Space-Frequency Localization as Bivariate Mother Wavelets Selecting Criterion for Hyperanalytic Bayesian Image Denoising (original) (raw)
Related papers
A Bayesian Approach of Hyperanalytic Wavelet Transform Based Denoising
2007 IEEE International Symposium on Intelligent Signal Processing, 2007
The property of shift-invariance associated with a good directional selectivity is important for the application of a wavelet transform, (WT), in many fields of image processing. Generally, complex wavelet transforms, like for example the Double Tree Complex Wavelet Transform, (DTCWT), have these good properties. In this paper we propose the use of a new implementation of such a WT, recently introduced, namely the hyperanalytic wavelet transform, (HWT), in denoising applications. The proposed denoising method is very simple, implying three steps: the computation of the forward WT, the filtering in the wavelets domain and the computation of the inverse WT, (IWT). The goal of this paper is the association of a new implementation of the HWT, recently proposed, with a maximum a posteriori (MAP) filter. Some simulation examples and comparisons prove the performances of the proposed denoising method.
A Bayesian approach of wavelet based image denoising in a hyperanalytic multi-wavelet context
WSEAS Transactions on Signal Processing, 2010
We propose the use of a new implementation of the hyperanalytic wavelet transform, (HWT), in association with a Maximum a Posteriori (MAP) filter named bishrink. The denoising methods based on wavelets are sensitive to the selection of the mother wavelets. Taking into account the drawbacks of the bishrink filter and the sensitivity with the selection of the mother wavelets we propose a denoising method in two stages in a multi-wavelet context. It is based on diversification followed by wavelet fusion. Some simulation examples and comparisons prove the performances of the proposed method.
Image Denoising Using a New Implementation of the Hyperanalytic Wavelet Transform
IEEE Transactions on Instrumentation and Measurement, 2000
Shift invariance associated with good directional selectivity is important for the use of a wavelet transform (WT) in many fields of image processing. Generally, complex wavelet transforms, e.g., the double-tree complex WT (DTCWT), have these useful properties. In this paper, we propose the use of a recently introduced implementation of such a WT, namely, the hyperanalytic WT (HWT), in association with filtering techniques already used with the discrete WT (DWT). The result is a very simple and fast image denoising algorithm. Some simulation results and comparisons prove the performance obtained using the new method.
A Bayesian Approach of Hyperanalytic Denoising
2008
The property of shift-invariance associated with a good directional selectivity are important for the application of a wavelet transform, (WT), in many fields of image processing. Generally, complex wavelet transforms, like for example the Double Tree Complex Wavelet Transform, (DTCWT), poses these good properties. In this paper we propose the use of a new implementation of such a WT, recently introduced, namely the hyperanalytic wavelet transform, (HWT), in denoising applications. The proposed denoising method is very simple, implying three steps: the computation of the forward WT, the filtering in the wavelets domain and the computation of the inverse WT, (IWT). The goal of this paper is the association of a new implementation of the HWT, recently proposed, with a maximum a posteriori (MAP) filter. Some simulation examples and comparisons prove the performances of the proposed denoising method.
In this paper we propose the use of a new implementation of the hyperanalytic wavelet transform, (HWT), in association with a Maximum a Posteriori (MAP) filter named bishrink. Such a denoising method is sensitive to the selection of the mother wavelets used for the computation of the HWT. Taking into account the drawbacks of the bishrink filter and the sensibility with the selection of the mother wavelets we propose a denoising method in two stages in a multi-wavelet context. Some simulation examples and comparisons prove the performances of the proposed denoising method.
Searching appropriate mother wavelets for hyperanalytic denoising
Advances in Electrical and Computer Engineering, 2010
The aim of this paper is the association of a new variant of Hyperanalytic Wavelet Transform (HWT) with a maximum a posteriori (MAP) filter, named bishrink for the denoising of images affected by additive white Gaussian noise (AWGN). The best results are obtained with the biorthogonal mother wavelets Daubechies 9/7.
A wavelet-based image denoising technique using spatial priors
Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101), 2000
We propose a new wavelet-based method for image denoising that applies the Bayesian framework, using prior knowledge about the spatial clustering of the wavelet coefficients. Local spatial interactions of the wavelet coefficients are modeled by adopting a Markov Random Field model. An iterative updating technique known as iterated conditional modes (ICM) is applied to estimate the binary masks containing the positions of those wavelet coefficients that represent the useful signal in each subband. For each wavelet coefficient a shrinkage factor is determined, depending on its magnitude and on the local spatial neighbourhood in the estimated mask. We derive analytically a closed form expression for this shrinkage factor.
A joint inter-and intrascale statistical model for Bayesian wavelet based image denoising
… , IEEE Transactions on, 2002
This paper presents a new wavelet-based image denoising method, which extends a recently emerged "geometrical" Bayesian framework. The new method combines three criteria for distinguishing supposedly useful coefficients from noise: coefficient magnitudes, their evolution across scales and spatial clustering of large coefficients near image edges. These three criteria are combined in a Bayesian framework. The spatial clustering properties are expressed in a prior model. The statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model. The three main novelties with respect to related approaches are: (1) the interscale-ratios of wavelet coefficients are statistically characterized, and different local criteria for distinguishing useful coefficients from noise are evaluated; (2) a joint conditional model is introduced, and (3) a novel anisotropic Markov Random Field prior model is proposed. The results demonstrate an improved denoising performance over related earlier techniques.
Management Image Denoising Using Wavelet Thresholding Methods
2012
This paper presents a comparative analysis of vario us image denoising techniques using wavelet transfo rms. A lot of combinations have been applied in order to f ind the best method that can be followed for denois i g intensity images. In this paper, we analyzed severa l methods of noise removal from degraded images wit h Gaussian noise by using adaptive wavelet threshold (Bayes Shrink, Neigh Shrink, Sure Shrink, Bivariate Shrink and Block Shrink) and compare the results in term o f PSNR and MSE. Keywords— wavelet thresholding, Bayes Shrink, Neigh Shrink, SureShrink, Bivariate Shrink and Block Shr ink Introduction An image is often corrupted by noise in its acquisition and transmission. The goal of image denoising is to produce good estimates of the original image from noisy observations. Wavelet denoising attempts to remove the noise present in the signal while preserving the signal characteristics, regardless of its frequency conten t. In the recent years there has been a fair am...
Wavelet transform for the denoising of multivariate images
Multivariate image processing: methods and applications, 2009
An increasing attention is being paid to multispectral images for a great number of applications (medicine, agriculture, archeology, forestry, coastal management, remote sensing \ldots) because many features of the underlying scene have unique spectral characteristics that become apparent in imagery when viewing combinations of its different components. Hence, in satellite imaging, a better analysis of the nature of the materials covering the surface of the earth is achieved \cite{LANDGREBE_00}. Typically, multi\-spectral imaging systems employ radiometers as acquisition instruments which operate in different spectral channels. Each one delivers a digital image in a small range of the visible or non visible wavelengths. As a result, the spectral components form a multicomponent image corresponding to a single sensed area. Usually, satellites have three to a dozen of radiometers. Multispectral sensors offer a valuable advantage over color aerial photographs, thanks to their ability to record reflected light in the near infrared domain. Near infrared is the most sensitive spectral domain used to map vegetation canopy properties \cite{GUYOT_04}. There are several families of on-board multispectral radiometers in the different satellite systems. The first example is SPOT 3 which has two High Resolution Visible imaging systems (HRV1 and HRV2). Each HRV is designated to operate in two sensing modes: a 10 m resolution ``Panchromatic'' (P) mode over the range [0.5, 0.73] mu\mumum and a 20 m resolution multispectral mode. For the multispectral mode, the first channel is associated with the range [0.5, 0.59] mu\mumum, the second channel with the range [0.61, 0.78] mu\mumum and the third one with the range [0.79, 0.89] mu\mumum. The SPOT family provides a service continuity with the upgraded satellite SPOT 4 (launched on March 1998) and SPOT 5 (launched on May 2002). In addition to the former 3 channels, SPOT 4 and SPOT 5 imaging systems gather images in a fourth channel corresponding to a short wave infrared spectral range ([1.58, 1.75] mu\mumum). The fourth channel was introduced in order to allow early observations of plant growth. \\ Another well-known family of multispectral satellite imaging systems is the set of Thematic Mapper instruments with the launch of Landsat 1 in 1972. Since April 1999, Landsat 7 carries the Enhanced Thematic Mapper Plus (ETM+) sensors which are similar to the Thematic Mapper sensors with additional features. An ETM+ Landsat scene is formed by 7 spectral components at a 30 m spatial resolution (except in the thermal band with a spatial resolution of 60 m) and a panchromatic image with 15 m pixel resolution. Recently, commercial satellites like Ikonos and Quickbird have provided very high resolution images. For instance, Ikonos 4 (resp. Quickbird) collects data with a level of detail of 4 m (resp. 2.4 or 2.8 m) in 4 spectral ranges (blue, green, red, and near infrared). \\ Despite the dramatical technological advances in terms of spatial and spectral resolutions of the radiometers, data still suffer from several degradations. For instance, the sensor limited aperture, aberrations inherent to optical systems and mechanical vibrations create a blur effect in remote sensing images \cite{JAIN_89}. In optical remote sensing imagery, there are also many noise sources. Firstly, the number of photons received by each sensor during the obturation time may fluctuate around its average implying a photon noise. A thermal noise may be caused by the electronics of the recording and the communication channels during the data downlinking. Intermittent saturations of any detector in a radiometer may give rise to an impulsive noise whereas a structured periodic noise is generally caused by interferences between electronic components. Detector striping (resp. banding) are consequences of calibration differences among individual scanning detectors (resp. from scan-to-scan). Besides, component-to-component misregistration may occur: corresponding pixels in different components are not systematically associated with the same position on the ground.\\ As a result, it is mandatory to apply deblurring, denoising and geometric corrections to the degraded observations in order to fully exploit the information they contain. In this respect, it is used to distinguish between on-board and on-ground processing. Indeed, on-board procedures should simultaneously fulfill real-time constraints and low mass memory requirements. The involved acquisition bit-rates are high (especially for very high resolution missions) and hence, they complicate the software implementation of enhancement processing. This is the reason why ASIC (Application-Specific Integrated Circuit) hardware circuits are employed. Such on-board circuits enable very basic processing since they present a lower performance than ground-based ones. For instance, Landsat ETM+ raw data are corrected for scan line direction and band alignment only. No radiometric or geometric correction is applied. Consequently, most of the efforts for enhancing the data are performed after their reception at the terrestrial stations. In this context, denoising is a delicate task since it aims at attenuating the noise level while maintaining the significant image features. Generally, the focus is put on additive Gaussian noise. In this respect, many works have been carried out concerning single-component images. The pionnering ones were based on linear spatial filters and nonlinear ones \cite{JAIN_89,PITAS_VENETSAPOULOS_book}. In parallel to these efforts, a gain in performance can be achieved by attenuating the noise in a transform domain in which the image representation yields a tractable statistical modelling. The seminal work of Donoho has shown the potentialities of the Wavelet Transform (WT) for reducing a Gaussian additive noise thanks to its sparsity and decorrelation properties \cite{Donoho_D_1993_jacha_unc_bobdcse}. As a consequence, several wavelet-based image denoising methods were investigated.\\ The objective of this work is to give an overview of the most relevant on-ground wavelet-based noise reduction methods devoted to multicomponent images. %\textsf{Pourquoi seulement on-ground ? D'après ce que j'avais compris lors %de mes collaborations avec le CNES le débruitage serait plutôt on-board et %la déconvolution on-ground. Evidemment cela suppose que la technique %de débruitage employée ne soit pas trop lourde} Two approaches can be considered. The first one consists of independently applying any monochannel noise reduction method to each component. Although its principle is simple, this approach suffers from a serious drawback as it does not account for the cross-component dependences. This has motivated the development of an alternative approach in which the noisy components are jointly processed. In broad outline, it is also possible to classify all the denoising methods (whatever they are componentwise or multivariate ones) into non Bayesian and Bayesian methods. For the latter category, a prior distribution model is adopted for the unknown image. %\textbf{A completer selon contenu de la partie methodes} \\ This chapter is organized as follows. Notations and the observation model are presented in Section \ref{sec:mod_obs}. Section \ref{sec:wav} is a concise overview on wavelet transforms and filter banks. Componentwise and multichannel denoising methods are presented in Section \ref{sec:den_meth}: a wide panel of approaches is tackled (wavelet-based, Bayesian estimation, \ldots). Finally, some comparisons are drawn in Section \ref{sec:comp} before concluding the chapter with Section \ref{sec:concl}.