3,295 research outputs found
A proximal iteration for deconvolving Poisson noisy images using sparse representations
We propose an image deconvolution algorithm when the data is contaminated by
Poisson noise. The image to restore is assumed to be sparsely represented in a
dictionary of waveforms such as the wavelet or curvelet transforms. Our key
contributions are: First, we handle the Poisson noise properly by using the
Anscombe variance stabilizing transform leading to a {\it non-linear}
degradation equation with additive Gaussian noise. Second, the deconvolution
problem is formulated as the minimization of a convex functional with a
data-fidelity term reflecting the noise properties, and a non-smooth
sparsity-promoting penalties over the image representation coefficients (e.g.
-norm). Third, a fast iterative backward-forward splitting algorithm is
proposed to solve the minimization problem. We derive existence and uniqueness
conditions of the solution, and establish convergence of the iterative
algorithm. Finally, a GCV-based model selection procedure is proposed to
objectively select the regularization parameter. Experimental results are
carried out to show the striking benefits gained from taking into account the
Poisson statistics of the noise. These results also suggest that using
sparse-domain regularization may be tractable in many deconvolution
applications with Poisson noise such as astronomy and microscopy
Frequency-modulated continuous-wave LiDAR compressive depth-mapping
We present an inexpensive architecture for converting a frequency-modulated
continuous-wave LiDAR system into a compressive-sensing based depth-mapping
camera. Instead of raster scanning to obtain depth-maps, compressive sensing is
used to significantly reduce the number of measurements. Ideally, our approach
requires two difference detectors. % but can operate with only one at the cost
of doubling the number of measurments. Due to the large flux entering the
detectors, the signal amplification from heterodyne detection, and the effects
of background subtraction from compressive sensing, the system can obtain
higher signal-to-noise ratios over detector-array based schemes while scanning
a scene faster than is possible through raster-scanning. %Moreover, we show how
a single total-variation minimization and two fast least-squares minimizations,
instead of a single complex nonlinear minimization, can efficiently recover
high-resolution depth-maps with minimal computational overhead. Moreover, by
efficiently storing only data points from measurements of an
pixel scene, we can easily extract depths by solving only two linear equations
with efficient convex-optimization methods
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Divergence-free Wavelets for Navier-Stokes
In this paper, we investigate the use of compactly supported divergence-free
wavelets for the representation of the Navier-Stokes solution. After reminding
the theoretical construction of divergence-free wavelet vectors, we present in
detail the bases and corresponding fast algorithms for 2D and 3D incompressible
flows. In order to compute the nonlinear term, we propose a new method which
provides in practice with the Hodge decomposition of any flow: this
decomposition enables us to separate the incompressible part of the flow from
its orthogonal complement, which corresponds to the gradient component of the
flow. Finally we show numerical tests to validate our approach.Comment: novembre 200
Automation of Hessian-Based Tubularity Measure Response Function in 3D Biomedical Images
The blood vessels and nerve trees consist of tubular objects interconnected into a complex tree- or web-like structure that has a range of structural scale 5 μm diameter capillaries to 3 cm aorta. This large-scale range presents two major problems; one is just making the measurements, and the other is the exponential increase of component numbers with decreasing scale. With the remarkable increase in the volume imaged by, and resolution of, modern day 3D imagers, it is almost impossible to make manual tracking of the complex multiscale parameters from those large image data sets. In addition, the manual tracking is quite subjective and unreliable. We propose a solution for automation of an adaptive nonsupervised system for tracking tubular objects based on multiscale framework and use of Hessian-based object shape detector incorporating National Library of Medicine Insight Segmentation and Registration Toolkit (ITK) image processing libraries
Restoration of Poissonian Images Using Alternating Direction Optimization
Much research has been devoted to the problem of restoring Poissonian images,
namely for medical and astronomical applications. However, the restoration of
these images using state-of-the-art regularizers (such as those based on
multiscale representations or total variation) is still an active research
area, since the associated optimization problems are quite challenging. In this
paper, we propose an approach to deconvolving Poissonian images, which is based
on an alternating direction optimization method. The standard regularization
(or maximum a posteriori) restoration criterion, which combines the Poisson
log-likelihood with a (non-smooth) convex regularizer (log-prior), leads to
hard optimization problems: the log-likelihood is non-quadratic and
non-separable, the regularizer is non-smooth, and there is a non-negativity
constraint. Using standard convex analysis tools, we present sufficient
conditions for existence and uniqueness of solutions of these optimization
problems, for several types of regularizers: total-variation, frame-based
analysis, and frame-based synthesis. We attack these problems with an instance
of the alternating direction method of multipliers (ADMM), which belongs to the
family of augmented Lagrangian algorithms. We study sufficient conditions for
convergence and show that these are satisfied, either under total-variation or
frame-based (analysis and synthesis) regularization. The resulting algorithms
are shown to outperform alternative state-of-the-art methods, both in terms of
speed and restoration accuracy.Comment: 12 pages, 12 figures, 2 tables. Submitted to the IEEE Transactions on
Image Processin
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