1,352 research outputs found
Lapped transforms and hidden Markov models for seismic data filtering
International audienceSeismic exploration provides information about the ground substructures. Seismic images are generally corrupted by several noise sources. Hence, efficient denoising procedures are required to improve the detection of essential geological information. Wavelet bases provide sparse representation for a wide class of signals and images. This property makes them good candidates for efficient filtering tools, allowing the separation of signal and noise coefficients. Recent works have improved their performance by modelling the intra- and inter-scale coefficient dependencies using hidden Markov models, since image features tend to cluster and persist in the wavelet domain. This work focuses on the use of lapped transforms associated with hidden Markov modelling. Lapped transforms are traditionally viewed as block-transforms, composed of M pass-band filters. Seismic data present oscillatory patterns and lapped transforms oscillatory bases have demonstrated good performances for seismic data compression. A dyadic like representation of lapped transform coefficient is possible, allowing a wavelet-like modelling of coefficients dependencies. We show that the proposed filtering algorithm often outperforms the wavelet performance both objectively (in terms of SNR) and subjectively: lapped transform better preserve the oscillatory features present in seismic data at low to moderate noise levels
A Hierarchical Bayesian Model for Frame Representation
In many signal processing problems, it may be fruitful to represent the
signal under study in a frame. If a probabilistic approach is adopted, it
becomes then necessary to estimate the hyper-parameters characterizing the
probability distribution of the frame coefficients. This problem is difficult
since in general the frame synthesis operator is not bijective. Consequently,
the frame coefficients are not directly observable. This paper introduces a
hierarchical Bayesian model for frame representation. The posterior
distribution of the frame coefficients and model hyper-parameters is derived.
Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample
from this posterior distribution. The generated samples are then exploited to
estimate the hyper-parameters and the frame coefficients of the target signal.
Validation experiments show that the proposed algorithms provide an accurate
estimation of the frame coefficients and hyper-parameters. Application to
practical problems of image denoising show the impact of the resulting Bayesian
estimation on the recovered signal quality
Learning sparse representations of depth
This paper introduces a new method for learning and inferring sparse
representations of depth (disparity) maps. The proposed algorithm relaxes the
usual assumption of the stationary noise model in sparse coding. This enables
learning from data corrupted with spatially varying noise or uncertainty,
typically obtained by laser range scanners or structured light depth cameras.
Sparse representations are learned from the Middlebury database disparity maps
and then exploited in a two-layer graphical model for inferring depth from
stereo, by including a sparsity prior on the learned features. Since they
capture higher-order dependencies in the depth structure, these priors can
complement smoothness priors commonly used in depth inference based on Markov
Random Field (MRF) models. Inference on the proposed graph is achieved using an
alternating iterative optimization technique, where the first layer is solved
using an existing MRF-based stereo matching algorithm, then held fixed as the
second layer is solved using the proposed non-stationary sparse coding
algorithm. This leads to a general method for improving solutions of state of
the art MRF-based depth estimation algorithms. Our experimental results first
show that depth inference using learned representations leads to state of the
art denoising of depth maps obtained from laser range scanners and a time of
flight camera. Furthermore, we show that adding sparse priors improves the
results of two depth estimation methods: the classical graph cut algorithm by
Boykov et al. and the more recent algorithm of Woodford et al.Comment: 12 page
Wavelet Domain Image Separation
In this paper, we consider the problem of blind signal and image separation
using a sparse representation of the images in the wavelet domain. We consider
the problem in a Bayesian estimation framework using the fact that the
distribution of the wavelet coefficients of real world images can naturally be
modeled by an exponential power probability density function. The Bayesian
approach which has been used with success in blind source separation gives also
the possibility of including any prior information we may have on the mixing
matrix elements as well as on the hyperparameters (parameters of the prior laws
of the noise and the sources). We consider two cases: first the case where the
wavelet coefficients are assumed to be i.i.d. and second the case where we
model the correlation between the coefficients of two adjacent scales by a
first order Markov chain. This paper only reports on the first case, the second
case results will be reported in a near future. The estimation computations are
done via a Monte Carlo Markov Chain (MCMC) procedure. Some simulations show the
performances of the proposed method. Keywords: Blind source separation,
wavelets, Bayesian estimation, MCMC Hasting-Metropolis algorithm.Comment: Presented at MaxEnt2002, the 22nd International Workshop on Bayesian
and Maximum Entropy methods (Aug. 3-9, 2002, Moscow, Idaho, USA). To appear
in Proceedings of American Institute of Physic
WARP: Wavelets with adaptive recursive partitioning for multi-dimensional data
Effective identification of asymmetric and local features in images and other
data observed on multi-dimensional grids plays a critical role in a wide range
of applications including biomedical and natural image processing. Moreover,
the ever increasing amount of image data, in terms of both the resolution per
image and the number of images processed per application, requires algorithms
and methods for such applications to be computationally efficient. We develop a
new probabilistic framework for multi-dimensional data to overcome these
challenges through incorporating data adaptivity into discrete wavelet
transforms, thereby allowing them to adapt to the geometric structure of the
data while maintaining the linear computational scalability. By exploiting a
connection between the local directionality of wavelet transforms and recursive
dyadic partitioning on the grid points of the observation, we obtain the
desired adaptivity through adding to the traditional Bayesian wavelet
regression framework an additional layer of Bayesian modeling on the space of
recursive partitions over the grid points. We derive the corresponding
inference recipe in the form of a recursive representation of the exact
posterior, and develop a class of efficient recursive message passing
algorithms for achieving exact Bayesian inference with a computational
complexity linear in the resolution and sample size of the images. While our
framework is applicable to a range of problems including multi-dimensional
signal processing, compression, and structural learning, we illustrate its work
and evaluate its performance in the context of 2D and 3D image reconstruction
using real images from the ImageNet database. We also apply the framework to
analyze a data set from retinal optical coherence tomography
Review on Colour Image Denoising using Wavelet Soft Thresholding Technique
In this modern age of communication the image and video is important as Visual information transmitted in the form of digital images, but after the transmission image is often ruined with noise. Therefore the received image needs to be processing before it can be used for further applications. Image denoising implicates the manipulation of the image data to produce a high quality of image without any noise. Most of the work which had done in color scale image is by filter domain approach, but we think that the transform domain approach give great result in the field of color image denoising.. This paper reviews the several types of noise which corrupted the color image and also the existing denoising algorithms based on wavelet threshodling technique.
DOI: 10.17762/ijritcc2321-8169.15039
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