2,135 research outputs found
A Multi-Grid Iterative Method for Photoacoustic Tomography
Inspired by the recent advances on minimizing nonsmooth or bound-constrained
convex functions on models using varying degrees of fidelity, we propose a line
search multigrid (MG) method for full-wave iterative image reconstruction in
photoacoustic tomography (PAT) in heterogeneous media. To compute the search
direction at each iteration, we decide between the gradient at the target
level, or alternatively an approximate error correction at a coarser level,
relying on some predefined criteria. To incorporate absorption and dispersion,
we derive the analytical adjoint directly from the first-order acoustic wave
system. The effectiveness of the proposed method is tested on a total-variation
penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated
variant (FISTA), which have been used in many studies of image reconstruction
in PAT. The results show the great potential of the proposed method in
improving speed of iterative image reconstruction
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
A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution
To overcome the weakness of a total variation based model for image
restoration, various high order (typically second order) regularization models
have been proposed and studied recently. In this paper we analyze and test a
fractional-order derivative based total -order variation model, which
can outperform the currently popular high order regularization models. There
exist several previous works using total -order variations for image
restoration; however first no analysis is done yet and second all tested
formulations, differing from each other, utilize the zero Dirichlet boundary
conditions which are not realistic (while non-zero boundary conditions violate
definitions of fractional-order derivatives). This paper first reviews some
results of fractional-order derivatives and then analyzes the theoretical
properties of the proposed total -order variational model rigorously.
It then develops four algorithms for solving the variational problem, one based
on the variational Split-Bregman idea and three based on direct solution of the
discretise-optimization problem. Numerical experiments show that, in terms of
restoration quality and solution efficiency, the proposed model can produce
highly competitive results, for smooth images, to two established high order
models: the mean curvature and the total generalized variation.Comment: 26 page
Continuation of Nesterov's Smoothing for Regression with Structured Sparsity in High-Dimensional Neuroimaging
Predictive models can be used on high-dimensional brain images for diagnosis
of a clinical condition. Spatial regularization through structured sparsity
offers new perspectives in this context and reduces the risk of overfitting the
model while providing interpretable neuroimaging signatures by forcing the
solution to adhere to domain-specific constraints. Total Variation (TV)
enforces spatial smoothness of the solution while segmenting predictive regions
from the background. We consider the problem of minimizing the sum of a smooth
convex loss, a non-smooth convex penalty (whose proximal operator is known) and
a wide range of possible complex, non-smooth convex structured penalties such
as TV or overlapping group Lasso. Existing solvers are either limited in the
functions they can minimize or in their practical capacity to scale to
high-dimensional imaging data. Nesterov's smoothing technique can be used to
minimize a large number of non-smooth convex structured penalties but
reasonable precision requires a small smoothing parameter, which slows down the
convergence speed. To benefit from the versatility of Nesterov's smoothing
technique, we propose a first order continuation algorithm, CONESTA, which
automatically generates a sequence of decreasing smoothing parameters. The
generated sequence maintains the optimal convergence speed towards any globally
desired precision. Our main contributions are: To propose an expression of the
duality gap to probe the current distance to the global optimum in order to
adapt the smoothing parameter and the convergence speed. We provide a
convergence rate, which is an improvement over classical proximal gradient
smoothing methods. We demonstrate on both simulated and high-dimensional
structural neuroimaging data that CONESTA significantly outperforms many
state-of-the-art solvers in regard to convergence speed and precision.Comment: 11 pages, 6 figures, accepted in IEEE TMI, IEEE Transactions on
Medical Imaging 201
Recent Progress in Image Deblurring
This paper comprehensively reviews the recent development of image
deblurring, including non-blind/blind, spatially invariant/variant deblurring
techniques. Indeed, these techniques share the same objective of inferring a
latent sharp image from one or several corresponding blurry images, while the
blind deblurring techniques are also required to derive an accurate blur
kernel. Considering the critical role of image restoration in modern imaging
systems to provide high-quality images under complex environments such as
motion, undesirable lighting conditions, and imperfect system components, image
deblurring has attracted growing attention in recent years. From the viewpoint
of how to handle the ill-posedness which is a crucial issue in deblurring
tasks, existing methods can be grouped into five categories: Bayesian inference
framework, variational methods, sparse representation-based methods,
homography-based modeling, and region-based methods. In spite of achieving a
certain level of development, image deblurring, especially the blind case, is
limited in its success by complex application conditions which make the blur
kernel hard to obtain and be spatially variant. We provide a holistic
understanding and deep insight into image deblurring in this review. An
analysis of the empirical evidence for representative methods, practical
issues, as well as a discussion of promising future directions are also
presented.Comment: 53 pages, 17 figure
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