A Bayesian Approach of Hyperanalytic Wavelet Transform Based Denoising

Abstract

The property of shift-invariance associated with a a support of arbitrary shape. The SA-DCT is used in good directional selectivity is important for the application of a conjunction with the Anisotropic Local Polynomial wavelet transform, (WT), in many fields of image processing.Approximation (LPA) -Intersection of Confidence Intervals Generally, complex wavelet transforms, like for example the (ICI) technique, which defines the shape of the transform Double Tree Complex Wavelet Transform, (DTCWT), have these good properties. In this paper we propose the use of a new suppondin a pointwe ap e mnner. Snersupports implementation of such a WT, recently introduced, namely the crespondn etoiffe s are igera l oeapping hyperanalytic wavelet transform, (HWT), in denoising the local estimates are averaged together using adaptive applications. The proposed denoising method is very simple, weights that depend on the region's statistics. The denoising implying three steps: the computation of the forward WT, the system proposed in [3] is a M\AP filter that acts in the spatial filtering in the wavelets domain and the computation of the domain. It makes a different treatment of regions with inverse WT, (IWT). The goal of this paper is the association of a different homogeneity degree. These regions can be treated new implementation of the HWT, recently proposed, with a independent with the same M\AP filter choosing between maximum a posteriori (MAP) filter. Some simulation examples different prior models. The multi-resolution analysis and comparisons prove the performances of the proposed performed by the WT has been shown to be a powerful tool to denoising method. achieve good denoising. In the wavelet domain, the noise is uniformly spread throughout the coefficients, while most of Keywords -Directional selectivity, Hyperanalytic wavelet th img inomto is cocntae intefwlretoe transfom,Imag deosig Maiu a potrir fle. the image information iS concentrated in the few largest ones transform, ImaednoiingMaimmaposeri(sparsity of the wavelet representation), [4-7]. The corresponding denoising methods have three steps, [1]: 1) The computation of the forward WT, 2) the filtering of the wavelet coefficients, 3) the computation of the IWT of the During acquisition and transmission, imagesareof result obtained. Numerous WTs can be used to operate these Dfuringbyacquiition andis tr cansm ,images Garesftn treatments. The first one was the Discrete Wavelet Transform, cotoruthe byative.The nise tt can beag deledsing as gaussian DWT, [1]. It has three main disadvantages, [8]: lack of shift mostoftheno tme.uthe aoime ofvel, a himge-ren ingalgoithm is invariance, lack of symmetry of the mother wavelets and poor then to reduce the noise level, while preserving the image dietoa.eetv hs iavnae a be dimnihe features. Such a system must realize a big noise reduction in ty g the homogeneous regions and the preservation of the details using a complex wavelet transform [8, 9]. Over twenty years * * * -r-* r~~~~ago, Grossman and Morlet [10] developed the Co...

Retinopathy grading with deep learning and wavelet hyper-analytic activations

“…Through this study, the authors clearly present their experiment as the directional selectivity is enhanced by the 2D HWT by the linear combination of Hilbert transform of different Wavelet sub-bands [ 35 ]. In [ 13 , 36 ], the researchers claim that magnitude and phase spectra are combined to define texture, discriminative HF edges in an image.…”

“…Hyper-analytic Wavelet fosters the directional selectivity by the linear combination of Hilbert transform of different Wavelet sub-bands [ 35 ]. In [ 13 ], the researchers claim that the HWT optimizes the directional selectivity.…”

“…In [ 13 ], the researchers claim that the HWT optimizes the directional selectivity. Equivalent directional selectivity is possible to accomplish by adding/subtracting the different HWT pairs [ 35 ]. In [ 36 ], the researchers combine the magnitude and phase spectra for defining texture, discriminating HF edges in an image.…”

Optimal Hyper Analytic Wavelet Transform for Glaucoma Detection in Fundal Retinal Images

“…After pre-processing, the image is Hyper Analytic transformed from [15] which features would be extracted. The transformation is carried out after finding the optimal coefficients with the help of hybrid GSO cuckoo search optimization algorithm.…”