Open AccessBook
An Introduction to Sparse Stochastic Processes
TLDR
In this article, the theory of stochastic processes that admit a parsimonious representation in a matched wavelet-like basis is presented, which leads to two distinct types of behaviour -Gaussian and sparse -and is exploited to simplify the mathematical analysis.Abstract:
Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics.read more
Citations
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Journal ArticleDOI
Calcul des Probabilités. By Paul Lévy. Pp. 350. Fr. 40. 1925. (Gauthier-Villars.)
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A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix
TL;DR: Experimental results using in vivo data for single/multicoil imaging as well as dynamic imaging confirmed that the proposed method outperforms the state-of-the-art pMRI and CS-MRI.
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Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization
Ulugbek S. Kamilov,Ioannis N. Papadopoulos,Morteza H. Shoreh,Alexandre Goy,Cedric Vonesch,Michael Unser,Demetri Psaltis +6 more
TL;DR: A novel iterative imaging method for optical tomography that combines a nonlinear forward model based on the beam propagation method (BPM) with an edge-preserving three-dimensional (3-D) total variation (TV) regularizer and a time-reversal scheme that allows for an efficient computation of the derivative of the transmitted wave-field with respect to the distribution of the refractive index.
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Kernel-based Tests for Joint Independence
TL;DR: This work embeds the joint distribution and the product of the marginals in a reproducing kernel Hilbert space and defines the d‐variable Hilbert–Schmidt independence criterion dHSIC as the squared distance between the embeddings.
Tomographic phase microscopy: principles and applications in bioimaging [Invited]
TL;DR: The developments of TPM from the fundamental physics to its applications in bioimaging and selected TPM applications for cellular imaging, particularly in hematology, are reviewed.
References
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Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
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A theory for multiresolution signal decomposition: the wavelet representation
TL;DR: In this paper, it is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2 /sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.