Nonsubsampled Shearlet Transform Coefficients Research Articles

Medical image super-resolution reconstruction via multi-scale information distillation network under multi-scale geometric transform domain

High resolution (HR) magnetic resonance images (MRI) or computed tomography (CT) images can provide clearer anatomical details of human body, which facilitates early diagnosis of the diseases. However, due to the imaging system, imaging environment and human factors, it is difficult to obtain clear high-resolution images. In this paper, we proposed a novel medical image super resolution (SR) reconstruction method via multi-scale information distillation (MSID) network in the non-subsampled shearlet transform (NSST) domain, namely NSST-MSID network. We first proposed a MSID network that mainly consisted of a series of stacked MSID blocks to fully exploit features from images and effectively restore the low resolution (LR) images to HR images. In addition, most previous methods predict the HR images in the spatial domain, producing over-smoothed outputs while losing texture details. Thus, we viewed the medical image SR task as the prediction of NSST coefficients, which make further MSID network keep richer structure details than that in spatial domain. Finally, the experimental results on our constructed medical image datasets demonstrated that the proposed method was capable of obtaining better peak signal to noise ratio (PSNR), structural similarity (SSIM) and root mean square error (RMSE) values and keeping global topological structure and local texture detail better than other outstanding methods, which achieves good medical image reconstruction effect.

Local bit-plane neighbour dissimilarity pattern in non-subsampled shearlet transform domain for bio-medical image retrieval.

This paper introduces a novel descriptor non-subsampled shearlet transform (NSST) local bit-plane neighbour dissimilarity pattern (NSST-LBNDP) for biomedical image retrieval based on NSST, bit-plane slicing and local pattern based features. In NSST-LBNDP, the input image is first decomposed by NSST, followed by introduction of non-linearity on the NSST coefficients by computing local energy features. The local energy features are next normalized into 8-bit values. The multiscale NSST is used to provide translational invariance and has flexible directional sensitivity to catch more anisotropic information of an image. The normalised NSST subband features are next decomposed into bit-plane slices in order to capture very fine to coarse subband details. Then each bit-plane slices of all the subbands are encoded by exploiting the dissimilarity relationship between each neighbouring pixel and its adjacent neighbours. Experiments on two computed tomography (CT) and one magnetic resonance imaging (MRI) image datasets confirms the superior results of NSST-LBNDP when compared to many recent well known relevant descriptors both in terms of average retrieval precision (ARP) and average retrieval recall (ARR).

A novel statistical approach for multiplicative speckle removal using t-locations scale and non-sub sampled shearlet transform

One of the most interesting problems in denoising of images includes despeckling of multiplicative noise. This paper proposes a novel statistical processor in the framework of Non-sub Sampled Shearlet Transform (NSST) to reduce the effect of the multiplicative noise on images given preserving of structural and visual quality of image. First, we indicate that NSST coefficients of logarithmically transformed images can be statistically meaningful modeled by t-location scale (TLS). For designing our processor, we employ Minimum Mean Squared Error (MMSE) estimator to reduce noise distortion. We show by using TLS as the prior distribution, non-linear noise suppression behavior is obtained in test images. Finally, we compare our method by the state-of-the-art algorithms like soft and hard thresholding and also with well-known adaptive filters in this area like Wiener, Frost, Lee and one recent method in shearlet denoising framework.

Locally optimum watermark decoder in NSST domain using RSS-based Cauchy distribution

It is important to consider the tradeoff between imperceptibility and robustness requirements in developing an image-watermarking technique, some statistical model-based image watermarking schemes have been designed in the past decade. The effectiveness of a statistical watermark decoder depends highly on the modeling of the transform-domain coefficients and the use of hypothesis testing. In this study, a multiplicative image watermarking scheme is proposed in the nonsubsampled Shearlet transform (NSST) domain, where NSST coefficients are modeled by ranked set sample (RSS) based Cauchy statistical distribution and locally most powerful (LMP) test criterion is applied. Digital image watermarking technique consists of two parts, namely, embedding and extracting. In the embedding process, to achieve relatively good imperceptibility and robustness, watermark data is inserted into the significant NSST directional subband that has the highest energy value, by modifying nonlinearly the significant NSST coefficients. In the extracting phase, a scheme is proposed for designing a blind NSST domain watermark decoder incorporating the RSS based Cauchy statistical distribution and LMP test criterion. Here, the RSS method is used to estimate the location parameter and shape parameter of Cauchy statistical distribution instead of traditional maximum-likelihood (ML) method, which can provide the Cauchy model with higher precision parameters. Experimental results on a set of standard test images show significant improvements in imperceptibility and robustness using the proposed method compared with the best known state-of-the-art approaches.

Medical Image Fusion Method Based on Coupled Neural P Systems in Nonsubsampled Shearlet Transform Domain

Coupled neural P (CNP) systems are a recently developed Turing-universal, distributed and parallel computing model, combining the spiking and coupled mechanisms of neurons. This paper focuses on how to apply CNP systems to handle the fusion of multi-modality medical images and proposes a novel image fusion method. Based on two CNP systems with local topology, an image fusion framework in nonsubsampled shearlet transform (NSST) domain is designed, where the two CNP systems are used to control the fusion of low-frequency NSST coefficients. The proposed fusion method is evaluated on 20 pairs of multi-modality medical images and compared with seven previous fusion methods and two deep-learning-based fusion methods. Quantitative and qualitative experimental results demonstrate the advantage of the proposed fusion method in terms of visual quality and fusion performance.

Infrared and visible image fusion based on non‐subsampled shearlet transform, regional energy, and co‐occurrence filtering

The fusion of infrared and visible images has been playing an important role in various scenarios all over the world. For the fusion results from most of the existing techniques in this area, some features, such as the image contrast and edge details, are still needed to be improved. In this Letter, a new fusion method of the infrared and visible image is rendered. In this method, the infrared image is preprocessed to improve the contrast. Then, the two source images are decomposed based on non-subsampled shearlet transform (NSST). The fusion rules based on regional energy and co-occurrence filtering are proposed for the low-frequency and high-frequency NSST coefficients, respectively. Experimental results show that the proposed method can effectively retain the details of the source image, meanwhile improve the contrast of the fused image.

Multibaseline Interferometric Phase Denoising Based On Kurtosis In the NSST Domain.

Interferometric phase filtering is a crucial step in multibaseline interferometric synthetic aperture radar (InSAR). Current multibaseline interferometric phase filtering methods mostly follow methods of single-baseline InSAR and do not bring its data superiority into full play. The joint filtering of multibaseline InSAR based on statistics is proposed in this paper. We study and analyze the fourth-order statistical quantity of interferometric phase: kurtosis. An empirical assumption that the kurtosis of interferograms with different baselines keeps constant is proposed and is named as the baseline-invariant property of kurtosis in this paper. Some numerical experiments and rational analyses confirm its validity and universality. The noise level estimation of nature images is extended to multibaseline InSAR by dint of the baseline-invariant property of kurtosis. A filtering method based on the non-subsampled shearlet transform (NSST) and Wiener filter with estimated noise variance is proposed then. Firstly, multi-scaled and multi-directional coefficients of interferograms are obtained by NSST. Secondly, the noise variance is represented as the solution of a constrained non-convex optimization problem. A pre-thresholded Wiener filtering with estimated noise variance is employed for shrinking or zeroing NSST coefficients. Finally, the inverse NSST is utilized to obtain the filtered interferograms. Experiments on simulated and real data show that the proposed method has excellent comprehensive performance and is superior to conventional single-baseline filtering methods.

Seismic Random Noise Attenuation Based on PCC Classification in Transform Domain

Random noise attenuation of seismic data is an essential step in the processing of seismic signals. However, as the exploration environment is becoming more and more complicated, the energy of valid signals is weaker and the signal to noise (SNR) is much lower, which brings great difficulty to seismic data processing and interpretation. To this end, we propose an unconventional and effective seismic random noise attenuation method based on proximal classifier with consistency (PCC) in transform domain. Firstly, we analyze various transforms for seismic data from traditional wavelet transform and curvelet transform to emerging non-subsampled shearlet transform (NSST) and non-subsampled contourlet transform (NSCT). And, we select the excellent NSST to decompose the noisy seismic data into different sub-bands of frequency and orientation responses. Secondly, unlike traditional sparse transform based seismic denoising methods that often directly use a thresholding operator and corresponding inverse transform to denoise seismic data, our proposed method employs a superior performance PCC to classify the NSST coefficients of seismic data before thresholding operator. The added step can effectively divide the NSST coefficients into reflected useful signal coefficients and noise-related coefficients, which can preserve the edge of reflected signals and keep the information of events intact as much as possible. In addition, we also introduce an adaptive threshold computing method and a soft-thresholding method to achieve seismic data denoising better. Finally, the experimental results on the typical synthetic example and real seismic data show the superior performance of the proposed method.

Synchronization correction-based robust digital image watermarking approach using Bessel K-form PDF

Robustness has played extremely important role in the multiple applications of digital watermarking technology. The reason lies in its influence on the watermarking system’s practicability. As one of the most difficult kinds of digital signal processing for a digital watermark to survive, geometric distortions have become a central problem in digital image watermarking research. Therefore, resigning a greatly robust digital image watermarking approach which can withstand geometric distortions is still a quite challenging work. On account of Bessel K-form (BKF) probability density function (PDF), this paper proposes an optimal synchronization correction-based digital image watermarking method which can resist geometric distortions. This approach consists of watermark embedding, synchronization correction and watermark extraction. Using the quantization index modulation (QIM), the watermark is inserted into the original host images in the nonsubsampled shearlet transform (NSST) domain by adjusting the selected blocks’ low-frequency NSST coefficients. The BKF PDF describes the NSST coefficients’ statistical features. Besides, the BKF statistical model parameters can be used in constructing a compact image characteristic space. Utilizing the compact image feature, the least squares support vector regression (LS-SVR) synchronization correction is performed to estimate the geometric distortions parameters. After LS-SVR synchronization correction, the inverse QIM is performed to recover blindly the inserted watermark. Simulation results demonstrate that the presented digital image watermarking method not only has good imperceptibility performance, but also can well resist challenging common signal processing operations as well as geometric distortions, which can be superior to the most advanced approaches.

Image NSST-HMT model with associated multi-state coefficients

In recent years, due to its anisotropy, multi-directional capture characteristics,and translation invariance, the non-subsampled shearlet transform (NSST) hasplayed an important stabilizing role inthe process of image restoration. In this study, weanalyze an images NSST coefficients, including the relationship betweencoefficients in the same subband, the relationship between“father-son” coefficients, and the relationship between “brotherhood”coefficients in different subbands. The results reveal that thecoefficients in the NSST subbands are sparse, and both “father-sonrelationship” and “brotherhood relationship” coefficients exhibitaggregation and transitivity. On this basis, a hidden Markov tree (HMT)model with associated multi-state coefficients (M-NSST-HMT) isproposed. This model estimates the reconstructed coefficientsusing “father-son relationship” and “brotherhood relationship”of the NSST subband coefficients as joint states of guiding thecoefficients transfer between subbands. In addition, the model integrates thereconstructed coefficients using the mutual information betweenthese two associated states. Finally, the proposed model is appliedto image denoising with favorable results. The results indicatethat the proposed model can reveal the relationship ofcoefficients in NSST subbands and improve the prediction accuracy ofcoefficients more effectively than the traditional HMT model.

Edge-preserving image denoising using a deep convolutional neural network

Abstract This paper introduces a novel denoising approach making use of a deep convolutional neural network to preserve image edges. The network is trained by using the edge map obtained from the well-known Canny algorithm and aims at determining if a noisy patch in non-subsampled shearlet domain corresponds to the location of an edge. In the first step of the proposed denoising algorithm, we use the non-subsampled shearlet transform to decompose the noisy image into a low-frequency subband and a series of high-frequency subbands. Subsequently, 3D blocks are formed by stacking 2D blocks of high-frequency subbands along a specific direction. Each 3D patch is then fed to the trained deep convolutional neural network to determine if it belongs to the edge-related class or not. Finally, the NSST (non-subsampled shearlet transform) coefficients belonging to the edge-related class remain unchanged, and those not belonging to the edge-related class are denoised by the shrinkage method using an adaptive threshold. Experimental results on various test images including benchmark grayscale images and medical ultrasound images demonstrate that the proposed method achieves better performance compared to some state-of-the-art denoising approaches.

Multimodal Neuroimaging Fusion in Nonsubsampled Shearlet Domain Using Location-Scale Distribution by Maximizing the High Frequency Subband Energy

A fusion of medical imaging data obtained from different modalities plays an important role in the current clinical practice. In this paper, we propose a novel multimodal fusion algorithm for brain imaging data based on the statistical properties of nonsubsampled shearlet transform (NSST) coefficients and a novel energy maximization fusion rule. The marginal distributions of the high-frequency NSST coefficients exhibit heavier tails than the Gaussian distribution. As a consequence, after studying its characteristics, we use a heavy-tailed probability density function, student’s $t$ location-scale distribution, to describe the highly non-Gaussian statistics of empirical NSST coefficients by learning the parameters using maximum likelihood estimation. Then, we employ this model to develop a maximum a posteriori estimator to obtain the noise-free coefficients. Then, for the first time, a novel fusion rule for obtaining the fused NSST coefficients based on maximizing the energy in the high-frequency subbands is proposed. Experiments are carried out on fusing two or more multimodal neuroimages taken from the BrainWeb, Alzheimer’s Disease Neuroimaging Initiative (ADNI), and Whole Brain Atlas databases. It is seen from the subjective and objective results that the proposed multimodal neuroimaging fusion method significantly outperforms the state-of-the-art methods including under noisy scenarios, and hence, it is more robust. It is also observed that the signal intensities in the fused images are better enhanced when a more number of source images are being fused. The proposed technique should benefit the medical professionals in diagnosing neurological disorders, such as Alzheimer, epilepsy, and multiple sclerosis.

RETRACTED ARTICLE: Performance analysis of pre-cancerous mammographic image enhancement feature using non-subsampled shearlet transform

Breast cancer is the second highest death causing disease in female. From the data it’s clear that one of the eight women is affected by breast cancer. The most effective way to detect the cancer is by using mammography technique and also it detects masses and abnormal conditions. The cluster shaped white spots on mammograms are used the cancer in the early stages. The importance of breast cancer detection to reduce different noises which are commonly found in mammogram images and provides better image quality. Here the multi-scale and the multi-directional analysis would produce optimal approximation and detail coefficients of Non-subsampled shearlet transform (NSST). Hence in this paper, the noisy image is amended into piecewise smooth function in different subbands of frequency. NSST coefficients are amended into information and noise related coefficients are noise is removed by using the adaptive threshold. To evaluate the performance of this proposed algorithm, Mean Square Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) are used. Testing these experimental results show that the proposed algorithm can preserve the edges and textures very well while weakening the noise can obtain better suppressed noise and enhances the objective of evaluations than other noise removal methods.

A novel retrieval method for remote sensing image based on statistical model

With the increasing number of high-resolution remote sensing (HRRS) image technologies, there is an interest in seeking a way to retrieve images efficiently. In order to describe the images with abundant texture information more concisely and accurately, we propose a novel remote sensing image retrieval approach based on the statistical features of non-subsampled shearlet transform (NSST) coefficients, according to which we set up a model using Bessel K form (BKF). First, the remote sensing (RS) image is decomposed into several subbands of frequency and orientation using the non-subsampled shearlet transform. Then, we use the Bessel K distribution model is utilized to describe the coefficients of NSST high-frequency subband. Next, the BKF parameters are selected to serve as the texture feature to represent the characteristics of image, namely BKF statistical model feature (BSMF), and the feature vector of each image is created by combination with parameters at each high-pass subband. Both the experiment and theory indicate that the BKF distribution is highly matched with the statistical features of NSST coefficients within high-pass subbands. In our experiments, we applied the proposed method to two general RS image datasets- The UC Merced land use dataset and the Sydney dataset. The results show that our proposed method can achieve a more robust and commendable performance than the state-of-the-art approaches.

Image Fusion With Contextual Statistical Similarity and Nonsubsampled Shearlet Transform

Image fusion has the capability to integrate useful information from source images into a more comprehensive image. How to obtain the effective representation of source images is a key step to image fusion. Due to the loss of the dependence of coefficients, most of traditional multi-scale decomposition-based image fusion methods suffer from an inaccurate image representation. To solve this problem, a novel image fusion method with contextual statistical similarity in nonsubsampled shearlet transform (NSST) is presented. The key contributions include: 1) the dependence of NSST coefficients is captured by the contextual hidden Markov model (CHMM); 2) the contextual statistical similarity of coefficients is proposed; 3) an effective fusion rule based on the characteristic of CHMM is developed for high-frequency subbands in NSST domain. By the visual analysis and quantitative evaluations on experimental results, the superiority of the proposed method is demonstrated.

Structure tensor and nonsubsampled shearlet transform based algorithm for CT and MRI image fusion

Multimodal medical image fusion technique contributes to the reduction of information uncertainty and improves the clinical diagnosis accuracy, the aim of which is to preserve salient image features and detail information of multiple source images to produce a visual enhanced single fused image. In this paper, by taking full advantages of structure tensor and nonsubsampled shearlet transform (NSST) to effectively extract geometric features, a novel unified optimization model is proposed for fusing computed tomography and magnetic resonance imaging images. The proposed model includes two terms, which constrain the gradient and NSST coefficients of the final fused image close to the pre-fused gradient and NSST coefficients. The pre-fused gradient is obtained from weighted structure tensor and the pre-fused NSST coefficients are generated by fusing NSST coefficients of source images with proposed fusion rules. The final fused image can be obtained by solving the constructed optimization problem via conjugate gradient method. Experimental results demonstrate that the proposed approach outperforms the compared multi-resolution and gradient based methods in both visual effects and quantitative assessments.

Blind optimum detector for robust image watermarking in nonsubsampled shearlet Domain

In this paper, we propose a blind robust image watermarking approach in the nonsubsampled Shearlet domain using Bessel K Form (BKF) modeling. Nonsubsampled shearlet transform (NSST) is an effective multi-scale and multi-direction analysis method, it not only can exactly compute the shearlet coefficients based on a multiresolution analysis, but also can provide nearly optimal approximation for a piecewise smooth function. In order to achieve more robustness and imperceptibility, watermark information is embedded into the most significant NSST directional subband with the highest energy, by simply modifying the NSST coefficient amplitude according to the watermark data. By modeling the NSST coefficients with BKF probability density function, the distribution of watermarked noisy coefficients is analytically calculated. The tradeoff between the imperceptibility and robustness of watermark data is solved in a novel fashion. At the receiver, based on the Maximum Likelihood (ML) decision rule, a blind statistical watermark detector is proposed. Experimental results on test images demonstrate that the proposed approach can provide better imperceptibility and robustness against various attacks, such as additive white Gaussian noise, salt & pepper noise, median filtering, JPEG compression, rotation, and scaling, in comparison with the recently proposed techniques.

Image denoising using local Wiener filter and its method noise

This paper proposed a new image denoising method on local Wiener filter. Firstly, nonsubsampled shearlet transform (NSST) is used to decompose noisy image since NSST is an effective multi-scale and multi-direction analysis tool in image processing. And then the high frequency NSST coefficients are denoised by a shrinkage function based on local Wiener filter. In this new shrinkage function, the method noise of local Wiener filter is employed effectively by using the Stein’s unbiased risk estimate and linear expansion of thresholds (SURE-LET) strategy. Finally, the inverse NSST is used to obtain the denoised image. Experimental results show that the proposed method is very good in performance compared to the state-of-the-art wavelet-based algorithms.

Combination of anisotropic diffusion and non-subsampled shearlet transform for image denoising

In this work, a non-subsampled shearlet transform (NSST) based anisotropic diffusion method is proposed. In the proposed method, the NSST transform is firstly applied to the noisy image to provide several scale and directional components. Then, the NSST coefficients are classified into textured regions and noise-related ones by using Sparse Un-mixing by the variable Splitting and Augmented Lagrangian (SUnSAL) classifier. Subsequently, an energy function is formed by the noise-related coefficients to be minimized by diffusion equations. The noisy free image is approximated from the denoised coefficients obtained by the anisotropic diffusion method and textured coefficients which are remained unchanged. Visual and quantitative assessments demonstrate that the proposed method outperforms the state-of-art denoising methods in terms of noise removal and detail preservation.

Using two coefficients modeling of nonsubsampled Shearlet transform for despeckling

Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise. Two approaches based on modeling the nonsubsampled Shearlet transform (NSST) coefficients are presented. Two-sided generalized Gamma distribution and normal inverse Gaussian probability density function have been used to model the statistics of NSST coefficients. Bayesian maximum a posteriori estimator is applied to the corrupted NSST coefficients in order to estimate the noise-free NSST coefficients. Finally, experimental results, according to objective and subjective criteria, carried out on both artificially speckled images and the true SAR images, demonstrate that the proposed methods outperform other state of art references via two points of view, speckle noise reduction and image quality preservation.