62 research outputs found
Constrained Overcomplete Analysis Operator Learning for Cosparse Signal Modelling
We consider the problem of learning a low-dimensional signal model from a
collection of training samples. The mainstream approach would be to learn an
overcomplete dictionary to provide good approximations of the training samples
using sparse synthesis coefficients. This famous sparse model has a less well
known counterpart, in analysis form, called the cosparse analysis model. In
this new model, signals are characterised by their parsimony in a transformed
domain using an overcomplete (linear) analysis operator. We propose to learn an
analysis operator from a training corpus using a constrained optimisation
framework based on L1 optimisation. The reason for introducing a constraint in
the optimisation framework is to exclude trivial solutions. Although there is
no final answer here for which constraint is the most relevant constraint, we
investigate some conventional constraints in the model adaptation field and use
the uniformly normalised tight frame (UNTF) for this purpose. We then derive a
practical learning algorithm, based on projected subgradients and
Douglas-Rachford splitting technique, and demonstrate its ability to robustly
recover a ground truth analysis operator, when provided with a clean training
set, of sufficient size. We also find an analysis operator for images, using
some noisy cosparse signals, which is indeed a more realistic experiment. As
the derived optimisation problem is not a convex program, we often find a local
minimum using such variational methods. Some local optimality conditions are
derived for two different settings, providing preliminary theoretical support
for the well-posedness of the learning problem under appropriate conditions.Comment: 29 pages, 13 figures, accepted to be published in TS
Fine-Grained MRI Reconstruction Using Attentive Selection Generative Adversarial Networks
Compressed sensing (CS) leverages the sparsity prior to provide the
foundation for fast magnetic resonance imaging (fastMRI). However, iterative
solvers for ill-posed problems hinder their adaption to time-critical
applications. Moreover, such a prior can be neither rich to capture complicated
anatomical structures nor applicable to meet the demand of high-fidelity
reconstructions in modern MRI. Inspired by the state-of-the-art methods in
image generation, we propose a novel attention-based deep learning framework to
provide high-quality MRI reconstruction. We incorporate large-field contextual
feature integration and attention selection in a generative adversarial network
(GAN) framework. We demonstrate that the proposed model can produce superior
results compared to other deep learning-based methods in terms of image
quality, and relevance to the MRI reconstruction in an extremely low sampling
rate diet.Comment: 5 pages, 2 figures, 1 table, 22 reference
Adaptive sparse coding and dictionary selection
Grant no. D000246/1.The sparse coding is approximation/representation of signals with the minimum number of
coefficients using an overcomplete set of elementary functions. This kind of approximations/
representations has found numerous applications in source separation, denoising, coding and
compressed sensing. The adaptation of the sparse approximation framework to the coding
problem of signals is investigated in this thesis. Open problems are the selection of appropriate
models and their orders, coefficient quantization and sparse approximation method. Some of
these questions are addressed in this thesis and novel methods developed. Because almost all
recent communication and storage systems are digital, an easy method to compute quantized
sparse approximations is introduced in the first part.
The model selection problem is investigated next. The linear model can be adapted to better
fit a given signal class. It can also be designed based on some a priori information about the
model. Two novel dictionary selection methods are separately presented in the second part
of the thesis. The proposed model adaption algorithm, called Dictionary Learning with the
Majorization Method (DLMM), is much more general than current methods. This generality
allowes it to be used with different constraints on the model. Particularly, two important cases
have been considered in this thesis for the first time, Parsimonious Dictionary Learning (PDL)
and Compressible Dictionary Learning (CDL). When the generative model order is not given,
PDL not only adapts the dictionary to the given class of signals, but also reduces the model
order redundancies. When a fast dictionary is needed, the CDL framework helps us to find a
dictionary which is adapted to the given signal class without increasing the computation cost
so much.
Sometimes a priori information about the linear generative model is given in format of a parametric
function. Parametric Dictionary Design (PDD) generates a suitable dictionary for sparse
coding using the parametric function. Basically PDD finds a parametric dictionary with a minimal
dictionary coherence, which has been shown to be suitable for sparse approximation and
exact sparse recovery.
Theoretical analyzes are accompanied by experiments to validate the analyzes. This research
was primarily used for audio applications, as audio can be shown to have sparse structures.
Therefore, most of the experiments are done using audio signals
FROB:Few-shot ROBust Model for Classification and Out-of-Distribution Detection
Nowadays, classification and Out-of-Distribution (OoD) detection in the
few-shot setting remain challenging aims due to rarity and the limited samples
in the few-shot setting, and because of adversarial attacks. Accomplishing
these aims is important for critical systems in safety, security, and defence.
In parallel, OoD detection is challenging since deep neural network classifiers
set high confidence to OoD samples away from the training data. To address such
limitations, we propose the Few-shot ROBust (FROB) model for classification and
few-shot OoD detection. We devise FROB for improved robustness and reliable
confidence prediction for few-shot OoD detection. We generate the support
boundary of the normal class distribution and combine it with few-shot Outlier
Exposure (OE). We propose a self-supervised learning few-shot confidence
boundary methodology based on generative and discriminative models. The
contribution of FROB is the combination of the generated boundary in a
self-supervised learning manner and the imposition of low confidence at this
learned boundary. FROB implicitly generates strong adversarial samples on the
boundary and forces samples from OoD, including our boundary, to be less
confident by the classifier. FROB achieves generalization to unseen OoD with
applicability to unknown, in the wild, test sets that do not correlate to the
training datasets. To improve robustness, FROB redesigns OE to work even for
zero-shots. By including our boundary, FROB reduces the threshold linked to the
model's few-shot robustness; it maintains the OoD performance approximately
independent of the number of few-shots. The few-shot robustness analysis
evaluation of FROB on different sets and on One-Class Classification (OCC) data
shows that FROB achieves competitive performance and outperforms benchmarks in
terms of robustness to the outlier few-shot sample population and variability.Comment: Paper, 22 pages, Figures, Table
Boundary Of Distribution Support Generator (BDSG): Sample Generation On The Boundary
Generative models, such as Generative Adversarial Networks (GANs), have been
used for unsupervised anomaly detection. While performance keeps improving,
several limitations exist particularly attributed to difficulties at capturing
multimodal supports and to the ability to approximate the underlying
distribution closer to the tails, i.e. the boundary of the distribution's
support. This paper proposes an approach that attempts to alleviate such
shortcomings. We propose an invertible-residual-network-based model, the
Boundary of Distribution Support Generator (BDSG). GANs generally do not
guarantee the existence of a probability distribution and here, we use the
recently developed Invertible Residual Network (IResNet) and Residual Flow
(ResFlow), for density estimation. These models have not yet been used for
anomaly detection. We leverage IResNet and ResFlow for Out-of-Distribution
(OoD) sample detection and for sample generation on the boundary using a
compound loss function that forces the samples to lie on the boundary. The BDSG
addresses non-convex support, disjoint components, and multimodal
distributions. Results on synthetic data and data from multimodal
distributions, such as MNIST and CIFAR-10, demonstrate competitive performance
compared to methods from the literature.Comment: 5 pages, 2020 IEEE International Conference on Image Processing
(ICIP
DeepMP for Non-Negative Sparse Decomposition
Non-negative signals form an important class of sparse signals. Many
algorithms have already beenproposed to recover such non-negative
representations, where greedy and convex relaxed algorithms are among the most
popular methods. The greedy techniques are low computational cost algorithms,
which have also been modified to incorporate the non-negativity of the
representations. One such modification has been proposed for Matching Pursuit
(MP) based algorithms, which first chooses positive coefficients and uses a
non-negative optimisation technique that guarantees the non-negativity of the
coefficients. The performance of greedy algorithms, like all non-exhaustive
search methods, suffer from high coherence with the linear generative model,
called the dictionary. We here first reformulate the non-negative matching
pursuit algorithm in the form of a deep neural network. We then show that the
proposed model after training yields a significant improvement in terms of
exact recovery performance, compared to other non-trained greedy algorithms,
while keeping the complexity low
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