9 research outputs found
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
PRAT: PRofiling Adversarial aTtacks
Intrinsic susceptibility of deep learning to adversarial examples has led to
a plethora of attack techniques with a broad common objective of fooling deep
models. However, we find slight compositional differences between the
algorithms achieving this objective. These differences leave traces that
provide important clues for attacker profiling in real-life scenarios. Inspired
by this, we introduce a novel problem of PRofiling Adversarial aTtacks (PRAT).
Given an adversarial example, the objective of PRAT is to identify the attack
used to generate it. Under this perspective, we can systematically group
existing attacks into different families, leading to the sub-problem of attack
family identification, which we also study. To enable PRAT analysis, we
introduce a large Adversarial Identification Dataset (AID), comprising over
180k adversarial samples generated with 13 popular attacks for image
specific/agnostic white/black box setups. We use AID to devise a novel
framework for the PRAT objective. Our framework utilizes a Transformer based
Global-LOcal Feature (GLOF) module to extract an approximate signature of the
adversarial attack, which in turn is used for the identification of the attack.
Using AID and our framework, we provide multiple interesting benchmark results
for the PRAT problem
A Parallel Inertial Proximal Optimization Method
International audienceThe Douglas-Rachford algorithm is a popular iterative method for finding a zero of a sum of two maximal monotone operators defined on a Hilbert space. In this paper, we propose an extension of this algorithm including inertia parameters and develop parallel versions to deal with the case of a sum of an arbitrary number of maximal operators. Based on this algorithm, parallel proximal algorithms are proposed to minimize over a linear subspace of a Hilbert space the sum of a finite number of proper, lower semicontinuous convex functions composed with linear operators. It is shown that particular cases of these methods are the simultaneous direction method of multipliers proposed by Stetzer et al., the parallel proximal algorithm developed by Combettes and Pesquet, and a parallelized version of an algorithm proposed by Attouch and Soueycatt
영상 복원 문제의 변분법적 접근
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 강명주.Image restoration has been an active research area in image processing and computer vision during the past several decades. We explore variational partial
differential equations (PDE) models in image restoration problem. We start our discussion by reviewing classical models, by which the works of this dissertation are highly motivated. The content of the dissertation is divided
into two main subjects. First topic is on image denoising, where we propose non-convex hybrid total variation model, and then we apply iterative reweighted algorithm to solve the proposed model. Second topic is on image
decomposition, in which we separate an image into structural component and oscillatory component using local gradient constraint.Abstract i
1 Introduction 1
1.1 Image restoration 2
1.2 Brief overview of the dissertation 3
2 Previous works 4
2.1 Image denoising 4
2.1.1 Fundamental model 4
2.1.2 Higher order model 7
2.1.3 Hybrid model 9
2.1.4 Non-convex model 12
2.2 Image decomposition 22
2.2.1 Meyers model 23
2.2.2 Nonlinear filter 24
3 Non-convex hybrid TV for image denoising 28
3.1 Variational model with non-convex hybrid TV 29
3.1.1 Non-convex TV model and non-convex HOTV model 29
3.1.2 The Proposed model: Non-convex hybrid TV model 31
3.2 Iterative reweighted hybrid Total Variation algorithm 33
3.3 Numerical experiments 35
3.3.1 Parameter values 37
3.3.2 Comparison between the non-convex TV model and
the non-convex HOTV model 38
3.3.3 Comparison with other non-convex higher order regularizers 40
3.3.4 Comparison between two non-convex hybrid TV models 42
3.3.5 Comparison with Krishnan et al. [39] 43
3.3.6 Comparison with state-of-the-art 44
4 Image decomposition 59
4.1 Local gradient constraint 61
4.1.1 Texture estimator 62
4.2 The proposed model 65
4.2.1 Algorithm : Anisotropic TV-L2 67
4.2.2 Algorithm : Isotropic TV-L2 69
4.2.3 Algorithm : Isotropic TV-L1 71
4.3 Numerical experiments and discussion 72
5 Conclusion and future works 80
Abstract (in Korean) 92Docto
Sparse and Redundant Representations for Inverse Problems and Recognition
Sparse and redundant representation of data enables the
description of signals as linear combinations of a few atoms from
a dictionary. In this dissertation, we study applications of
sparse and redundant representations in inverse problems and
object recognition. Furthermore, we propose two novel imaging
modalities based on the recently introduced theory of Compressed
Sensing (CS).
This dissertation consists of four major parts. In the first part
of the dissertation, we study a new type of deconvolution
algorithm that is based on estimating the image from a shearlet
decomposition. Shearlets provide a multi-directional and
multi-scale decomposition that has been mathematically shown to
represent distributed discontinuities such as edges better than
traditional wavelets. We develop a deconvolution algorithm that
allows for the approximation inversion operator to be controlled
on a multi-scale and multi-directional basis. Furthermore, we
develop a method for the automatic determination of the threshold
values for the noise shrinkage for each scale and direction
without explicit knowledge of the noise variance using a
generalized cross validation method.
In the second part of the dissertation, we study a reconstruction
method that recovers highly undersampled images assumed to have a
sparse representation in a gradient domain by using partial
measurement samples that are collected in the Fourier domain. Our
method makes use of a robust generalized Poisson solver that
greatly aids in achieving a significantly improved performance
over similar proposed methods. We will demonstrate by experiments
that this new technique is more flexible to work with either
random or restricted sampling scenarios better than its
competitors.
In the third part of the dissertation, we introduce a novel
Synthetic Aperture Radar (SAR) imaging modality which can provide
a high resolution map of the spatial distribution of targets and
terrain using a significantly reduced number of needed transmitted
and/or received electromagnetic waveforms. We demonstrate that
this new imaging scheme, requires no new hardware components and
allows the aperture to be compressed. Also, it
presents many new applications and advantages which include strong
resistance to countermesasures and interception, imaging much
wider swaths and reduced on-board storage requirements.
The last part of the dissertation deals with object recognition
based on learning dictionaries for simultaneous sparse signal
approximations and feature extraction. A dictionary is learned
for each object class based on given training examples which
minimize the representation error with a sparseness constraint. A
novel test image is then projected onto the span of the atoms in
each learned dictionary. The residual vectors along with the
coefficients are then used for recognition. Applications to
illumination robust face recognition and automatic target
recognition are presented
Real-time Ultrasound Signals Processing: Denoising and Super-resolution
Ultrasound acquisition is widespread in the biomedical field, due to its properties of low cost, portability, and non-invasiveness for the patient. The processing and analysis of US signals, such as images, 2D videos, and volumetric images, allows the physician to monitor the evolution of the patient's disease, and support diagnosis, and treatments (e.g., surgery). US images are affected by speckle noise, generated by the overlap of US waves. Furthermore, low-resolution images are acquired when a high acquisition frequency is applied to accurately characterise the behaviour of anatomical features that quickly change over time. Denoising and super-resolution of US signals are relevant to improve the visual evaluation of the physician and the performance and accuracy of processing methods, such as segmentation and classification. The main requirements for the processing and analysis of US signals are real-time execution, preservation of anatomical features, and reduction of artefacts. In this context, we present a novel framework for the real-time denoising of US 2D images based on deep learning and high-performance computing, which reduces noise while preserving anatomical features in real-time execution. We extend our framework to the denoise of arbitrary US signals, such as 2D videos and 3D images, and we apply denoising algorithms that account for spatio-temporal signal properties into an image-to-image deep learning model. As a building block of this framework, we propose a novel denoising method belonging to the class of low-rank approximations, which learns and predicts the optimal thresholds of the Singular Value Decomposition. While previous denoise work compromises the computational cost and effectiveness of the method, the proposed framework achieves the results of the best denoising algorithms in terms of noise removal, anatomical feature preservation, and geometric and texture properties conservation, in a real-time execution that respects industrial constraints. The framework reduces the artefacts (e.g., blurring) and preserves the spatio-temporal consistency among frames/slices; also, it is general to the denoising algorithm, anatomical district, and noise intensity. Then, we introduce a novel framework for the real-time reconstruction of the non-acquired scan lines through an interpolating method; a deep learning model improves the results of the interpolation to match the target image (i.e., the high-resolution image). We improve the accuracy of the prediction of the reconstructed lines through the design of the network architecture and the loss function. %The design of the deep learning architecture and the loss function allow the network to improve the accuracy of the prediction of the reconstructed lines. In the context of signal approximation, we introduce our kernel-based sampling method for the reconstruction of 2D and 3D signals defined on regular and irregular grids, with an application to US 2D and 3D images. Our method improves previous work in terms of sampling quality, approximation accuracy, and geometry reconstruction with a slightly higher computational cost. For both denoising and super-resolution, we evaluate the compliance with the real-time requirement of US applications in the medical domain and provide a quantitative evaluation of denoising and super-resolution methods on US and synthetic images. Finally, we discuss the role of denoising and super-resolution as pre-processing steps for segmentation and predictive analysis of breast pathologies
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Mathematical Challenges in Electron Microscopy
Development of electron microscopes first started nearly 100 years ago and they are now a mature imaging modality with many applications and vast potential for the future. The principal feature of electron microscopes is their resolution; they can be up to 1000 times more powerful than a visible light microscope and resolve even the smallest atoms. Furthermore, electron microscopes are also sensitive to many material properties due to the very rich interactions between electrons and other matter. Because of these capabilities, electron microscopy is used in applications as diverse as drug discovery, computer chip manufacture, and the development of solar cells.
In parallel to this, the mathematical field of inverse problems has also evolved dramatically. Many new methods have been introduced to improve the recovery of unknown structures from indirect data, typically an ill-posed problem. In particular, sparsity promoting functionals such as the total variation and its extensions have been shown to be very powerful for recovering accurate physical quantities from very little and/or poor quality data. While sparsity-promoting reconstruction methods are powerful, they can also be slow, especially in a big-data setting. This trade-off forms an eternal cycle as new numerical tools are found and more powerful models are developed.
The work presented in this thesis aims to marry the tools of inverse problems with the problems of electron microscopy: bringing state-of-the-art image processing techniques to bear on challenges specific to electron microscopy, developing new optimisation methods for these problems, and modelling new inverse problems to extend the capabilities of existing microscopes. One focus is the application of a directional total variation to overcome the limited angle problem in electron tomography, another is the proposal of a new inverse problem for the reconstruction of 3D strain tensor fields from electron microscopy diffraction data. The remaining contributions target numerical aspects of inverse problems, from new algorithms for non-convex problems to convex optimisation with adaptive meshes.Cantab Capital Institute for Mathematics of Informatio