Today, quasi-Monte Carlo (QMC) methods are widely used in finance to price derivative securities. The QMC approach is popular because for many types of derivatives it yields an estimate of the price, to a given accuracy, faster than other competitive approaches, like Monte Carlo (MC) methods. The calculation of the large number of underlying asset pathways consumes a significant portion of the overall run-time and energy of modern QMC derivative pricing simulations. Therefore, we present an FPGA-based accelerator for the calculation of asset pathways suitable for use in the QMC pricing of several types of derivative securities. Although this implementation uses constructs (recursive algorithms and double-precision floating point) not normally associated with successful FPGA computing, we demonstrate performance in excess of 50times that of a 3 GHz multi-core processor.

In this paper, we propose a maximum a posteriori ramework for the super-resolution problem, i.e., reconstructing high-resolution images from shifted, rotated, low-resolution degraded observations. The main contributions of this work are two; first, the use of a new locally adaptive edge preserving prior for the super-resolution problem. Second an efficient two-step reconstruction methodology that includes first an initial registration using only the low-resolution degraded observations. This is followed by a fast iterative algorithm implemented in the discrete Fourier transform domain in which the restoration, interpolation and the registration subtasks of this problem are preformed simultaneously. We present examples with both synthetic and real data that demonstrate the advantages of the proposed framework.

Using a stochastic framework, we propose two algorithms for the problem of obtaining a single high-resolution image from multiple noisy, blurred, and undersampled images. The first is based on a Bayesian formulation that is implemented via the expectation maximization algorithm. The second is based on a maximum a posteriori formulation. In both of our formulations, the registration, noise, and image statistics are treated as unknown parameters. These unknown parameters and the high-resolution image are estimated jointly based on the available observations. We present an efficient implementation of these algorithms in the frequency domain that allows their application to large images. Simulations are presented that test and compare the proposed algorithms.

We propose a new solution to the problem of obtaining a single high-resolution image from multiple blurred, noisy, and undersampled images. Our estimator, derived using the Bayesian stochastic framework, is novel in that it employs a new hierarchical non-stationary image prior. This prior adapts the restoration of the super-resolved image to the local spatial statistics of the image. Numerical experiments demonstrate the effectiveness of the proposed approach.

A maximum likelihood (ML) solution to the problem of obtaining high-resolution images from sequences of noisy, blurred, and low-resolution images is presented. In our formulation, the registration parameters of the low-resolution images, the degrading blur, and noise variance are unknown. Our algorithm has the advantage that all unknown parameters are obtained simultaneously using all of the available data. An efficient implementation is presented in the frequency domain, based on the expectation maximization (EM) algorithm. Simulations demonstrate the effectiveness of the algorithm.