Corina Nafornita

Image Denoising Using a New Implementation of the Hyperanalytic Wavelet Transform

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.

Bayesian Hyperanalytic Denoising of SONAR Images

The SOund Navigation And Ranging (SONAR) images are perturbed by speckle noise. This paper presents a new denoising method in the wavelet domain, which tends to reduce the speckle, preserving the structural features and the textural information of the scene. Shift invariance associated with good directional selectivity is important for the use of a wavelet transform (WT) in denoising of SONAR images. In this paper, we propose the use of a variant of hyperanalytic WT, which is quasi-shift invariant and has good directional selectivity in association with a maximum a posteriori filter named bishrink. This filter makes a very good treatment of the contours. The corresponding denoising algorithm is simple and fast. Its performance was proved on images perturbed by synthesized speckle noise and on real SONAR images.

A New Implementation of the Hyperanalytic Wavelet Transform

The property of shift-invariance associated with a good directional selectivity are important for the application of a wavelet transform in many fields of image processing. Unfortunately, the 2D discrete wavelet transform is shift-variant and has a reduced directional selectivity. These disadvantages can be attenuated if a complex wavelet transform is used. In this paper, we propose a new implementation of such a wavelet transform, recently introduced, the hyper analytic wavelet transform. It is quasi shift-invariant, it has a good directional selectivity, and a reduced degree of redundancy of 4 in 2D. The implementation proposed is very simple. The properties already mentioned are proved by simulation.

Regularised, semi-local hurst estimation via generalised lasso and dual-tree complex wavelets

Semi-local Hurst estimation is considered for random fields where the regularity varies in a piecewise manner. The recently developed generalised lasso is exploited to propose a spatially regularised Hurst estimator. Dual-tree complex wavelets are used to formulate the usual log-spectrum regression problem and an interlaced penalty matrix is constructed to form a 2-d fused lasso constraint on the double-indexed parameters. We thus extend a regularity-based denoising approach and demonstrate the utility of our method with experiments.

Image Watermarking Based on the Discrete Wavelet Transform Statistical Characteristics

The current paper proposes a robust watermarking method for still images that embeds a binary watermark into the detail subbands of the image wavelet transform. The perceptually significant coefficients are selected for each subband using a different threshold. The threshold is computed based on the statistical analysis of the wavelet coefficients. For greater invisibility of the mark, the approximation subband is left unmodified. The watermark is embedded several times to achieve robustness. The method is tested against different types of attacks (lossy compression, AWGN, scaling, cropping, intensity adjustment, filtering and collusion attack). The proposed method was compared with a state-of-the-art watermarking method, highlighting its performances

A new pixel-wise mask for watermarking

Robust watermarking using pixel-wise masking in the wavelet domain proves to be quite robust against common signal processing. However, because embedding is made only in the highest resolution level, the watermark information can be easily erased by a potential attacker. In this paper, we propose a modified perceptual mask that models the human visual system behavior in a better way. The texture content is appreciated with the local standard deviation of the original image, which is further compressed in the wavelet domain. Since the approximation image of the coarsest level contains too little information, we appreciate the luminance content using a higher resolution level approximation subimage. Embedding is made in all the detail subbands except the coarsest level, for attack resilience; we propose three types of detectors that take advantage of the wavelet hierarchical decomposition. Tests were made for different attacks (JPEG compression, median filtering, resizing, cropping, gamma correction and blurring), that prove the effectiveness of the new pixel-wise mask in comparison with the previous system.

Semi-Local Scaling Exponent Estimation With Box-Penalty Constraints and Total-Variation Regularization

We here establish and exploit the result that 2D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least square problems and generalized Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-square estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators.

A Bayesian Approach of Hyperanalytic Wavelet Transform Based Denoising

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.

Generalised M-Lasso for robust, spatially regularised hurst estimation

A generalised Lasso iteratively reweighted scheme is here introduced to perform spatially regularised Hurst estimation on semi-local, weakly self-similar processes. This is extended further to the robust, heavy-tailed case whereupon the generalised M-Lasso is proposed. The design successfully incorporates both a spatial derivative in the generalised Lasso regulariser operator and a weight matrix formulated in the wavelet domain. The result simultaneously spatially smooths the Hurst estimates and downweights outliers. Experiments using a Hampel score function confirm that the method yields superior Hurst estimates in the presence of strong outliers. Moreover, it is shown that the inferred weight matrix can be used to perform wavelet shrinkage and denoise fractional Brownian surfaces in the presence of strong, localised, band-limited noise.

Barycentric distribution estimation for texture clustering based on information-geometry tools

The goal of the paper1 is to propose a new method for texture clustering based on the information-geometry tools. Considering textured images as a collection of heavy-tailed prior probability distributions related to some space/scale decomposition, an average of distributions, i.e. a barycentric distribution, is proposed for characterizing each cluster. We suggest the use of the Jeffrey divergence as a dissimilarity measure for the clustering of textured images. Taking into account the geometry of the probabilistic manifold associated to the prior family, we provide the steepest descent method used to estimate the barycentric distribution. The descent exploits the Fisher information matrix, which is the expected value of the Hessian matrix and the local metric to the manifold. The results of experimental evaluation conducted on well-known texture databases show that the Fisher information matrix approach provides a convergence speed significantly higher than the convergence speed of conventional methods of steepest descent.