Multi-resolution Analysis Tool Research Articles

When Ramanujan sums meet affine Fourier transform

Ramanujan Fourier transform is one of the efficient multiresolution analysis tools, but it only works for stationary or periodically characterized signals. Affine Fourier transform, a general form of Fourier transform, is suitable for nonstationary signal analysis but with fixed resolution. In this study, the Ramanujan sums are combined with the affine Fourier transform to provide affine multiresolution analysis tools for nonstationary signals. First, affine Ramanujan sums are proposed and their main properties are introduced, based on which the affine Ramanujan Fourier transform (ARFT) for infinite sequences is proposed. Then, the first type ARFT (ARFT-I) for finite sequences is obtained by truncating the ARFT. Meanwhile, the transform matrix of ARFT-I is not orthogonal in general. Thus, the affine Ramanujan subspaces are constructed by affine Ramanujan sums and their canonical circular time shifts, among which different subspaces are orthogonal. Subsequently, the second type ARFT (ARFT-II) for finite sequences is developed, where the transform matrix is block orthogonal. Independent variables of ARFTs are chirp periods, which provides novel and direct methods to estimate (hidden) chirp periods. Different simulations, such as radar moving target detection and velocity estimation, are designed to show superior performance of ARFTs than affine Fourier transform based algorithms.

Power Quality Disturbance Recognition Using Empirical Wavelet Transform and Feature Selection

With the growth of nonlinear electrical equipment, power quality disturbances (PQDs) often appear in electrical systems. To solve this, a practical heuristic methodology for PQD detection and classification based on empirical wavelet transform has been proposed. By using a multiresolution analysis tool, empirical wavelet transform, the voltage waveform signal is decomposed into several sub-signals, and some potential features are extracted in the statistical method. To reduce the feature vector dimensions, the ReliefF algorithm is used for feature selection and optimized for dimensionality reduction, which reduces the complexity of system calculation while ensuring accuracy. Finally, a classifier based on support vector machines (SVM) was built, and with the ranked feature vectors’ input, the PQD can be recognized. The experimental results verify that the classification results achieved high accuracy, which confirms the properties and robustness of the proposed approach in noisy environments.

The Empirical Watershed Wavelet.

The empirical wavelet transform is an adaptive multi-resolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the detected partitioning. In this paper, we provide theoretical results that permits us to build 2D empirical wavelet filters based on an arbitrary partitioning of the frequency domain. We also propose an algorithm to detect such partitioning from an image spectrum by combining a scale-space representation to estimate the position of dominant harmonic modes and a watershed transform to find the boundaries of the different supports making the expected partition. This whole process allows us to define the empirical watershed wavelet transform. We illustrate the effectiveness and the advantages of such adaptive transform, first visually on toy images, and next on both unsupervised texture segmentation and image deconvolution applications.

IWave: CNN-Based Wavelet-Like Transform for Image Compression

Wavelet transform is a powerful tool for multiresolution time-frequency analysis. It has been widely adopted in many image processing tasks, such as denoising, enhancement, fusion, and especially compression. Wavelets lead to the successful image coding standard JPEG-2000. Traditionally, wavelets were designed from the signal processing theory with certain assumption on the signal, but natural images are not as ideal as assumed by the theory. How to design content-adaptive wavelets for natural images remains a difficulty. Inspired by the recent progress of convolutional neural network (CNN), we propose iWave as a framework for deriving wavelet-like transform that is more suitable for natural image compression. iWave adopts an update-first lifting scheme, where the prediction filter is a trained CNN, to achieve wavelet-like transform. The CNN can be embedded into a deep network that is analogous to an auto-encoder, which is trained end-to-end. The trained wavelet-like transform still possesses the lifting structure, which ensures perfect reconstruction, supports multiresolution analysis, and is more interpretable than the deep networks trained as “black boxes.” We perform experiments to verify the generality as well as the speciality of iWave in comparison with JPEG-2000. When trained with a generic set of natural images and tested on the Kodak dataset, iWave achieves on average 4.4% and up to 14% BD-rate reductions. When trained and tested with a specific kind of textures, iWave provides as high as 27% BD-rate reduction.

Image Restoration for the MRA-Based Pansharpening Method

By merging high-resolution panchromatic (PAN) images with low-resolution multispectral (MS) images, high-resolution MS images with complementary information can be obtained, i.e., pansharpening. Multiresolution analysis (MRA) methods have attracted widespread attention in the pansharpening field. The spatial detail information injected into MS images is extracted from PAN images by MRA tools. Since such methods often suffer from spatial distortion and ringing artifacts, a restoration algorithm based on blind deblurring and iterative back-projection (IBP) is proposed in this paper. First, a blind deblurring method based on the Tikhonov regular constraint model is used to estimate the blurring filter. Second, spatial details extracted from PAN images are modulated into MS images using a high-pass modulation (HPM) framework, and then fusion images are spatially enhanced based on the modulation results and blurring filter. Finally, the IBP technique is used to project the reconstruction error back to iteratively update and optimize the desired high-resolution images. Experiments are performed on data sets acquired by different satellites at full and reduced resolution, and eight state-of-the-art MRA-based pansharpening methods are used for validation. Compared to the enhanced back-projection (EBP) algorithm, the proposed restoration method is better in improving spectral and spatial quality of MRA-based pansharpening. The results indicate the effectiveness and superiority of the proposed method.

A Review of Multi-resolution Analysis (MRA) and Multi-geometric Analysis (MGA) Tools Used in the Fusion of Remote Sensing Images

The availability of multi-sensor and multi-resolution images obtained through earth observation satellites has given rise to a greater need for fusion technology. Fusion can provide comprehensive information about a particular scene or area by bringing the information of two or more images into a single plane. The technique has been in use for the past three decades, and several methodologies have been introduced in the literature. However, with the invention of new sensors and technology, the number of challenges has increased. While several review and survey papers have explored different aspects of fusion, this paper provides a comprehensive discussion of the tools available and the implications of their use for the fusion of remote sensing images. Tools based on multi-resolution analysis (MRA) and multi-geometric analysis (MGA) are widely used in the field of image fusion. We provide a detailed study of MRA- and MGA-based tools, their effectiveness, and the impacts of the corresponding fusion schema in retaining the desired information.

Tight framelets and fast framelet filter bank transforms on manifolds

Tight framelets on a smooth and compact Riemannian manifold $\mathcal{M}$ provide a tool of multiresolution analysis for data from geosciences, astrophysics, medical sciences, etc. This work investigates the construction, characterizations, and applications of tight framelets on such a manifold $\mathcal{M}$. Characterizations of the tightness of a sequence of framelet systems for $L_{2}(\mathcal{M})$ in both the continuous and semi-discrete settings are provided. Tight framelets associated with framelet filter banks on $\mathcal{M}$ can then be easily designed and fast framelet filter bank transforms on $\mathcal{M}$ are shown to be realizable with nearly linear computational complexity. Explicit construction of tight framelets on the sphere $\mathbb{S}^{2}$ as well as numerical examples are given.

Fabric defect detection using Discrete Curvelet Transform

With the increasing client demand for cloth selection in the fashion market, fabric texture becomes far more numerous, that brings nice challenges to correct fabric discover detection. A comparative study of the GLCM-based, wavelet-based additionally the curvelet-based techniques has also been enclosed. The high accuracy achieved by the planned technique suggests an economical resolution for fabric defect. Note that, this study is that the initial documented arrange to explore the probabilities of a brand new multiresolution analysis tool referred to as digital curvelet transform to deal with the matter of material defect. The recognizer acquires digital fabric pictures by image acquisition device and converts that image into the binary image using "Discrete Curvelet Transform". The proposed algorithmic rule is simulated in MATLAB. The performance of the proposed defect detection model was evaluated through in-depth experiments with varied kinds of real fabric samples. The planned detection model was tried to be effective and be superior to some representative detection models in terms of the detection accuracy and false alarm.

A Multiresolution Graphical Representation for Similarity Relationship and Multiresolution Clustering for Biological Sequences.

How we can describe the similarity relationship between the biological sequences is a basic but important problem in bioinformatics. The first graphical representation method for the similarity relationship rather than for single sequence is proposed in this article, which makes the similarity intuitional. Some properties such as sensitivity and continuity of the similarity are proved theoretically, which indicate that the similarity describer has the advantage of both alignment and alignment-free methods. With the aid of multiresolution analysis tools, we can exhibit the similarity's different profiles, from high resolution to low resolution. Then the idea of multiresolution clustering is raised first. A reassortment analysis on a benchmark flu virus genome data set is to test our method and it shows a better performance than alignment method, especially in dealing with problems involving segments' order.

Investigation of alterations in multifractality in optical coherence tomographic images of in vivo human retina.

Optical coherence tomography (OCT) enables us to monitor alterations in the thickness of the retinal layer as disease progresses in the human retina. However, subtle morphological changes in the retinal layers due to early disease progression often may not lead to detectable alterations in the thickness. OCT images encode depth-dependent backscattered intensity distribution arising due to the depth distributions of the refractive index from tissue microstructures. Here, such depth-resolved refractive index variations of different retinal layers were analyzed using multifractal detrended fluctuation analysis, a special class of multiresolution analysis tools. The analysis extracted and quantified microstructural multifractal information encoded in normal as well as diseased human retinal OCT images acquired <italic<in vivo</italic<. Interestingly, different layers of the retina exhibited different degrees of multifractality in a particular retina, and the individual layers displayed consistent multifractal trends in healthy retinas of different human subjects. In the retinal layers of diabetic macular edema (DME) subjects, the change in multifractality manifested prominently near the boundary of the DME as compared to the normal retinal layers. The demonstrated ability to quantify depth-resolved information on multifractality encoded in OCT images appears promising for the early diagnosis of diseases of the human eye, which may also prove useful for detecting other types of tissue abnormalities from OCT images.

Comparison of various texture classification methods using multiresolution analysis and linear regression modelling.

Textures play an important role in image classification. This paper proposes a high performance texture classification method using a combination of multiresolution analysis tool and linear regression modelling by channel elimination. The correlation between different frequency regions has been validated as a sort of effective texture characteristic. This method is motivated by the observation that there exists a distinctive correlation between the image samples belonging to the same kind of texture, at different frequency regions obtained by a wavelet transform. Experimentally, it is observed that this correlation differs across textures. The linear regression modelling is employed to analyze this correlation and extract texture features that characterize the samples. Our method considers not only the frequency regions but also the correlation between these regions. This paper primarily focuses on applying the Dual Tree Complex Wavelet Packet Transform and the Linear Regression model for classification of the obtained texture features. Additionally the paper also presents a comparative assessment of the classification results obtained from the above method with two more types of wavelet transform methods namely the Discrete Wavelet Transform and the Discrete Wavelet Packet Transform.

Fusion technique for multi-focus images based on NSCT–ISCM

The issue of fusing multi-focus images is meaningful and undoubtedly suitable for visual effects and further image processing tasks. In this study, a novel multi-focus image fusion technique based on non-subsampled contourlet transform (NSCT) and improved spiking cortical model (ISCM) is presented. Compared with the current multi-resolution geometric analysis (MRGA) tools, NSCT not only has much better competences of information capturing and feature extracting, but also overcomes the drawback of shift-invariance lacking from which the contourlet transform suffers. As a recently developed biological model, SCM combines the advantages of both pulse coupled neural network (PCNN) and intersecting cortical model (ICM), and has been considered to be an optimal neuron network model recently. The proposed technique is composed of three main phases. Firstly, by using NSCT, each source image is decomposed into a low-frequency sub-image and a series of high-frequency sub-images in different directions. Then, the classic SCM is improved to be ISCM with a less complex structure and much more effective function mechanism, which is responsible for obtaining the fused sub-images. Finally, inverse NSCT is utilized to reconstruct the final fused image. The NSCT–ISCM based fusion algorithm is devised. Experimental results indicate that the proposed technique is superior to other current popular ones in both aspects of subjective visual and objective performance.

Technique for infrared and visible image fusion based on non-subsampled shearlet transform and spiking cortical model

Fusion of infrared and visible images is an active research area in image processing, and a variety of relevant algorithms have been developed. However, the existing techniques commonly cannot gain good fusion performance and acceptable computational complexity simultaneously. This paper proposes a novel image fusion approach that integrates the non-subsampled shearlet transform (NSST) with spiking cortical model (SCM) to overcome the above drawbacks. On the one hand, using NSST to conduct the decompositions and reconstruction not only consists with human vision characteristics, but also effectively decreases the computational complexity compared with the current popular multi-resolution analysis tools such as non-subsampled contourlet transform (NSCT). On the other hand, SCM, which has been considered to be an optimal neuron network model recently, is responsible for the fusion of sub-images from different scales and directions. Experimental results indicate that the proposed method is promising, and it does significantly improve the fusion quality in both aspects of subjective visual performance and objective comparisons compared with other current popular ones.

Medical image fusion using optimal feature selection methods based on second generation contourlet transform

As a novel of multi-resolution analysis tool, second generation contourlet transform SGCT provides flexible multiresolution, anisotropy, and directional expansion for medical imaging systems. In this paper, a novel fusion method for multimodal medical images based on SGCT is proposed. Firstly, we utilise the SGCT to decompose the multimodal medical images with highpass subbands and lowpass subbands. Then, for the highpass subbands, the weighted sum modified Laplacian WSML method is utilised to generate the high frequency coefficients to recovery image details. For the lowpass subbands, the maximum local energy MLE method is combined with 'local patch' idea for low frequency coefficients selection. Finally, the fused image is obtained by applying inverse SGCT to combine lowpass and highpass subbands. During abundant experiments, we evaluate the proposed method both human visual and quantitative analysis. Compare with the-state-of-the-art methods, the new strategy for attaining image fusion with satisfactory performance.

Treelets Binary Feature Retrieval for Fast Keypoint Recognition.

Fast keypoint recognition is essential to many vision tasks. In contrast to the classification-based approaches, we directly formulate the keypoint recognition as an image patch retrieval problem, which enjoys the merit of finding the matched keypoint and its pose simultaneously. To effectively extract the binary features from each patch surrounding the keypoint, we make use of treelets transform that can group the highly correlated data together and reduce the noise through the local analysis. Treelets is a multiresolution analysis tool, which provides an orthogonal basis to reflect the geometry of the noise-free data. To facilitate the real-world applications, we have proposed two novel approaches. One is the convolutional treelets that capture the image patch information locally and globally while reducing the computational cost. The other is the higher-order treelets that reflect the relationship between the rows and columns within image patch. An efficient sub-signature-based locality sensitive hashing scheme is employed for fast approximate nearest neighbor search in patch retrieval. Experimental evaluations on both synthetic data and the real-world Oxford dataset have shown that our proposed treelets binary feature retrieval methods outperform the state-of-the-art feature descriptors and classification-based approaches.

Image Fusion Algorithm Based on Contourlet Transform

Contourlet transform is a new multi-scale, multi-resolution analysis tool. This paper studied on the theory of Contourlet transform.,According to the practical application requirements of characteristics of data, much details in complex images it propose a novel image fusion method of remote sensing images based on contourlet Coefficients correlativity of directional region. Besides improving fused images spatial resolution, our method can better preserve original multi-spectral image’s color information.Extensive experimental results show that the proposed method is superior to conventional methods in terms of entropy, joint entropy, and average gradient. It can enhance the spatial resolution of target images. Meanwhile, it well preserves the color information of multi-spectral images.

ANFIS AND NEURAL NETWORK BASED FACIAL EXPRESSION RECOGNITION USING CURVELET FEATURES

Curvelet transform is a promising tool for multi-resolution analysis on images. This paper explains a new approach for facial expression recognition based on curvelet features extracted using curvelet transform. Curvelet transform is applied on the database images and curvelet coefficients are obtained for selected scale for image analysis. Facial curvelet features are compressed using singular value decomposition (SVD) approach. Back propagation neural network (BPNN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) are used as classifiers for classifying expressions into one of the seven categories like angry, disgust, fear, happy, neutral, sad and surprise. Experimentation is carried out on JAFFE database. The experimental results show that the novel approach is a better option for extracting feature values and classifying facial expressions.

Face recognition based on curvelets and local binary pattern features via using local property preservation

In this paper, we propose a new feature extraction approach for face recognition based on Curvelet transform and local binary pattern operator. The motivation of this approach is based on two observations. One is that Curvelet transform is a new anisotropic multi-resolution analysis tool, which can effectively represent image edge discontinuities; the other is that local binary pattern operator is one of the best current texture descriptors for face images. As the curvelet features in different frequency bands represent different information of the original image, we extract such features using different methods for different frequency bands. Technically, the lowest frequency band component is processed using the local binary pattern method, and only the medium frequency band components are normalized. And then, we combine them to create a feature set, and use the local preservation projection to reduce its dimension. Finally, we classify the test samples using the nearest neighbor classifier in the reduced space. Extensive experiments on the Yale database, the extended Yale B database, the PIE pose 09 database, and the FRGC database illustrate the effectiveness of the proposed method.

Novel fusion method for visible light and infrared images based on NSST–SF–PCNN

The purpose of image fusion is to combine the source images of the same scene into a single composite image with more useful information and much better visual effects, which is undoubtedly suitable for further image processing tasks. This paper presented a novel fusion method for visible light and infrared images based on non-subsampled shearlet transform (NSST)–spatial frequency (SF)–pulse coupled neural network (PCNN). As a recently developed multi-resolution geometric analysis tool, NSST not only has remarked superiorities over other past conventional tools in terms of information capturing and computational costs saving, but also overcomes the lack of shift-invariance in shearlet transform (ST), so NSST applies to conducting the decompositions and reconstructions. Besides, traditional PCNN model is also upgraded to be an improved one called IPCNN in this paper to fuse the low-frequency and high-frequency subband coefficients. In the IPCNN structure, on the one hand, the value of the linking strength β is determined by the SF which represents the gradient features of the subband image; on the other hand, the time matrix is utilized to adaptively decide the iteration number of the IPCNN model, which is helpful to increase the function efficiency and save computational resources. Experimental results indicate that the proposed method performs well and has obvious superiorities over other current typical ones in both subjective visual performance and objective criteria.

Multi-focus image fusion algorithm based on compound PCNN in Surfacelet domain

In order to effectively retain details and suppress noise, a multi-focus image fusion method based on Surfacelet transform and compound PCNN is proposed. Surfacelet transform is a powerful multi-resolution analysis tool which is able to decompose the original image into a number of different frequency band sub-images, compound PCNN model is a combined model of PCNN and dual-channel PCNN which is to select the fusion coefficients from the decomposed coefficients, the Local sum-modified-Laplacian (LSML) is selected as external stimulus of compound PCNN, fusion coefficients are decided by compound PCNN. The experimental results show that the new method has a good performance, fusion image has more texture details and it is more similar to the original images, the objective evaluation indexes show that this method is superior to the traditional image fusion methods.