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Medical image fusion is the process of deriving vital information from multimodality medical images. Some important applications of image fusion are medical imaging, remote control sensing, personal computer vision and robotics. For medical diagnosis, computerized tomography (CT) gives the best information about denser tissue with a lesser amount of distortion and magnetic resonance image (MRI) gives the better information on soft tissue with little higher distortion. The main scheme is to combine CT and MRI images for getting most significant information. The need is to focus on less power consumption and less occupational area in the implementations of the applications involving image fusion using discrete wavelet transform (DWT). To design the DWT processor with low power and area, a low power multiplier and shifter are incorporated in the hardware. This low power DWT improves the spatial resolution of fused image and also preserve the color appearance. Also, the adaptation of the lifting scheme in the 2D DWT process further improves the power reduction. In order to implement this 2D DWT processor in field-programmable gate array (FPGA) architecture as a very large scale integration (VLSI)-based design, the process is simulated with Xilinx 14.1 tools and also using MATLAB. When comparing the performance of this low power DWT and other available methods, this high performance processor has 24%, 54% and 53% of improvements on the parameters like standard deviation (SD), root mean square error (RMSE) and entropy. Thus, we are obtaining a low power, low area and good performance FPGA architecture suited for VLSI, for extracting the needed information from multimodality medical images with image fusion.

In the field of medical diagnostics, interested parties have resorted increasingly to medical imaging. It is well established that the accuracy and completeness of diagnosis are initially connected with the image quality, but the quality of the image is itself dependent on a number of factors including primarily the processing that an image must undergo to enhance its quality. The quality evaluation of compressed image is necessary to judge the performance of a compression method. This paper introduces an algorithm for medical image compression based on hybrid nonsubsampled contourlet (NSCT) and quincunx wavelet transforms (QWT) coupled with set partitioning in hierarchical trees (SPIHT) coding algorithm, of which we present the objective measurements (PSNR, EDGE, WPSNR, MSSIM, VIF, and WSNR) in order to evaluate the quality of the image.

We investigate the lifting scheme as a method for constructing compactly supported biorthogonal scaling functions and wavelets. A well-known issue arising with the use of this scheme is that the resulting functions are only formally biorthogonal. It is not guaranteed that the new wavelet bases actually exist in an acceptable sense. To verify that these bases do exist one must test an associated linear operator to ensure that it has a simple eigenvalue at one and that all its remaining eigenvalues have modulus less than one, a task which becomes numerically intensive if undertaken repeatedly. We simplify this verification procedure in two ways: (i) we show that one need only test an identifiable half of the eigenvalues of the operator, (ii) we show that when the operator depends upon a single parameter, the test first fails for values of that parameter at which the eigenvalue at one becomes a multiple eigenvalue. We propose that this new verification procedure comprises a first step towards determining simple conditions, supplementary to the lifting scheme, to ensure existence of the new wavelets generated by the scheme and develop an algorithm to this effect.

In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are prefered. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang.² A characteristic feature of this class of wavelets is that the support of the corresponding filter comprises only two rows. We are concerned with the biorthogonal extension of this kind of wavelets. It turns out that the 2D wavelets in this class are intimately related to some underlying 1D wavelet. We explore this relation in detail, and we explain how the 2D wavelet transforms can be realized by means of a lifting scheme, thus allowing an efficient implementation. We also describe an easy way to construct wavelets with more rows and shorter columns.

Classical linear wavelet representations of images have the drawback that they are not optimally suited to represent edge information. To overcome this problem, nonlinear multiresolution decompositions have been designed to take into account the characteristics of the input signal/image. In our previous work^20,22,23 we have introduced an adaptive lifting framework, that does not require bookkeeping but has the property that it processes edges and homogeneous image regions in a different fashion. The current paper discusses the effects of quantization in such an adaptive wavelet decomposition. We provide conditions for recovering the original decisions at the synthesis and for relating the reconstruction error to the quantization error. Such an analysis is essential for the application of these adaptive decompositions in image compression.

The dyadic lifting schemes, which generalize Sweldens lifting schemes, have been proposed for custom-design of dyadic and bi-orthogonal wavelets and their duals. Starting with dyadic wavelets and exploiting the control provided in the form of free parameters, one can custom-design dyadic as well as bi-orthogonal wavelets adapted to a particular application. To validate the usefulness of the schemes, two construction methods have been proposed for designing dyadic wavelet filters with higher number of vanishing moments; using these design techniques, spline dyadic wavelet filters have been custom-designed for denoising of digital images, which exhibit enhanced denoising effects.

In recent years, image coding based on wavelet transform has made rapid progress. In this paper, quincunx lifting scheme in wavelet transform is introduced and all phase interpolation filter banks which can be used in the lifting scheme for prediction and update are designed. Based on the basic idea of set partitioning in hierarchical trees (SPIHT) algorithm, the binary tree image coding algorithm is proposed. Just like SPIHT, the encoding algorithms can be stopped at any compressed file size or let run until the compressed file is a representation of a nearly lossless image. The experimental results on test images show that compared with SPIHT algorithm, the PSNRs of the proposed algorithm are superior by about 0.5 dB at the same bit rates and the subjective quality of reconstructed images is also better.

In this paper, we present an efficient biorthogonal wavelet construction for the ternary Loop subdivision based on the lifting scheme, and give the corresponding decomposition and reconstruction formulas. We apply the proposed algorithm to the progressive transmission and the denoising of 3D graphics, and show its sufficient stability and good performance by some numerical experiments. Since the usual input mesh does not possess the property of subdivision connectivity, while the multiresolution analysis based on subdivision surface requires the processed initial mesh to be semi-regular, we further propose a new rapid algorithm of constructing the initial mesh which not only possesses ternary subdivision connectivity but also approximates the given input mesh.

Partial differential equation (PDE) occurs in the mathematical modeling of many physical phenomena arising in science and engineering. In this paper, we present wavelet-based lifting scheme for the numerical solution of nonlinear PDEs using different wavelet filter coefficients. The numerical results obtained by this scheme are compared with the exact solution to demonstrate the accuracy and also speeds up convergence in lesser computational time as compared with the existing schemes. Some test problems are presented for the validity and applicability of the scheme.

Graves’ disease is a common condition that is diagnosed clinically by determining the smoothness of the thyroid texture and its morphology in ultrasound images. Currently, the most widely used approach for the automated diagnosis of Graves’ disease utilizes Convolutional Neural Networks (CNNs) for both feature extraction and classification. However, these methods demonstrate limited efficacy in capturing texture features. Given the high capacity of wavelets in describing texture features, this research integrates learnable wavelet modules utilizing the Lifting Scheme into CNNs and incorporates a parallel wavelet branch into the ResNet18 model to enhance texture feature extraction. Our model can analyze texture features in spatial and frequency domains simultaneously, leading to optimized classification accuracy. We conducted experiments on collected ultrasound datasets and publicly available natural image texture datasets, our proposed network achieved 97.27% accuracy and 95.60% recall on ultrasound datasets, 60.765% accuracy on natural image texture datasets, surpassing the accuracy of ResNet and confirming the effectiveness of our approach.

Recently, wavelet theory has become a well recognized promising tool in science and engineering field; especially, wavelets are successfully used in fast algorithms for easy execution. In this paper, we developed wavelet lifting scheme using orthogonal and biorthogonal wavelets for the numerical solution of dynamic Reynolds equation for micropolar fluid lubrication. The numerical results gained through proposed scheme are compared with the exact solution to expose the accuracy with speed of convergence in lesser computational time as compared with the existing methods. The examples are given to demonstrate the applicability and attractiveness of proposed method.

The paper proposes a lifting scheme-based wavelet transform clustering method as a better alternative to traditional alignment-based virus genome classification and grouping techniques. The efficiency of the proposed alignment-free algorithm have been tested using Coronavirus datasets obtained from NCBI database, against established results from proven techniques. In the proposed approach, the nucleotide sequences are converted into numerical ones leveraging purine–pyrimidine mapping and a DNA walk is calculated to visually interpret them. Second-generation wavelet transform employing Cohen–Daubechies–Feauveau wavelet is applied to the numerical sequences of Coronavirus to determine the approximate coefficients. Approximate coefficients are used to cluster Coronavirus sequences using UPGMA phylogenetic tree for three different datasets of Coronaviruses comprising Coronavirus groups, Human Coronaviruses (HCoVs) and $\alpha$–$\beta$–$\delta$–$\gamma$ Coronavirus genre. The proposed algorithm has successfully classified all the datasets with more than 97% of average accuracy compared in terms of complexity and accuracy against FFT, first-generation DWT, MEGA, and CLUSTAL-W. The obtained accuracy for Corona group is 100%, HCoV dataset is 100%, and for $\alpha$–$\beta$–$\delta$–$\gamma$ CoV is 92%. The runtimes of the algorithm are 0.70, 1.22, and 0.63 sec for the respective Coronavirus datasets.

The lifting scheme provides a new ideal for constructing multiwavelets. Through the introduction and discussion of constructing wavelets and multiwavelets with lifting scheme. A new constructing multiwavelets method with lifting scheme based on equivalent scalar filter bank is proposed in the paper, and the example has proved its feasibility.

Lifting scheme is not only a fast algorithm of existing wavelet transforms, but also a tool to produce new wavelet transforms. According to the characteristic of the lifting scheme and the 9-7 wavelet, we present a new constructing of simple rational coefficient filters for lifting 9-7 wavelets in this paper. The new lifting wavelets reduce its float and integer operations, and applied the new lifting 9-7 wavelet filters to image compression, we have achieved better results.

The lifting scheme based on spatial domain has been widely used in the digital image processing that its computes fast and simple, and it is calculated for the reversible from integer to integer wavelet transform. According to M-channels wavelet transform theory and the signal being subdivided, it is carried out the lifting to M-channels wavelet transform, and a new fast algorithm of M-channels lifting wavelet transform is presented in this paper. The algorithm is easy to compare with the traditional wavelet transform that it has only the decomposed algorithm, the composed algorithm is given. However, integer to integer wavelet transform can be achieved when the operation result is taken the proximal integer. The algorithm is used to image processing. The experiment result shows the algorithm is very useful for image compression.