37,250 research outputs found
A* Orthogonal Matching Pursuit: Best-First Search for Compressed Sensing Signal Recovery
Compressed sensing is a developing field aiming at reconstruction of sparse
signals acquired in reduced dimensions, which make the recovery process
under-determined. The required solution is the one with minimum norm
due to sparsity, however it is not practical to solve the minimization
problem. Commonly used techniques include minimization, such as Basis
Pursuit (BP) and greedy pursuit algorithms such as Orthogonal Matching Pursuit
(OMP) and Subspace Pursuit (SP). This manuscript proposes a novel semi-greedy
recovery approach, namely A* Orthogonal Matching Pursuit (A*OMP). A*OMP
performs A* search to look for the sparsest solution on a tree whose paths grow
similar to the Orthogonal Matching Pursuit (OMP) algorithm. Paths on the tree
are evaluated according to a cost function, which should compensate for
different path lengths. For this purpose, three different auxiliary structures
are defined, including novel dynamic ones. A*OMP also incorporates pruning
techniques which enable practical applications of the algorithm. Moreover, the
adjustable search parameters provide means for a complexity-accuracy trade-off.
We demonstrate the reconstruction ability of the proposed scheme on both
synthetically generated data and images using Gaussian and Bernoulli
observation matrices, where A*OMP yields less reconstruction error and higher
exact recovery frequency than BP, OMP and SP. Results also indicate that novel
dynamic cost functions provide improved results as compared to a conventional
choice.Comment: accepted for publication in Digital Signal Processin
Dynamic dictionary matching with failure functions
AbstractAmir and Farach (1991) and Amir et al. (to appear) recently initiated the study of the dynamic dictionary pattern matching problem. The dictionary D contains a set of patterns that can change over time by insertion and deletion of individual patterns. The user may also present a text string and ask to search for all occurrences of any patterns in the text. For the static dictionary problem, Aho and Corasick (1975) gave a strategy based on a failure function automaton that takes O(|D|log|Σ|) time to build a dictionary of size |D| and searches a text T in time O(|T|log|Σ|+tocc), where tocc, is the total number of pattern occurrences in the text.Amir et al. (to appear) used an automaton based on suffix trees to solve the dynamic problem. Their method can insert or delete a pattern P in time O(|P|log|D|) and can search a text in time O((|T|+tocc)log|D|).We show that the same bounds can be achieved using a framework based on failure functions. We then show that our approach also allows us to achieve faster search times at the expense of the update times; for constant k, we can achieve linear O(|T|(k+log|Σ|)+k tocc) search time with an update time of O(k|P∥D|1k). This is advantageous if the search texts are much larger than the dictionary or searches are more frequent than updates.Finally, we show how to build the initial dictionary in O(|D|log|Σ|) time, regardless of what combination of search and update times is used
Model Transformations in MT
Model transformations are recognised as a vital aspect of Model Driven Development,but current approaches cover only a small part of the possible spectrum. In this paper I present the MT model transformation which shows how a QVT-like language can be extended with novel pattern matching constructs, how tracing information can be automatically constructed and visualized, and how the transformed model is pruned of extraneous elements. As MT is implemented as a DSL within the Converge language, this paper also demonstrates how a general purpose language can be embedded in a model transformation language, and how DSL development can aid experimentation and exploration of new parts of the model transformation spectrum
Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age
Simultaneous Localization and Mapping (SLAM)consists in the concurrent
construction of a model of the environment (the map), and the estimation of the
state of the robot moving within it. The SLAM community has made astonishing
progress over the last 30 years, enabling large-scale real-world applications,
and witnessing a steady transition of this technology to industry. We survey
the current state of SLAM. We start by presenting what is now the de-facto
standard formulation for SLAM. We then review related work, covering a broad
set of topics including robustness and scalability in long-term mapping, metric
and semantic representations for mapping, theoretical performance guarantees,
active SLAM and exploration, and other new frontiers. This paper simultaneously
serves as a position paper and tutorial to those who are users of SLAM. By
looking at the published research with a critical eye, we delineate open
challenges and new research issues, that still deserve careful scientific
investigation. The paper also contains the authors' take on two questions that
often animate discussions during robotics conferences: Do robots need SLAM? and
Is SLAM solved
Feature detection using spikes: the greedy approach
A goal of low-level neural processes is to build an efficient code extracting
the relevant information from the sensory input. It is believed that this is
implemented in cortical areas by elementary inferential computations
dynamically extracting the most likely parameters corresponding to the sensory
signal. We explore here a neuro-mimetic feed-forward model of the primary
visual area (VI) solving this problem in the case where the signal may be
described by a robust linear generative model. This model uses an over-complete
dictionary of primitives which provides a distributed probabilistic
representation of input features. Relying on an efficiency criterion, we derive
an algorithm as an approximate solution which uses incremental greedy inference
processes. This algorithm is similar to 'Matching Pursuit' and mimics the
parallel architecture of neural computations. We propose here a simple
implementation using a network of spiking integrate-and-fire neurons which
communicate using lateral interactions. Numerical simulations show that this
Sparse Spike Coding strategy provides an efficient model for representing
visual data from a set of natural images. Even though it is simplistic, this
transformation of spatial data into a spatio-temporal pattern of binary events
provides an accurate description of some complex neural patterns observed in
the spiking activity of biological neural networks.Comment: This work links Matching Pursuit with bayesian inference by providing
the underlying hypotheses (linear model, uniform prior, gaussian noise
model). A parallel with the parallel and event-based nature of neural
computations is explored and we show application to modelling Primary Visual
Cortex / image processsing.
http://incm.cnrs-mrs.fr/perrinet/dynn/LaurentPerrinet/Publications/Perrinet04tau
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