1,978 research outputs found
Synthesis versus analysis in patch-based image priors
In global models/priors (for example, using wavelet frames), there is a well
known analysis vs synthesis dichotomy in the way signal/image priors are
formulated. In patch-based image models/priors, this dichotomy is also present
in the choice of how each patch is modeled. This paper shows that there is
another analysis vs synthesis dichotomy, in terms of how the whole image is
related to the patches, and that all existing patch-based formulations that
provide a global image prior belong to the analysis category. We then propose a
synthesis formulation, where the image is explicitly modeled as being
synthesized by additively combining a collection of independent patches. We
formally establish that these analysis and synthesis formulations are not
equivalent in general and that both formulations are compatible with analysis
and synthesis formulations at the patch level. Finally, we present an instance
of the alternating direction method of multipliers (ADMM) that can be used to
perform image denoising under the proposed synthesis formulation, showing its
computational feasibility. Rather than showing the superiority of the synthesis
or analysis formulations, the contributions of this paper is to establish the
existence of both alternatives, thus closing the corresponding gap in the field
of patch-based image processing.Comment: To appear in ICASSP 201
Network Inference from Co-Occurrences
The recovery of network structure from experimental data is a basic and
fundamental problem. Unfortunately, experimental data often do not directly
reveal structure due to inherent limitations such as imprecision in timing or
other observation mechanisms. We consider the problem of inferring network
structure in the form of a directed graph from co-occurrence observations. Each
observation arises from a transmission made over the network and indicates
which vertices carry the transmission without explicitly conveying their order
in the path. Without order information, there are an exponential number of
feasible graphs which agree with the observed data equally well. Yet, the basic
physical principles underlying most networks strongly suggest that all feasible
graphs are not equally likely. In particular, vertices that co-occur in many
observations are probably closely connected. Previous approaches to this
problem are based on ad hoc heuristics. We model the experimental observations
as independent realizations of a random walk on the underlying graph, subjected
to a random permutation which accounts for the lack of order information.
Treating the permutations as missing data, we derive an exact
expectation-maximization (EM) algorithm for estimating the random walk
parameters. For long transmission paths the exact E-step may be computationally
intractable, so we also describe an efficient Monte Carlo EM (MCEM) algorithm
and derive conditions which ensure convergence of the MCEM algorithm with high
probability. Simulations and experiments with Internet measurements demonstrate
the promise of this approach.Comment: Submitted to IEEE Transactions on Information Theory. An extended
version is available as University of Wisconsin Technical Report ECE-06-
On the Use of Suffix Arrays for Memory-Efficient Lempel-Ziv Data Compression
Much research has been devoted to optimizing algorithms of the Lempel-Ziv
(LZ) 77 family, both in terms of speed and memory requirements. Binary search
trees and suffix trees (ST) are data structures that have been often used for
this purpose, as they allow fast searches at the expense of memory usage.
In recent years, there has been interest on suffix arrays (SA), due to their
simplicity and low memory requirements. One key issue is that an SA can solve
the sub-string problem almost as efficiently as an ST, using less memory. This
paper proposes two new SA-based algorithms for LZ encoding, which require no
modifications on the decoder side. Experimental results on standard benchmarks
show that our algorithms, though not faster, use 3 to 5 times less memory than
the ST counterparts. Another important feature of our SA-based algorithms is
that the amount of memory is independent of the text to search, thus the memory
that has to be allocated can be defined a priori. These features of low and
predictable memory requirements are of the utmost importance in several
scenarios, such as embedded systems, where memory is at a premium and speed is
not critical. Finally, we point out that the new algorithms are general, in the
sense that they are adequate for applications other than LZ compression, such
as text retrieval and forward/backward sub-string search.Comment: 10 pages, submited to IEEE - Data Compression Conference 200
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