Multiresolution Markov models for signal and image processing

By Alan S. Willsky. Proceedings of the IEEE, 2002

350 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/6a5e6244b225845766921da4bf3147e7dc5e2cc5

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In Analytical Chemistry

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Gaussian sampling by local perturbations (2010, methodology): “A related direct approach which in the context of GMRFs has been studied in detail by [21, 22] relies on the Cholesky factorization of the precision matrix by efficient sparse matrix techniques, which typically re-order the variables in x so as to minimize the bandwidth W of J.”
Multi-scale Graphical Models for Spatio-Temporal Processes (2014, background): “Multi-scale graphical models have been constructed as pyramids of latent variables, where higher levels aggregate interactions at progressively larger scales [25].”
Graph Signal Processing: Overview, Challenges, and Applications (2017, background): “inference and find application in many areas such as modeling texture and other features in image processing [36], [37], [38], [39], [40], [41], see [42] for illustrative applications in several domains.”
3-D Depth Reconstruction from a Single Still Image (2007, background): “Objects at diﬀerent depths exhibit very diﬀerent behaviors at diﬀerent resolutions, and us-ing multiscale features allows us to capture these variations [58].”
Discrete Signal Processing on Graphs (2012, background): “Undirected graphical models, also referred to as Markov random fields [13], [14], describe data where the variables defined on two sets of nodes separated by a boundary set of nodes are statistically independent given the variables on the boundary set.”
Learning Depth from Single Monocular Images (2005, background): “Objects at different depths exhibit very different behaviors at different resolutions , and using multiscale features allows us to capture these variations [16].”
Graphical Models, Exponential Families, and Variational Inference (2008, methodology): “For Gaussian max-product applied to a tree-structured problem, the updates are guaranteed to converge, and compute both the correct means μs = E[Xs] and variances σ 2 s = E[X 2 s ] − μ 2 s at each node [257].”
An Ensemble Multiscale Filter for Large Nonlinear Data Assimilation Problems (2008, methodology): “A detailed discussion of multiscale modeling is provided in Willsky (2002).”
Data-driven non-Markovian closure models (2014, background): “Furthermore, the scalar field 2Note that, in some sense, the EMR methodology can also be viewed as an extension of hidden Markov models (HMMs) [70, 71] or of artificial neural networks (ANNs) [72, 73, 74], since the latter are generally nonlinear but do not involve the memory effects inherent in the”
Efficient Belief Propagation for Early Vision (2004, methodology): “W ile hierarchical BP methods have been used in other work such as [14], our method differs i n that we use the hierarchy only to initialize solutions at successively finer levels so as to reduce the number of message passing iterations at each level.”