467 research outputs found
Convolutional Deblurring for Natural Imaging
In this paper, we propose a novel design of image deblurring in the form of
one-shot convolution filtering that can directly convolve with naturally
blurred images for restoration. The problem of optical blurring is a common
disadvantage to many imaging applications that suffer from optical
imperfections. Despite numerous deconvolution methods that blindly estimate
blurring in either inclusive or exclusive forms, they are practically
challenging due to high computational cost and low image reconstruction
quality. Both conditions of high accuracy and high speed are prerequisites for
high-throughput imaging platforms in digital archiving. In such platforms,
deblurring is required after image acquisition before being stored, previewed,
or processed for high-level interpretation. Therefore, on-the-fly correction of
such images is important to avoid possible time delays, mitigate computational
expenses, and increase image perception quality. We bridge this gap by
synthesizing a deconvolution kernel as a linear combination of Finite Impulse
Response (FIR) even-derivative filters that can be directly convolved with
blurry input images to boost the frequency fall-off of the Point Spread
Function (PSF) associated with the optical blur. We employ a Gaussian low-pass
filter to decouple the image denoising problem for image edge deblurring.
Furthermore, we propose a blind approach to estimate the PSF statistics for two
Gaussian and Laplacian models that are common in many imaging pipelines.
Thorough experiments are designed to test and validate the efficiency of the
proposed method using 2054 naturally blurred images across six imaging
applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin
An Examination of Some Signi cant Approaches to Statistical Deconvolution
We examine statistical approaches to two significant areas of deconvolution - Blind
Deconvolution (BD) and Robust Deconvolution (RD) for stochastic stationary signals.
For BD, we review some major classical and new methods in a unified framework of
nonGaussian signals. The first class of algorithms we look at falls into the class
of Minimum Entropy Deconvolution (MED) algorithms. We discuss the similarities
between them despite differences in origins and motivations. We give new theoretical
results concerning the behaviour and generality of these algorithms and give evidence
of scenarios where they may fail. In some cases, we present new modifications to the
algorithms to overcome these shortfalls.
Following our discussion on the MED algorithms, we next look at a recently
proposed BD algorithm based on the correntropy function, a function defined as a
combination of the autocorrelation and the entropy functiosn. We examine its BD
performance when compared with MED algorithms. We find that the BD carried
out via correntropy-matching cannot be straightforwardly interpreted as simultaneous
moment-matching due to the breakdown of the correntropy expansion in terms
of moments. Other issues such as maximum/minimum phase ambiguity and computational
complexity suggest that careful attention is required before establishing the
correntropy algorithm as a superior alternative to the existing BD techniques.
For the problem of RD, we give a categorisation of different kinds of uncertainties
encountered in estimation and discuss techniques required to solve each individual
case. Primarily, we tackle the overlooked cases of robustification of deconvolution
filters based on estimated blurring response or estimated signal spectrum. We do
this by utilising existing methods derived from criteria such as minimax MSE with imposed uncertainty bands and penalised MSE. In particular, we revisit the Modified
Wiener Filter (MWF) which offers simplicity and flexibility in giving improved RDs
to the standard plug-in Wiener Filter (WF)
Convolutive Blind Source Separation Methods
In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks
Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media
The resistive or non-resistive nature of the extracellular space in the brain
is still debated, and is an important issue for correctly modeling
extracellular potentials. Here, we first show theoretically that if the medium
is resistive, the frequency scaling should be the same for electroencephalogram
(EEG) and magnetoencephalogram (MEG) signals at low frequencies (<10 Hz). To
test this prediction, we analyzed the spectrum of simultaneous EEG and MEG
measurements in four human subjects. The frequency scaling of EEG displays
coherent variations across the brain, in general between 1/f and 1/f^2, and
tends to be smaller in parietal/temporal regions. In a given region, although
the variability of the frequency scaling exponent was higher for MEG compared
to EEG, both signals consistently scale with a different exponent. In some
cases, the scaling was similar, but only when the signal-to-noise ratio of the
MEG was low. Several methods of noise correction for environmental and
instrumental noise were tested, and they all increased the difference between
EEG and MEG scaling. In conclusion, there is a significant difference in
frequency scaling between EEG and MEG, which can be explained if the
extracellular medium (including other layers such as dura matter and skull) is
globally non-resistive.Comment: Submitted to Journal of Computational Neuroscienc
Restoration of Atmospheric Turbulence Degraded Video using Kurtosis Minimization and Motion Compensation
In this thesis work, the background of atmospheric turbulence degradation in imaging was reviewed and two aspects are highlighted: blurring and geometric distortion. The turbulence burring parameter is determined by the atmospheric turbulence condition that is often unknown; therefore, a blur identification technique was developed that is based on a higher order statistics (HOS). It was observed that the kurtosis generally increases as an image becomes blurred (smoothed). Such an observation was interpreted in the frequency domain in terms of phase correlation. Kurtosis minimization based blur identification is built upon this observation. It was shown that kurtosis minimization is effective in identifying the blurring parameter directly from the degraded image. Kurtosis minimization is a general method for blur identification. It has been tested on a variety of blurs such as Gaussian blur, out of focus blur as well as motion blur. To compensate for the geometric distortion, earlier work on the turbulent motion compensation was extended to deal with situations in which there is camera/object motion. Trajectory smoothing is used to suppress the turbulent motion while preserving the real motion. Though the scintillation effect of atmospheric turbulence is not considered separately, it can be handled the same way as multiple frame denoising while motion trajectories are built.Ph.D.Committee Chair: Mersereau, Russell; Committee Co-Chair: Smith, Mark; Committee Member: Lanterman, Aaron; Committee Member: Wang, May; Committee Member: Tannenbaum, Allen; Committee Member: Williams, Dougla
Computational Inverse Problems
Inverse problem typically deal with the identification of unknown quantities from indirect measurements and appear in many areas in technology, medicine, biology, finance, and econometrics. The computational solution of such problems is a very active, interdisciplinary field with close connections to optimization, control theory, differential equations, asymptotic analysis, statistics, and probability. The focus of this workshop was on hybrid methods, model reduction, regularization in Banach spaces, and statistical approaches
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