High-pass Subbands Research Articles

A New Pan-Sharpening Method Using Statistical Model and Shearlet Transform

ABSTRACTA statistical model-based pan-sharpening method under the framework of Shearlet transform is developed in this paper. The approximation coefficients of multi-spectral (MS) image are used for reconstruction level of fusion algorithm. The weighted average method is used to fuse the high-pass subbands. The weights are estimated by a statistical model in which a new objective function is proposed. It is partitioned into two parts: the first term maximizes the local variance of the high-pass subband of fused image, which means the details can be injected into MS image as much as possible. The second term is the correlation restriction between the high-pass subband of fused image and that of MS image, which is indirectly beneficial to avoid generating the unreasonable high-frequency information. Finally, the pan-sharpening result is obtained by performing the inverse Shearlet transform. A series of experiments conducted on real remote sensing images demonstrate the effectiveness of our model.

Image Sequence Fusion and Denoising Based on 3D Shearlet Transform

We propose a novel algorithm for image sequence fusion and denoising simultaneously in 3D shearlet transform domain. In general, the most existing image fusion methods only consider combining the important information of source images and do not deal with the artifacts. If source images contain noises, the noises may be also transferred into the fusion image together with useful pixels. In 3D shearlet transform domain, we propose that the recursive filter is first performed on the high-pass subbands to obtain the denoised high-pass coefficients. The high-pass subbands are then combined to employ the fusion rule of the selecting maximum based on 3D pulse coupled neural network (PCNN), and the low-pass subband is fused to use the fusion rule of the weighted sum. Experimental results demonstrate that the proposed algorithm yields the encouraging effects.

A novel multi-modal medical image fusion method based on shift-invariant shearlet transform

Medical image fusion plays an important role in clinical applications, such as image-guided surgery, image-guided radiotherapy, non-invasive diagnosis and treatment planning. Shearlet is a novel multi-scale geometric analysis (MGA) tool proposed recently. In order to overcome the drawback of the shearlet-based fusion methods that the pseudo-Gibbs phenomenon is easily caused around the singularities of the fused image, a new multi-modal medical image fusion method is proposed in shift-invariant shearlet transform domain. First, the original images are decomposed into lowpass sub-bands and highpass sub-bands; then, the lowpass sub-bands and high sub-bands are combined according to the fusion rules, respectively. All the operations are performed in shift-invariant shearlet domain. The final fused image is obtained by directly applying inverse shift-invariant shearlet transform to the fused lowpass sub-bands and highpass sub-bands. Experimental results demonstrate that the proposed method can not only suppress the pseudo-Gibbs phenomenon efficiently, but perform better than the popular wavelet transform-based method, contourlet transform-based method and non-subsampled contourlet transform-based method.

Multimodal Medical Volumetric Data Fusion Using 3-D Discrete Shearlet Transform and Global-to-Local Rule

Traditional two-dimensional (2-D) fusion framework usually suffers from the loss of the between-slice information of the third dimension. For example, the fusion of three-dimensional (3-D) MRI slices must account for the information not only within the given slice but also the adjacent slices. In this paper, a fusion method is developed in 3-D shearlet space to overcome the drawback. On the other hand, the popularly used average-maximum fusion rule can capture only the local information but not any of the global information for it is implemented in a local window region. Thus, a global-to-local fusion rule is proposed. We firstly show the 3-D shearlet coefficients of the high-pass subbands are highly non-Gaussian. Then, we show this heavy-tailed phenomenon can be modeled by the generalized Gaussian density (GGD) and the global information between two subbands can be described by the Kullback-Leibler distance (KLD) of two GGDs. The finally fused global information can be selected according to the asymmetry of the KLD. Experiments on synthetic data and real data demonstrate that better fusion results can be obtained by the proposed method.

Differential evolution algorithm for the selection of optimal scaling factors in image watermarking

In this paper, an innovative watermarking scheme based on differential evolution (DE) in the transform domain is proposed. The insertion and extraction of the watermark are performed in discrete wavelet transform-singular value decomposition (DWT–SVD) transform domain. In the embedding process, the host image is transformed into sub-bands of different frequencies by third-level DWT and then subsequent application of SVD on low pass (LL) and high pass (HH) sub-bands at level third. The watermark image is properly scaled down by multiplying with different scaling factors (SFs) and embedded in the Singular value matrix of LL and HH sub-bands of the host image to make the watermark invisible and robust. We applied an optimization technique, differential evolution, to search optimal scaling factors to improve the quality of watermarked image and robustness of the watermark. In order to overcome the false positive problem, a binary watermark is also embedded in the host image in a lossless manner. According to the numerical results, the quality of watermarked image is satisfactory and embedded watermark is extracted successfully even if the watermarked image is exposed to various image processing and geometric attacks.

Counteracting geometrical attacks on robust image watermarking by constructing a deformable pyramid transform

Counteracting geometrical attacks remains one of the most challenging problems in robust watermarking. In this paper, we resist rotation, scaling, and translation (RST) by constructing a kind of deformable pyramid transform (DPT) that is shift-invariant, steerable, and scalable. The DPT is extended from a closed-form polar-separable steerable pyramid transform (SPT). The radial component of the SPT's basis filters is taken as the kernel of the scalable basis filters, and the angular component is used for the steerable basis filters. The shift-invariance is inherited from the SPT by retaining undecimated high-pass and band-pass subbands. Based on the designed DPT, we theoretically derive interpolation functions for steerability and scalability and synchronization mechanisms for translation, rotation, and scaling. By exploiting the preferable characteristics of DPT, we develop a new template-based robust image watermarking scheme that is resilient to RST. Translation invariance is achieved by taking the Fourier magnitude of the cover image as the DPT's input. The resilience to rotation and scaling is obtained using the synchronization mechanisms for rotation and scaling, for which an efficient template-matching algorithm has been devised. Extensive simulations show that the proposed scheme is highly robust to geometrical attacks, such as RST, cropping, and row/column line removal, as well as common signal processing attacks such as JPEG compression, additive white Gaussian noise, and median filtering.

Robust digital watermarking in PDTDFB domain based on least squares support vector machine

Geometric distortion is known as one of the most difficult attacks to resist, for it can desynchronize the location of the watermark and hence causes incorrect watermark detection. It is a challenging work to design a robust image watermarking scheme against geometric distortions. Based on the least squares support vector machine (LS-SVM) geometric distortions correction, we propose a new image watermarking scheme in shiftable complex directional pyramid (PDTDFB) domain with good visual quality and reasonable resistance toward geometric distortions in this paper. Firstly, the PDTDFB decomposition is performed on the original host image. Then, the corresponding lowpass subband is divided into small blocks. Finally, the digital watermark is embedded into host image by modulating the selected lowpass PDTDFB coefficients in small blocks. The main steps of digital watermark detecting procedure include: (1) the PDTDFB decomposition is performed on the test images, and some low-order Gaussian–Hermite moment energy of highpass subbands are computed, which are regarded as the effective feature vectors; (2) the appropriate kernel function is selected for training, and a LS-SVM training model can be obtained; (3) the watermarked image is corrected with the well trained LS-SVM model; and (4) the digital watermark is extracted from the corrected watermarked image. Experimental results show that the proposed image watermarking is not only invisible and robust against common image processing operations such as filtering, noise adding, and JPEG compression etc, but also robust against the geometrical distortions.

EGGDD: An explicit dependency model for multi-modal medical image fusion in shift-invariant shearlet transform domain

Most of the traditional medical image fusion methods that use the multi-scale decomposition schemes suffer from the bad image representations and the loss of the dependency in different highpass subbands. To deal with these problems, a novel dependency model, named Explicit Generalized Gaussian Density Dependency (EGGDD) model, is developed by the shift-invariant shearlet transform (SIST). Substantially different from describing the dependency by two hidden states in the Hidden Markov Tree (HMT) model, we provide the scheme to explicitly describe the marginal statistics of each highpass subband using the Generalized Gaussian Density (GGD), as well as the dependency between different subbands by the Kullback–Leibler distance (KLD). After embedding the obtained dependency into each highpass subband, an efficient fusion scheme, inspired by the divisive normalization response in the V1 visual cortex model, is developed to combine the highpass-subband coefficients. The experiments demonstrate that the developed method can produce better fusion results than those of some existing methods by the comparison of visual sense and quantitative measurements in terms of mutual information, entropy, spatial frequency, standard deviation, QAB/F and QW.

A Novel Multifocus Image Fusion Algorithm Based on Nonsubsampled Contourlet Transform

A novel multifocus image fusion algorithm based on NSCT is proposed in this paper. In order to not only attain the image focusing properties and more visual information in the fused image, but also sensitive to the human visual perception, a local multidirection variance (LEOV) fusion rule is proposed for lowpass subband coefficient. In order to introduce more visual saliency, a modified local contrast is defined. In addition, according to the feature of distribution of highpass subband coefficients, a direction vector is proposed to constrain the modified local contrast and construct the new fusion rule for highpass subband coefficients selection The NSCT is a flexible multiscale, multidirection, and shift-invariant tool for image decomposition, which can be implemented via the atrous algorithm. The proposed fusion algorithm based on NSCT not only can prevent artifacts and erroneous from introducing into the fused image, but also can eliminate block effect and frequency aliasing phenomenon. Experimental results show that the proposed method achieved better fusion results than wavelet-based and CT-based fusion method in contrast and clarity.

Image Fusion Based on Nonsubsampled Contourlet Transform and Saliency-Motivated Pulse Coupled Neural Networks

In the nonsubsampled contourlet transform (NSCT) domain, a novel image fusion algorithm based on the visual attention model and pulse coupled neural networks (PCNNs) is proposed. For the fusion of high-pass subbands in NSCT domain, a saliency-motivated PCNN model is proposed. The main idea is that high-pass subband coefficients are combined with their visual saliency maps as input to motivate PCNN. Coefficients with large firing times are employed as the fused high-pass subband coefficients. Low-pass subband coefficients are merged to develop a weighted fusion rule based on firing times of PCNN. The fused image contains abundant detailed contents from source images and preserves effectively the saliency structure while enhancing the image contrast. The algorithm can preserve the completeness and the sharpness of object regions. The fused image is more natural and can satisfy the requirement of human visual system (HVS). Experiments demonstrate that the proposed algorithm yields better performance.

An evident sidelobe control method based on NSCT for ship target in SAR images

Evident sidelobe on faint ship target seriously affects the accuracy of the target segmentation in Synthetic Aperture Radar (SAR) images. To avoid this problem, a novel sidelobe control method based on NonSubsampled Contourlet Transform (NSCT) for ship targets in SAR images is presented in this paper. This method enhances the SAR images in NSCT domain based on target azimuth estimation and then inhibits the sidelobe directionally in NSCT high-pass frequency subbands. Experimental results on RADARSAT-2 images demonstrate that the proposed method can not only reduce the strong sidelobes effectively, but also enhance the intensity of the objects successfully. Therefore, it gives a good segmentation result on the dark ship images with strong sidelobe, and enhances the detection rate on these targets.

可见光偏振图像的自适应融合算法

In consideration of the characteristic of polarization image which can enhance the target identification,a polarization system in visible light and the dual-tree complex wavelet transform(DTCWT) fusion algorithm of polarization image were proposed.In the low-pass sub-band of wavelet coefficients,the fuse rule based window energy was adopted,and in the high-pass sub-band,the rule of spatial frequency self-adaption weighted at window was selected.The setting of autocorrelation and the application of simulated annealing algorithm improved the robustness and adaptability of fusion.The results show that the fused image has good subjective quality and objective evaluation of performance which will enhance the target and background contrast.

Bayesian texture classification and retrieval based on multiscale feature vector

This paper proposes a supervised multiscale Bayesian texture classifier. The classifier exploits the dual-tree complex wavelet transform (DT-CWT) to obtain complex-valued multiscale representations of training texture samples for each texture class. The high-pass subbands of DT-CWT decomposition of a texture image are used to form a multiscale feature vector representing magnitude and phase features. For computational efficiency, the dimensionality of feature vectors is reduced using principal component analysis (PCA). The class conditional probability density function of low-dimensional feature vectors for each texture class is then estimated by using Parzen-window estimate with identical Gaussian kernels and is used to represent the texture class. A query texture image is classified as the corresponding texture class with the highest a posteriori probability according to a Bayesian inferencing. The superior performance and robustness of the proposed classifier is demonstrated for classifying texture images from image databases. The proposed multiscale texture feature vector extracted from both magnitude and phase of DT-CWT subbands of a query image is also shown to be effective for texture retrieval.

A Novel Multi-Focus Image Fusion Method Using Shearlet Transform

According to the different frequency areas decomposed by shearlet transform, the selection principles of the lowpass subbands and highpass subbands were discussed respectively. The lowpass subband coefficients of the fused image can be obtained by means of the fusion rule based on the region variation, the highpass subband coefficients can be selected by means of the fusion rule based on the region energy. Experimental results show that comparing with traditional image fusion algorithms, the proposed approach can provide more satisfactory fusion outcome.

Unsupervised Change Detection for Satellite Images Using Dual-Tree Complex Wavelet Transform

In this paper, an unsupervised change-detection method for multitemporal satellite images is proposed. The algorithm exploits the inherent multiscale structure of the dual-tree complex wavelet transform (DT-CWT) to individually decompose each input image into one low-pass subband and six directional high-pass subbands at each scale. To avoid illumination variation issue possibly incurred in the low-pass subband, only the DT-CWT coefficient difference resulted from the six high-pass subbands of the two satellite images under comparison is analyzed in order to decide whether each subband pixel intensity has incurred a change. Such a binary decision is based on an unsupervised thresholding derived from a mixture statistical model, with a goal of minimizing the total error probability of change detection. The binary change-detection mask is thus formed for each subband, and all the produced subband masks are merged by using both the intrascale fusion and the interscale fusion to yield the final change-detection mask. For conducting the performance evaluation of change detection, the proposed DT-CWT-based unsupervised change-detection method is exploited for both the noise-free and the noisy images. Extensive simulation results clearly show that the proposed algorithm not only consistently provides more accurate detection of small changes but also demonstrates attractive robustness against noise interference under various noise types and noise levels.

一种基于方向窗特性的Contourlet域的多聚焦图像融合算法

Utilizing the contourlet's advantages of multiscale,localization,directionality and anisotropy,a multifocus image fusion algorithm based on directional windows statistics in contourlet domain is developed.Source images are firstly decomposed to the domain of the contourlet transform,then the image fusion is implemented in subbands with different scale and direction combining with region statistics.Regional variance and local energy are adopted as fusion rules in lowpass and highpass subbands,respectively.And the fused image is obtained through inverse transform.Compared to traditional gradient pyramid algorithm and wavelet based algorithm,experimental results show that the directional windows method can detect image features more effectively and the fused image has better subjective visual effect.

Rate Distortion Analysis and Bit Allocation Scheme for Wavelet Lifting-Based Multiview Image Coding

This paper studies the distortion and the model-based bit allocation scheme of wavelet lifting-based multiview image coding. Redundancies among image views are removed by disparity-compensated wavelet lifting (DCWL). The distortion prediction of the low-pass and high-pass subbands of each image view from the DCWL process is analyzed. The derived distortion is used with different rate distortion models in the bit allocation of multiview images. Rate distortion models including power model, exponential model, and the proposed combining the power and exponential models are studied. The proposed rate distortion model exploits the accuracy of both power and exponential models in a wide range of target bit rates. Then, low-pass and high-pass subbands are compressed by SPIHT (Set Partitioning in Hierarchical Trees) with a bit allocation solution. We verify the derived distortion and the bit allocation with several sets of multiview images. The results show that the bit allocation solution based on the derived distortion and our bit allocation scheme provide closer results to those of the exhaustive search method in both allocated bits and peak-signal-to-noise ratio (PSNR). It also outperforms the uniform bit allocation and uniform bit allocation with normalized energy in the order of 1.7-2 and 0.3-1.4 dB, respectively.

Multimodality medical image fusion based on multiscale geometric analysis of contourlet transform

As a novel multiscale geometric analysis tool, contourlet has shown many advantages over the conventional image representation methods. In this paper, a new fusion algorithm for multimodal medical images based on contourlet transform is proposed. All fusion operations are performed in contourlet domain. A novel contourlet contrast measurement is developed, which is proved to be more suitable for human vision system. Other fusion rules like local energy, weighted average and selection are combined with “region” idea for coefficient selection in the lowpass and highpass subbands, which can preserve more details in source images and further improve the quality of fused image. The final fusion image is obtained by directly applying inverse contourlet transform to the fused lowpass and highpass subbands. Extensive fusion experiments have been made on three groups of multimodality CT/MR dataset, both visual and quantitative analysis show that comparing with conventional image fusion algorithms, the proposed approach can provide a more satisfactory fusion outcome.

A Cross-Resolution Leaky Prediction Scheme for In-Band Wavelet Video Coding With Spatial Scalability

In most existing in-band wavelet video coding schemes, over-complete wavelet transform is used for the motion-compensated temporal filtering (MCTF) of each spatial subband. It can overcome the shift-variance of critical sampling wavelet transform and improve the coding efficiency of the in-band scheme. However, a dilemma exists in the current implementations of in-band MCTF (IBMCTF), which is whether or not to exploit the spatial highpass subbands in motion compensation of the spatial lowpass subband. The absence of the spatial highpass subbands will result in significant quality loss in the reconstructed full-resolution video, whereas the presence of the spatial highpass subbands may bring serious mismatch error in the decoded low-resolution video since the corresponding highpass subbands may be unavailable at the decoder. In this paper, we first analyze the mismatch error propagation in decoding the low-resolution video. Based on our analysis, we then propose a frame-based cross-resolution leaky prediction scheme for IBMCTF. It can make a good tradeoff between alleviating the low-resolution mismatch and improving the full-resolution coding efficiency. Experimental results show that the proposed scheme can dramatically reduce the mismatch error by 0.3-2.5 dB for low resolution, while the performance loss is marginal for high resolution.

Breast volume denoising and noise characterization by 3D wavelet transform

Breast imaging through cone-beam computed tomography provides a digital breast volume, with which the three-dimensional (3D) breast tissues can be analyzed. Data denoising, as a preprocessing step for subsequent volumetric breast segmentation is always needed. In this paper, we report a volumetric denoising technique by a separable 3D wavelet transform (WT), i.e. a ‘2D WT plus 1D WT’ scheme. Specifically, the scheme performs two-dimensional (2D) wavelet denoising on a stack of slice images of the breast volume, followed by one-dimensional (1D) wavelet denoising along the stacking direction. The denoising is achieved by wavelet decomposition, high-pass subband attenuation, and wavelet synthesis. A one-level 3D WT produces eight subbands occupying the octants of the 3D wavelet space. Multilevel WT also provides a multiresolution representation of breast volume, i.e. a sequence of low-pass subbands. In general, most noise and irregularity features are imparted into the high-pass subbands, which are removed or reduced for denoising purpose. Meanwhile, the information in a subband can be characterized in terms of energy, variance, and entropy. Through 3D visualization, the spatial structure in a subband can also be visually perceived. Experimental demonstration with the breast volume reconstructed from a specimen is provided.