Space-varying convolution often arises in the modeling or restoration of images captured by optical imaging
systems. For example, in applications such as microscopy or photography the distortions introduced by lenses
typically vary across the field of view, so accurate restoration also requires the use of space-varying convolution.
While space-invariant convolution can be efficiently implemented with the Fast Fourier Transform (FFT),
space-varying convolution requires direct implementation of the convolution operation, which can be very computationally
expensive when the convolution kernel is large.
In this paper, we develop a general approach to the efficient implementation of space-varying convolution
through the use of matrix source coding techniques. This method can dramatically reduce computation by
approximately factoring the dense space-varying convolution operator into a product of sparse transforms. This
approach leads to a tradeoff between the accuracy and speed of the operation that is closely related to the
distortion-rate tradeoff that is commonly made in lossy source coding.
We apply our method to the problem of stray light reduction for digital photographs, where convolution
with a spatially varying stray light point spread function is required. The experimental results show that our
algorithm can achieve a dramatic reduction in computation while achieving high accuracy.
KEYWORDS: Signal to noise ratio, Detection and tracking algorithms, Data modeling, Scanners, Image restoration, Hemodynamics, Algorithm development, Performance modeling, Functional magnetic resonance imaging, Brain
The objective of fMRI data analysis is to detect the region of the brain that gets activated in response to a specific
stimulus presented to the subject. We develop a new algorithm for activation detection in event-related fMRI
data. We utilize a forward model for fMRI data acquisition which explicitly incorporates physiological noise,
scanner noise and the spatial blurring introduced by the scanner. After slice-by-slice image restoration procedure
that independently restores each data slice corresponding to each time index, we estimate the parameters of the
hemodynamic response function (HRF) model for each pixel of the restored data. In order to enforce spatial
regularity in our estimates, we model the prior distribution of the HRF parameters as a generalized Gaussian
Markov random field (GGMRF) model. We develop an algorithm to compute the maximum a posteriori (MAP)
estimates of the parameters. We then threshold the amplitude parameters to obtain the final activation map. We
illustrate our algorithm by comparing it with the widely used general linear model (GLM) method. In synthetic
data experiments, under the same probability of false alarm, the probability of correct detection for our method
is up to 15% higher than GLM. In real data experiments, through anatomical analysis and benchmark testing
using block paradigm results, we demonstrate that our algorithm produces fewer false alarms than GLM.
In optical imaging systems, specifically digital cameras, part of the incoming light flux is misdirected to undesired locations due to scattering, undesired reflections, diffraction and lens aberrations. The portion due mainly to scattering and undesired reflections is called stray light. Stray light reduces contrast and causes color inaccuracy in images. The point spread function (PSF) model for stray light is shift variant and has been studied by Jansson et al. (1998) and Bitlis et al. (2007). In this paper, we keep the model's shift variant nature and improve it by first normalizing it and then incorporating the shading effect inherent in the optical system. We then develop an efficient method to estimate the model parameters by using a locally shift invariant approximation. Finally, we
reduce the stray light by deconvolution. We conducted extensive experiments with two camera models. Results from these experiments show the reduction of stray light and thus the improvement of image quality and fidelity.
Multicast protection strategies have been widely explored in current literature. However, the leaf availability requirements are not taken into account. In this paper, we investigated approaches and algorithms for establishing a multicast session with differentiated leaf availability requirements in WDM mesh network while protecting it against single link failure. An effcient and cost-effective heuristic is presented to solve the problem and is compared with two other schemes, one with no protection (Scheme I) and the other with dedicated protection (Scheme II). We also formulated a possible improvement of the proposed algorithm. Simulation results based
on 14 node NSFNET topology and comparisons among these schemes are also discussed. The performance of an algorithm is measured in terms of Average Cost and Average Satisfaction Ratio. The improved algorithm shows much better performance than the other ones, thus achieving the goal of effectively establishing protected multicast sessions with differentiated destination availability requirements. Finally, through numerical simulation results, we find that some links are critical to the performance of the network. Increasing the availability and capacity of these links will greatly enhance the network performance. This result is helpful to network planning
Multicast applications have attracted more and more attention due to more efficient bandwidth usage and the increasing popularity of the point-multipoint multimedia applications. Optical multicasting outperforms the electronic multicasting in some aspects. Service level agreement (SLA) and quality of service (QoS) are important to service providers and users. Service providers always first maximize revenue to accept as many as connection requests as possible and then to minimize the capacity of all accepted connection. In this paper, the problem of cost-effective optical multicasting connection provisioning to satisfy the connections' availability requirements on a given physical topology is formally stated. We propose a mixed integer linear program (MILP) based approach for static multicast traffic. The feature of our algorithm lies on without considering any protection schemes, and when the system adapts dedicated protection or the sharing protection, the problem is more complicated.