476 research outputs found
Flexible Multi-layer Sparse Approximations of Matrices and Applications
The computational cost of many signal processing and machine learning
techniques is often dominated by the cost of applying certain linear operators
to high-dimensional vectors. This paper introduces an algorithm aimed at
reducing the complexity of applying linear operators in high dimension by
approximately factorizing the corresponding matrix into few sparse factors. The
approach relies on recent advances in non-convex optimization. It is first
explained and analyzed in details and then demonstrated experimentally on
various problems including dictionary learning for image denoising, and the
approximation of large matrices arising in inverse problems
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
Dictionary Learning for Deblurring and Digital Zoom
This paper proposes a novel approach to image deblurring and digital zooming
using sparse local models of image appearance. These models, where small image
patches are represented as linear combinations of a few elements drawn from
some large set (dictionary) of candidates, have proven well adapted to several
image restoration tasks. A key to their success has been to learn dictionaries
adapted to the reconstruction of small image patches. In contrast, recent works
have proposed instead to learn dictionaries which are not only adapted to data
reconstruction, but also tuned for a specific task. We introduce here such an
approach to deblurring and digital zoom, using pairs of blurry/sharp (or
low-/high-resolution) images for training, as well as an effective stochastic
gradient algorithm for solving the corresponding optimization task. Although
this learning problem is not convex, once the dictionaries have been learned,
the sharp/high-resolution image can be recovered via convex optimization at
test time. Experiments with synthetic and real data demonstrate the
effectiveness of the proposed approach, leading to state-of-the-art performance
for non-blind image deblurring and digital zoom
Sparsity-Based Super Resolution for SEM Images
The scanning electron microscope (SEM) produces an image of a sample by
scanning it with a focused beam of electrons. The electrons interact with the
atoms in the sample, which emit secondary electrons that contain information
about the surface topography and composition. The sample is scanned by the
electron beam point by point, until an image of the surface is formed. Since
its invention in 1942, SEMs have become paramount in the discovery and
understanding of the nanometer world, and today it is extensively used for both
research and in industry. In principle, SEMs can achieve resolution better than
one nanometer. However, for many applications, working at sub-nanometer
resolution implies an exceedingly large number of scanning points. For exactly
this reason, the SEM diagnostics of microelectronic chips is performed either
at high resolution (HR) over a small area or at low resolution (LR) while
capturing a larger portion of the chip. Here, we employ sparse coding and
dictionary learning to algorithmically enhance LR SEM images of microelectronic
chips up to the level of the HR images acquired by slow SEM scans, while
considerably reducing the noise. Our methodology consists of two steps: an
offline stage of learning a joint dictionary from a sequence of LR and HR
images of the same region in the chip, followed by a fast-online
super-resolution step where the resolution of a new LR image is enhanced. We
provide several examples with typical chips used in the microelectronics
industry, as well as a statistical study on arbitrary images with
characteristic structural features. Conceptually, our method works well when
the images have similar characteristics. This work demonstrates that employing
sparsity concepts can greatly improve the performance of SEM, thereby
considerably increasing the scanning throughput without compromising on
analysis quality and resolution.Comment: Final publication available at ACS Nano Letter
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