-
Article
A sustainable approach to universal metabolic cancer diagnosis
Over a billion people across the world experience a high rate of missed disease diagnosis, an issue that highlights the need for diagnostic tools showing increased accuracy and affordability. In addition, such...
-
Article
Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system
The Sobolev space Hς (ℝd), where ς > d/2, is an important function space that has many applications in various areas of research. Attributed to the inertia of a measurement instrument, it is desirable in sampling...
-
Article
Chaotic image encryption based on bidimensional empirical mode decomposition and double random phase encoding
In this paper, to enhance the security of double random phase encoding (DRPE), Lorenz system and bidimensional empirical mode decomposition (BEMD) are introduced into an image encryption process. By means of B...
-
Article
Image encryption scheme combining a modified Gerchberg–Saxton algorithm with hyper-chaotic system
We propose a new image encryption algorithm based on a modified Gerchberg–Saxton algorithm and hyper-chaotic system. First, original image is encoded into a phase function by using the modified Gerchberg–Saxto...
-
Article
Open AccessA novel method of constructing compactly supported orthogonal scaling functions from splines
A novel construction of compactly supported orthogonal scaling functions and wavelets with spline functions is presented in this paper. Let ...
-
Article
Construction of two-direction tight wavelet frames
We investigate the construction of two-direction tight wavelet frames. First, a sufficient condition for a two-direction refinable function generating two-direction tight wavelet frames is derived. Second, a s...
-
Article
Bessel multiwavelet sequences and dual multiframelets in Sobolev spaces
The dual 2I d -framelets in \( (H^{s}(\mathbb{R}^{d}), H^{-s}(\mathbb{R}^{d})) \) ...
-
Article
Multiwavelet sampling theorem in Sobolev spaces
This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon samp...
-
Article
Construction of multiwavelets with high approximation order and symmetry
In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x):= (φ1(x), ..., φr(x)) ...
-
Article
Orthogonal two-direction multiscaling functions
The concept of a two-direction multiscaling functions is introduced. We investigate the existence of solutions of the two-direction matrix refinable equation
-
Article
Construction of high order balanced multiscaling functions via PTST
The concept of paraunitary two-scale similarity transform (PTST) is introduced. We discuss the property of PTST, and prove that PTST preserves the orthogonal, approximation order and smoothness of the given or...
-
Article
Raising approximation order of refinable vector by increasing multiplicity
An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor α. Let Φ(x)=[φ 1(x)Φ 2(x),...Φr(x)]T be an orthogonal multiscaling function with...
-
Chapter and Conference Paper
Orthogonal Multiwavelets with Dilation Factor a
There are perfect construction formulas for the orthonormal uniwavelet. However, it seems that there is not such a good formula with similar structure for multiwavelets. Especially, construction of multiwavele...
