. This dissertation focuses on building appearance models for object recognition and exploring the relationship between shape and appearance for two key types of objects, human and vehicle. The dissertation proposes a generic framework that models the appearance while incorporating certain geometric prior information, or the so-called geometric context. Then under this framework, special methods are developed for recognizing humans and vehicles based on their appearance and shape attributes in surveillance videos. The first part of the dissertation presents a unified framework based on a general definition of geometric transform (GeT) which is applied to modeling object appearances under geometric context. The GeT models the appearance by applying designed functionals over certain geometric sets. GeT unifies Radon transform, trace transform, image warping etc. Moreover, five novel types of GeTs are introduced and applied to fingerprinting the appearance inside a contour. They include GeT based on level sets, GeT based on shape matching, GeT based on feature curves, GeT invariant to occlusion, and a multi-resolution GeT (MRGeT) that combines both shape and appearance information. The second part focuses on how to use the GeT to build appearance models for objects like walking humans, which have articulated motion of body parts. This part also illustrates the application of GeT for object recognition, image segmentation, video retrieval, and image synthesis. The proposed approach produces promising results when applied to automatic body part segmentation and fingerprinting the appearance of a human and body parts despite the presence of non-rigid deformations and articulated motion. It is very important to understand the 3D structure of vehicles in order to recognize them. To reconstruct the 3D model of a vehicle, the third part presents a factorization method for structure from planar motion. Experimental results show that the algorithm is accurate and fairly robust to noise and inaccurate calibration. Differences and the dual relationship between planar motion and planar object are also clarified in this part. Based on our method, a fully automated vehicle reconstruction system has been designed

Option pricing under the double exponential jump‐diffusion model with stochastic volatility and interest rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate (SIR), stochastic volatility (SV), and double exponential jump into the jump‐diffusion settings. The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns, rare events, and an SIR. Using the model, we deduce the pricing characteristic function and pricing formula of a European option. Then, we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump‐diffusion model with SIR and SV. For verification purposes, we conduct time efficiency analysis, goodness of fit analysis, and jump/drift term analysis of the proposed model. In addition, we compare the pricing accuracy of the proposed model with those of the Black–Scholes and the Kou (2002) models. The empirical results show that the proposed option pricing model has high time efficiency, and the goodness of fit and pricing accuracy are significantly higher than those of the other two models

Biologically-Inspired Motion Encoding for Robust Global Motion Estimation.

The growing use of cameras embedded in autonomous robotic platforms and worn by people is increasing the importance of accurate global motion estimation (GME). However, existing GME methods may degrade considerably under illumination variations. In this paper, we address this problem by proposing a biologically-inspired GME method that achieves high estimation accuracy in the presence of illumination variations. We mimic the early layers of the human visual cortex with the spatio-temporal Gabor motion energy by adopting the pioneering model of Adelson and Bergen and we provide the closed-form expressions that enable the study and adaptation of this model to different application needs. Moreover, we propose a normalisation scheme for motion energy to tackle temporal illumination variations. Finally, we provide an overall GME scheme which, to the best of our knowledge, achieves the highest accuracy on the Pose, Illumination, and Expression (PIE) database