Independent Multiresolution Component Analysis and Matching Pursuit

Capobianco, Enrico

doi:10.1016/s0167-9473(02)00217-7

Cited by 15 publications

(6 citation statements)

References 28 publications

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“…This algorithm is exactly equivalent to Matching Pursuit [Mallat and Zhang, 1993]. This algorithm is familiar in signal processing and is increasingly used for image and video processing [Neff and Zakhor, 1997;Durka et al, 2001;Capobianco, 2003;Fischer et al, , 2007a and signal processing [Blinowska and Durka, 1994]. Moreover, we have shown that the use of the statistics of natural images statistically optimizes the coding efficiency by modifying the image space metric [Perrinet et al, 2004] compared to an heuristic optimization of Matching Pursuit [Pati et al, 1993].…”

Section: Properties Of the Greedy Pursuitmentioning

confidence: 96%

Dynamical neural networks: Modeling low-level vision at short latencies

Perrinet

2007

Eur. Phys. J. Spec. Top.

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Our goal is to understand the dynamics of neural computations in low-level vision. We study how the substrate of this system, that is local biochemical neural processes, could combine to give rise to an efficient and global perception. We will study these neural computations at different scales from the single-cell to the whole visual system to infer generic aspects of the underlying neural code which may help to understand this cognitive ability. In fact, the architecture of cortical areas, such as the Primary Visual Cortex (V1), is massively parallel and we will focus on cortical columns as generic adaptive micro-circuits. To stress on the dynamical aspect of the processing, we will also focus on the transient response, that is during the first milliseconds after the presentation of a stimulus. In a generic model of a visual area, we propose to study the neural code as implementing visual pattern matching, that is as efficiently inverting a known model of image synthesis. A possible solution offered by the architecture of the visual pathways could be to represent at first on the surface of the cortical area how well the prototypical visual features are matched by a combination of inferential mechanisms as ideal observers. We studied the efficiency of this representation by rating the statistics of the output using natural scenes, that is scenes occurring frequently. We show that this may be finally used to provide a behavioral output such as an eye movement. However, constraints specific to the visual system imply that the set of prototypical features is not independent and that the cortical columns should communicate to produce an efficient, sparse solution. We will present efficient algorithms and representations based on the event-based nature of neural computations. By explicitely defining this efficiency, we propose then a simple implementation of Sparse Spike Coding using greedy inference mechanisms but also how the system may adapt in a unsupervised fashion. These computations may be implemented in simple models of neural networks by explicitly setting the lateral connectivity between populations of columns. Using natural scenes, this algorithm provides a model of V1 which exhibit prototypical properties of neural activities in that area. We show simple applications in the field of image processing as a quantitative method to evaluate these different cortical models.

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Section: Properties Of the Greedy Pursuitmentioning

confidence: 96%

Dynamical neural networks: Modeling low-level vision at short latencies

Perrinet

2007

Eur. Phys. J. Spec. Top.

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“…However, because a wavelet family is built by restricting its frequency parameters to be inversely proportional to the scale, the expansion coefficients in a wavelet frame do not provide precise estimates of the frequency content of waveforms whose Fourier transform is well-localized, especially at high frequencies [53]. In MPD, signal structures are represented by wavelets that match their time-frequency signature, with better local adaptation and a better time-frequency resolution [62][63][64][65].…”

Section: Matching Pursuitmentioning

confidence: 99%

Spectral Decomposition and a Waveform Cluster to Characterize Strongly Heterogeneous Paleokarst Reservoirs in the Tarim Basin, China

Shan

Tian

Fang

et al. 2019

Water

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The main components of the Ordovician carbonate reservoirs in the Tahe Oilfield are paleokarst fracture-cavity paleo-channel systems formed by karstification. Detailed characterization of these paleokarst reservoirs is challenging because of heterogeneities in characteristics and strong vertical and lateral non-uniformities. Traditional seismic analysis methods are not able to solve the identification problem of such strongly heterogeneous reservoirs. Recent developments in seismic interpretation have heightened the need to describe the fracture-cavity structure of a paleo-channel with more accuracy. We propose a new prediction model for fracture-cavity carbonate reservoirs based on spectral decomposition and a waveform cluster. By the Matching Pursuit decomposition algorithm, the single-frequency data volumes are obtained. The specific frequency data volume that is the most sensitive to the reservoir is chosen based on seismic synthesis traces of well-logging data and geological interpretability. The waveform cluster is then applied to delineate the complex paleokarst systems, particularly the fracture-caves in the runoff zone. This method was applied to the area around Well T615 in the Tahe oilfield, and a paleokarst fracture-cavity system with strong heterogeneity in the runoff zone was delineated and characterized. The findings of this research provide insights for predicting other similar karst systems, such as karstic groundwater and karst hydrogeological systems.

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“…Its idea is to adopt optimization methods to identify parametric waveforms that match the signal best and express the signal with the superimposition of optimum waveforms. According to different principles, various methods have been developed for AD, such as methods of frame (MOF) Daubechies (1990), best orthogonal basis (BOB) [Coifman and Wickerhauser (1992)], matching pursuit (MP) [Zeng and Malgouyres (2011); Averbuch et al (2011);Capobianco (2003)] and basis pursuit (BP). In these approaches, the collection of waveforms is called a dictionary and the waveforms are called atoms.…”

Section: Introductionmentioning

confidence: 99%

Atomic Decomposition Method Based on Adaptive Chirplet Dictionary

2012

Adv. Adapt. Data Anal.

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We propose an atomic decomposition method (AD) based on adaptive chirplet dictionary for decomposing multicomponent nonstationary signals with polygonal instantaneous frequencies (IFs). These signals are waveforms of the very general form P A i (t) cos(ϕ i (t)), where the phase ϕ i (t) is time-varying and the amplitude A i (t) is slowly varying. Different from the traditional four-parameters chirplet, the one applied in this paper only contains two parameters (chirp offset and chirp rate) and its IF can be regarded as a line on the time-frequency (TF) plane. The idea is to use matching pursuit (MP) algorithm to search for the chirplets, which provide the best trade-off between complexity and goodness of fitting and chain the chirplets together adaptively as to form the desired signals. Our particular application in conjunction with this problem is the decomposition of meshing frequency component and its modulating frequency components in gear fault diagnosis. This strategy is general and may be applied in many other problems. We complement our study with numerical experiments showing that our algorithm boasts of many advantages, such as favorable TF resolution, strong noise robust property (NRP), good decomposition precision, and acceptable algorithm efficiency and is highly competitive compared to the current TF analysis methods.

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Independent Multiresolution Component Analysis and Matching Pursuit

Cited by 15 publications

References 28 publications

Dynamical neural networks: Modeling low-level vision at short latencies

Dynamical neural networks: Modeling low-level vision at short latencies

Spectral Decomposition and a Waveform Cluster to Characterize Strongly Heterogeneous Paleokarst Reservoirs in the Tarim Basin, China

Atomic Decomposition Method Based on Adaptive Chirplet Dictionary

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