Related papers: Composite Wavelet Matrix-Based Transforms and Appl…
The details of an image with noise may be restored by removing noise through a suitable image de-noising method. In this research, a new method of image de-noising based on using median filter (MF) in the wavelet domain is proposed and…
Framelets (a.k.a. wavelet frames) are of interest in both theory and applications. Quite often, tight or dual framelets with high vanishing moments are constructed through the popular oblique extension principle (OEP). Though OEP can…
This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…
An approach to watermarking digital images using non-regular wavelets is advanced. Non-regular transforms spread the energy in the transform domain. The proposed method leads at the same time to increased image quality and increased…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
Orthogonality regularization has been developed to prevent deep CNNs from training instability and feature redundancy. Among existing proposals, kernel orthogonality regularization enforces orthogonality by minimizing the residual between…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…
Convolutional Neural Networks (CNNs) are known for requiring extensive computational resources, and quantization is among the best and most common methods for compressing them. While aggressive quantization (i.e., less than 4-bits) performs…
Classical orthogonal wavelets guarantee perfect reconstruction but rely on fixed bases optimized for polynomial smoothness, achieving suboptimal compression on signals with fractal spectral signatures. Conversely, learned methods offer…
Compared to scalar framelets, multiframelets have certain advantages, such as relatively smaller supports on generators, high vanishing moments, etc. The balancing property of multiframelets is very desired, as it reflects how efficient…
We study image compression by a separable wavelet basis $\big\{\psi(2^{k_1}x-i)\psi(2^{k_2}y-j),$ $\phi(x-i)\psi(2^{k_2}y-j),$ $\psi(2^{k_1}(x-i)\phi(y-j),$ $\phi(x-i)\phi(y-i)\big\},$ where $k_1, k_2 \in \mathbb{Z}_+$; $i,j\in\mathbb{Z}$;…
Medical imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound are essential for accurate diagnosis and treatment planning in modern healthcare. However, noise contamination during image…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
With the growth of digital networks such as the Internet, digital media have been explosively developed in e-commerce and online services. This causes problems such as illegal copy and fake ownership. Watermarking is proposed as one of the…
Digital array orthogonal transformations that can be presented as a decomposition over basis items or basis images are considered. The orthogonal transform provides digital data scattering, a process of pixel energy redistributing, that is…
Recently, novel quaternion-valued wavelets on the plane were constructed using an optimisation approach. These wavelets are compactly supported, smooth, orthonormal, non-separable and truly quaternionic. However, they have not been tested…
A non-decimated wavelet transform (NDWT) is a popular version of wavelet transforms because of its many advantages in applications. The inherent redundancy of this transform proved beneficial in tasks of signal denoising and scaling…
We propose a novel neural architecture for computer vision -- WaveMix -- that is resource-efficient and yet generalizable and scalable. While using fewer trainable parameters, GPU RAM, and computations, WaveMix networks achieve comparable…
Classical image filters, such as those for averaging or differencing, are carefully normalized to ensure consistency, interpretability, and to avoid artifacts like intensity shifts, halos, or ringing. In contrast, convolutional filters…