561 research outputs found
A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction
We consider tomographic reconstruction using priors in the form of a
dictionary learned from training images. The reconstruction has two stages:
first we construct a tensor dictionary prior from our training data, and then
we pose the reconstruction problem in terms of recovering the expansion
coefficients in that dictionary. Our approach differs from past approaches in
that a) we use a third-order tensor representation for our images and b) we
recast the reconstruction problem using the tensor formulation. The dictionary
learning problem is presented as a non-negative tensor factorization problem
with sparsity constraints. The reconstruction problem is formulated in a convex
optimization framework by looking for a solution with a sparse representation
in the tensor dictionary. Numerical results show that our tensor formulation
leads to very sparse representations of both the training images and the
reconstructions due to the ability of representing repeated features compactly
in the dictionary.Comment: 29 page
Sample Complexity of Dictionary Learning and other Matrix Factorizations
Many modern tools in machine learning and signal processing, such as sparse
dictionary learning, principal component analysis (PCA), non-negative matrix
factorization (NMF), -means clustering, etc., rely on the factorization of a
matrix obtained by concatenating high-dimensional vectors from a training
collection. While the idealized task would be to optimize the expected quality
of the factors over the underlying distribution of training vectors, it is
achieved in practice by minimizing an empirical average over the considered
collection. The focus of this paper is to provide sample complexity estimates
to uniformly control how much the empirical average deviates from the expected
cost function. Standard arguments imply that the performance of the empirical
predictor also exhibit such guarantees. The level of genericity of the approach
encompasses several possible constraints on the factors (tensor product
structure, shift-invariance, sparsity \ldots), thus providing a unified
perspective on the sample complexity of several widely used matrix
factorization schemes. The derived generalization bounds behave proportional to
w.r.t.\ the number of samples for the considered matrix
factorization techniques.Comment: to appea
Sparse Non-negative Matrix Factorization for Mesh Segmentation
We present a method for 3D mesh segmentation based on sparse non-negative matrix factorization (NMF). Image analysis techniques based on NMF have been shown to decompose images into semantically meaningful local features. Since the features and coefficients are represented in terms of non-negative values, the features contribute to the resulting images in an intuitive, additive fashion. Like spectral mesh segmentation, our method relies on the construction of an affinity matrix which depends on the geometric properties of the mesh. We show that segmentation based on the NMF is simpler to implement, and can result in more meaningful segmentation results than spectral mesh segmentation
Principles of Image Reconstruction in Interferometry
This book is a collection of 19 articles which reflect the courses given at the CollĂšge de France/Summer school âReconstruction d'images â Applications astrophysiquesâ held in Nice and FrĂ©jus, France, from June 18 to 22, 2012. The articles presented in this volume address emerging concepts and methods that are useful in the complex process of improving our knowledge of the celestial objects, including Earth
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Hierarchical Models in the Brain
This paper describes a general model that subsumes many parametric models for
continuous data. The model comprises hidden layers of state-space or dynamic
causal models, arranged so that the output of one provides input to another. The
ensuing hierarchy furnishes a model for many types of data, of arbitrary
complexity. Special cases range from the general linear model for static data to
generalised convolution models, with system noise, for nonlinear time-series
analysis. Crucially, all of these models can be inverted using exactly the same
scheme, namely, dynamic expectation maximization. This means that a single model
and optimisation scheme can be used to invert a wide range of models. We present
the model and a brief review of its inversion to disclose the relationships
among, apparently, diverse generative models of empirical data. We then show
that this inversion can be formulated as a simple neural network and may provide
a useful metaphor for inference and learning in the brain
Multichannel Online Dereverberation based on Spectral Magnitude Inverse Filtering
This paper addresses the problem of multichannel online dereverberation. The
proposed method is carried out in the short-time Fourier transform (STFT)
domain, and for each frequency band independently. In the STFT domain, the
time-domain room impulse response is approximately represented by the
convolutive transfer function (CTF). The multichannel CTFs are adaptively
identified based on the cross-relation method, and using the recursive least
square criterion. Instead of the complex-valued CTF convolution model, we use a
nonnegative convolution model between the STFT magnitude of the source signal
and the CTF magnitude, which is just a coarse approximation of the former
model, but is shown to be more robust against the CTF perturbations. Based on
this nonnegative model, we propose an online STFT magnitude inverse filtering
method. The inverse filters of the CTF magnitude are formulated based on the
multiple-input/output inverse theorem (MINT), and adaptively estimated based on
the gradient descent criterion. Finally, the inverse filtering is applied to
the STFT magnitude of the microphone signals, obtaining an estimate of the STFT
magnitude of the source signal. Experiments regarding both speech enhancement
and automatic speech recognition are conducted, which demonstrate that the
proposed method can effectively suppress reverberation, even for the difficult
case of a moving speaker.Comment: Paper submitted to IEEE/ACM Transactions on Audio, Speech and
Language Processing. IEEE Signal Processing Letters, 201
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