Directionlet Domain Research Articles

Image denoising with multidirectional shrinkage in directionlet domain

The efficient representation of edges is key to improving the image denoising performance. This motivates us to capture the edges and represent them with a sparse description. A novel image denoising method is proposed by exploiting the sparse representation of the edges and the multidirectional shrinkage. The enhancement of the sparsity is achieved by applying directionlet transforms constructed with the directions of the edges. Because the constructed directionlet transforms are performed along different directions, for each pixel we obtain many different estimates, one of which is optimal. The final denoised output is obtained by a weighted averaging of all individual estimates. Experimental results show that our method, compared with other multidirectional wavelet-based denoising algorithms, can effectively remove noise and preserve detail information such as edges and textures while avoiding the border effect.

Image denoising based on adaptive spatial segmentation and multi-scale correlation in directionlet domain

Directionlet transform DT has become popular over the last few years as an efficient image representation tool due to its fine frequency tiling and directional vanishing moments along any two directions. A novel denoising algorithm based on DT is proposed here for images corrupted with Gaussian noise. The image is first spatially segmented based on the content directionality. Then an undecimated version of DT is applied to effectively capture the directional features and edge information of these segments. The DT coefficients so obtained are then modelled using a bivariate heavy tailed Gaussian distribution and the noise free coefficients are computed using MAP estimator. By employing bivariate probability distribution, the heavy-tail behaviour of natural images is accurately modelled and the interscale properties of DT coefficients are properly exploited. In addition, the local variance parameter of the model is estimated based on classification of DT coefficients within a particular scale using context modelling. Due to this the intrascale dependency of the directionlet coefficients is also well exploited in the enhancement process. The proposed algorithm is competitive with the existing algorithms with better results in terms of output peak signal-to-noise ratio while having comparable computational complexity. It exhibits good capability to preserve edges, contours and textures especially in images with abundant high frequency contents.

SAR speckle reduction using Laplace mixture model and spatial mutual information in the directionlet domain

The reduction of multiplicative speckle noise which always complicates the human and automatic interpretation of objects is very significant for the practical applications of synthetic aperture radar (SAR) image. In this paper, a new maximum a posteriori (MAP) despeckling method based on directionlet transform is proposed. To convert the multiplicative noise into an additive one, the logarithmic transform is first applied to the SAR images. Then, the directionlet coefficients of the noise-free (or underlying backscatter) image and of the speckle noise are modeled as Laplace mixture distribution with zero-mean and Gaussian distribution, respectively. Within Bayesian framework, a MAP estimator is constructed using these assumed prior distributions. After obtaining the parameter estimates using expectation–maximization algorithm, the noise-free coefficients are estimated by a non-linear shrinkage function based on the average version of Bayesian estimator. To improve the denoising performance, we combine the intra-scale dependency in terms of mutual information with the MAP estimator to refine the estimated results. Finally, we compare the proposed algorithm with several other speckle filters applied on synthetic and actual SAR images. Experimental results show that the proposed method outperforms other filters in terms of signal-to-noise ratio, edge preservation and equivalent number of looks measures in most cases.

Spatially adaptive image denoising using inter‐scale dependence in directionlet domain

The performance of image processing algorithms can be significantly improved by the application of multi-resolution image representation with directional features. Directionlet transform (DT) is one such representation which has gained popularity over the past few years as an anisotropic, perfect reconstruction and critically sampled basis function with directional vanishing moments along any two directions. In this study, the authors propose a spatially adaptive image denoising scheme for Gaussian noise based on DT by considering the dependences of the directionlet coefficients across different scales. The image is first decomposed using DT and the coefficients so obtained are modelled using a bivariate heavy tailed ‘pdf’ with a local variance parameter to account for inter- and intra-scale dependencies of the coefficients. The DT is made adaptive to the local dominant directions in the image by identifying the dominant directions in the spatially segmented image through the computation of a parameter called ‘directional variance’. Bayesian ‘maximum a posteriori’ estimator is then used to compute the noise free coefficients from the bivariate models of the signal and noise. The denoised image is obtained from the transform coefficients, which were modified using the bivariate shrinkage function, using directional information and inverse DT. Experimental results show that the bivariate shrinkage in directionlet domain achieves better performance than that in wavelet domain, in terms of numerical and perceptual quality.

Directionlet-based method using the Gaussian mixture prior to SAR image despeckling

In this article, a new denoising algorithm is proposed based on the directionlet transform and the maximum a posteriori (MAP) estimation. The detailed directionlet coefficients of the logarithmically transformed noise-free image are considered to be Gaussian mixture probability density functions (PDFs) with zero means, and the speckle noise in the directionlet domain is modelled as additive noise with a Gaussian distribution. Then, we develop a Bayesian MAP estimator using these assumed prior distributions. Because the estimator that is the solution of the MAP equation is a function of the parameters of the assumed mixture PDF models, the expectation-maximization (EM) algorithm is also utilized to estimate the parameters, including weight factors and variances. Finally, the noise-free SAR image is restored from the estimated coefficients yielded by the MAP estimator. Experimental results show that the directionlet-based MAP method can be successfully applied to images and real synthetic aperture radar images to denoise speckle.

Spatially adaptive despeckling of SAR image using bivariate thresholding in directionlet domain

A novel spatially adaptive despeckling algorithm is presented for a synthetic aperture radar (SAR) image by taking into account the statistical interscale dependency of the directionlet transform (DT) coefficients. The DT is first computed along the dominant directions of the spatially segmented image. The signal and the noise coefficients are modelled using bivariate distributions which take into account the statistical dependence between the adjacent scale coefficients. The nonlinear threshold functions derived from the models employing a maximum a posteriori estimator are then used for estimating the noise-free coefficients. The experimental results show that the proposed method outperforms similar methods in terms of numerical and perceptual quality.

Spatially Adaptive Image Denoising using Undecimated Directionlet Transform

paper a novel de-noising method based on directionlet transform and on sub band adaptive Bayesian threshold is presented. The denoising scheme used in wavelet domain has been extended to the directionlet domain to make the image features to concentrate on fewer coefficients so that more effective thresholding is possible. Here the directionality of the spatially segmented image is first computed using a parameter called directional variance for selecting the optimum direction for decomposing the image using undecimated directionlet transform. The decomposed images with directional energy are used for threshold computation using Bayes scheme. This threshold is then applied to the sub- bands except the LLL subband. The threshold corrected sub- bands with the unprocessed first sub-band are given as input to the inverse directionlet algorithm for getting the de-noised image. Experimental results show that the proposed method outperforms the standard wavelet-based denoising methods in terms of perceptual and numerical estimates.

SAR image despeckling using adaptive multiscale products thresholding in directionlet domain

A directionlet transform (DT)-based multiscale products thresholding is presented which uses a generalised cross-validation (GCV) technique for synthetic aperture radar image despeckling. DT has gained popularity over the past few years as an anisotropic, critically sampled and perfect reconstruction transform with directional vanishing moments along any two directions. In this reported work, the multiscale correlation of DT is exploited by multiplying the adjacent scale coefficients to enhance edge structures while weakening noise. An optimal subband adaptive threshold based on GCV is then computed using this multiscale product. The despeckled image is finally synthesised by using the threshold applied DT coefficients. The employment of DT results in the significant features in images evolving with high magnitudes across scales, while the noise decays rapidly. The proposed scheme outperforms many of the traditional despeckling schemes in terms of speckle reduction and edge preservation.

SAR image despeckling in directionlet domain based on edge detection

Presented is a novel directionally adaptive despeckling algorithm for a SAR image using a multi-direction anisotropic wavelet transform, called a directionlet . It efficiently extracts edge information along dominant directions from the spatially segmented SAR image. Then an optimal scale dependent subband adaptive threshold, based on the generalised cross-validation technique, is applied to the edge removed image. The despeckled image is finally synthesised using the extracted edge information to preserve the sharpness of edges and the texture. The proposed scheme outperforms many of the traditional despeckling schemes such as the Lee filter and the wavelet and bandlet based edge detection methods in terms of numeric and perceptual quality.

Image Denoising Using Sure-Based Adaptive Thresholding in Directionlet Domain

The standard separable two dimensional wavelet transform has achieved a great success in image denoising applications due to its sparse representation of images. However it fails to capture efficiently the anisotropic geometric structures like edges and contours in images as they intersect too many wavelet basis functions and lead to a non-sparse representation. In this paper a novel de-noising scheme based on multi directional and anisotropic wavelet transform called directionlet is presented. The image denoising in wavelet domain has been extended to the directionlet domain to make the image features to concentrate on fewer coefficients so that more effective thresholding is possible. The image is first segmented and the dominant direction of each segment is identified to make a directional map. Then according to the directional map, the directionlet transform is taken along the dominant direction of the selected segment. The decomposed images with directional energy are used for scale dependent subband adaptive optimal threshold computation based on SURE risk. This threshold is then applied to the sub-bands except the LLL subband. The threshold corrected sub-bands with the unprocessed first sub-band (LLL) are given as input to the inverse directionlet algorithm for getting the de-noised image. Experimental results show that the proposed method outperforms the standard wavelet-based denoising methods in terms of numeric and visual quality.

Locally Adaptive De-speckling of SAR Image using GCV Thresholding in Directionlet Domain

Speckle noise usually occurs in Synthetic Aperture Radar (SAR) images due to coherent radiation. Speckle reduction is a mandatory step prior to the processing of SAR images. Here a novel de-speckling scheme is presented which is in line with the wavelet transform based schemes with several modifications due to the implementation of directionlet transform. As in any transform based de-speckling schemes, the directionlet based de-speckling also involves mainly three steps. First transform the input image using an orthogonal transform, then threshold the transform coefficients using a non-linear algorithm and finally reconstruct the image using the modified coefficients. The effectiveness of a despeckling algorithm basically depends on two factors- one is the efficient representation of the image to be despeckled using a local, directional and multi resolution expansion and second is the efficient computation of an optimal threshold. Here the first requirement is met by using a locally adaptive directionlet transform and the second by optimal threshold computation using Generalized Cross Validation (GCV) technique. Experimental results on simulated and actual SAR images show that minimizing GCV in the directionlet domain results in better de-speckling performance when compared to minimizing it in the wavelet domain. The proposed scheme outperforms many of the traditional de-speckling schemes in terms of numeric and perceptual quality.

SAR Image Denoising Based on Lifting Directionlet Domain Gaussian Scale Mixtures Model

In this paper,a new speckle suppression method for SAR image is proposed.By combining Directionlet transform with a version of the hidden Markov model—Gaussian scale mixtures(GSM),the marginal distributions of neighbor coefficients in the lifting Directionlet domain are modeled.For removing the speckle noise,the Bayes least square estimation is adopted to evaluate each coefficient.Being regarded as a novel multiscale geometrical analysis tool,Directionlet transform retains the separable filtering,computation simplicity and filter design from the standard two-dimensional wavelet transform,which can capture anisotropic geometrical structures efficiently by multi-direction selection.The introduction of lifting scheme reduces computation amount greatly.Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables:A Gaussian vector and a hidden positive scalar multiplier.Under this model,the marginal of neighbor coefficients are well described and the strong correlation among the amplitudes of neighbor coefficients is also presented adequately.Experiments using plentiful real SAR images indicate that the proposed method outperforms the spatial filters and other methods based on wavelets in terms of speckle reduction as well as image detail preservation.