International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we describe a method for removing Gaussian noise from digital images, based on edge detection and prethresholding Wiener filtering of multi-wavelets fusion. First, we decompose the noisy image by using multiple wavelets, then the edge of image is detected via wavelet multi-scale edge detection. On this basis, the wavelet coefficients belonging to the edge position are dealt with the improved wavelet threshold method and the others are dealt with the prethresholding Wiener filtering. Finally, we use the fusion algorithm based on wavelet analysis to obtain the denoised image. The experimental results show that this method not only can remove the noise without blurring the edges and the important characteristics of the images effectively, but also can highlight the characteristics of image edge compared with the existing methods. The denoised images have higher peak signal to noise ratio (PSNR) and mean structural similarity (MSSIM), hence the method is of great application value.

In this paper, the sufficient condition for the integrability of the kernel of the inverse Bessel wavelet transform is obtained by using the theory of Hankel transform and Hankel convolution.

This paper describes a study on evaluation of mental stress using adaptive wavelet packets filtering techniques. For mental stress to become chronic or if it remains for longer periods of time, then it can cause or trigger diseases such as hypertension, diabetes, insomnia, depression etc. There is a need for objective assessment of stress and develop counter conditions to relieve the body from stress. We have designed a wireless wearable sensor platform that can be used to capture a vast range of biomedical signals including heart rate, skin conductance and respiration rates. As stress is a reactionary phenomenon and its response vary from person to person, so an adaptive wavelet filtering packet is proposed to minimize intra subjective variations. The filtering technique has two folded effects; it reduces the classification error and it provides tuning to adapt it to users requirements. The wearable sensor platform is based on ease of use and a subject can be monitored for days and changes in his/her physiological conditions are recorded. The main advantage in monitoring stress is that if required in needs than necessary actions can be taken to remove stressful conditions.

For a dyadic wavelet set W, Ionascu [A new construction of wavelet sets, Real Anal. Exchange28 (2002) 593–610] obtained a measurable self-bijection on the interval [0, 1), called the wavelet induced isomorphism of [0, 1), denoted by . Extending the result for a d-dilation wavelet set, we characterize a joint (d, -d)-dilation wavelet set, where |d| is an integer greater than 1, in terms of wavelet induced isomorphisms. Its analogue for a joint (d, -d)-dilation multiwavelet set has also been provided. In addition, denoting by , the wavelet induced isomorphism associated with a d-dilation wavelet set W, we show that for a joint (d, -d)-dilation wavelet set W, the measures of the fixed point sets of and are equal almost everywhere.

In this paper, we propose a learning scheme for regression generated by atomic norm regularization and data independent hypothesis spaces. The hypothesis spaces based on polynomial kernels are trained from finite datasets, which is independent of the given sample. We also present an error analysis for the proposed atomic norm regularization algorithm with polynomial kernels. When dealing with algorithms with polynomial kernels, the regularization error is a main difficulty. We estimate the regularization error by local polynomial reproduction formula. Better error estimates are derived by applying projection and iteration techniques. Our study shows that the proposed algorithm has a fast convergence rate with O(m^ζ-1), which is the best convergence rate in the literature.

An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate Walsh polynomial is described. Approximation properties of tight wavelet frames are also studied. In contrast to the real setting, it appeared that a wavelet tight frame decomposition has an arbitrary large approximation order whenever all wavelet functions are compactly supported.

We consider a class of (N, M)-elementary step functions on the p-adic Vilenkin group. We prove that (N, M)-elementary step function generates a MRA on p-adic Vilenkin group if and only if it is generated by a special N-valid rooted tree on the set of vertices {0,1,…p - 1} with the vector (0,…,0) ∈ ℤ^N as a root.

Detail enhancement of color images is required in many applications. Unsharp masking (UM) is the most classical tool for detail enhancement. Many generalizing UM approaches have been proposed, for example, the rational UM technique, the cubic unsharp technique, the adaptive UM technique and so on. For color images, these algorithms have three steps: (a) Implement the color2gray step; (b) design an extracting method of high frequency information (HFI) based on the luminance component (LC); (c) complete the enhancing process utilizing the HFI. However, using only the HFI of the LC may lose the HFI of the chrominance component (CC). This paper proposes a quaternion based detail enhancement algorithm to extract details of the color image using both of the luminance and CCs. The proposed algorithm is designed to address three tasks: (1) designing an extraction method of the color high frequency information (CHFI) based on quaternion description of the 3D vector rotation; (2) performing an effective fusion strategy of the CHFI and the gray high frequency information (GHFI); (3) designing a quaternion based measure method of the local dynamic range, based on which the enhancement coefficients of the proposed algorithm can be determined. The performance of the proposed algorithm compares favorably with many other similar enhancement algorithms. The eight parameters can be adjusted to control the sharpness to produce the desired results, which makes the proposed algorithm practically useful.

This paper presents a new method for the segmentation of Magnetic Resonance Imaging (MRI) of brain tumor. First, discrete wavelet transform (DWT)-based soft-thresholding technique is used for removing noise in the MRI. Second, intensity inhomogeneity (IIH) independent of noise is removed from the MRI image. Third, again DWT is used to sharpen the de-noised and IIH corrected image. In this method, the image is decomposed into first level using wavelet decomposition and approximate values are assigned to zero and reconstruct the image results in detailed image. The detailed image is added with the pre-processed image to produce sharpened image. Entropy maximization using Grammatical Swarm (GS) algorithm is used to obtain a set of threshold values and a threshold value is selected with the expert knowledge to separate the lesion part from the other non-diseased cells in the image.

We propose a new digital image watermarking method based on the dyadic wavelet packet transform (DYWPT) and fast interval arithmetic (IA) techniques. Because the DYWPT has a redundant representation, like the dyadic wavelet transform (DYWT), the amount of information that the watermark must contain is greater than in the case of methods based on ordinary discrete wavelet transforms (DWTs) and the discrete wavelet packet transform (DWPT). However, the order of the high frequency components is not necessarily the same as the order of their frequency domain. Therefore, in our approach, we rearrange the order of the high frequency components in descending order of frequency components and embed a watermark selectively into higher frequency components. Our watermark is a ternary-valued logo that is embedded into higher frequency components through use of the DYWPT and fast IA techniques. We describe our watermarking procedure in detail and present experimental results demonstrating that our method produces watermarked images that have better quality and are robust with respect to various types of attacks, including marking, clipping, median filtering, contrast tuning (histeq and imadjust commands in the MATLAB Image Processing Toolbox), addition of Gaussian white noise, addition of salt & pepper noise, JPEG and JPEG 2000 compressions, rotation, and resizing.

By combining the T-spline and wavelet techniques together, this paper proposes a new local fairing algorithm for B-spline surfaces. There are two steps of operations in the new algorithm. The first is to decompose a local region into a scale part and a detail one by wavelet analysis. The second is to reconstruct the surface by removing the detail part and then replacing the local region by the scale one. Because the scale part constitutes a T-spline, the new algorithm can not only realize local fairing, but also simultaneously reduce the control points. The effectiveness of the new approach is verified by three examples, which also demonstrate that the major advantage of the new algorithm over the traditional ones lies in its local fairing capability.