We investigate biorthogonal spline wavelets on the interval. We give sufficient and necessary conditions for the reconstruction and decomposition matrices to be sparse. Furthermore, we give numerical estimates for the Riesz stability of such bases. §

We describe a wavelet based X-ray rendering method in the frequency domain with a smaller time complexity than wavelet splatting. Standard Fourier volume rendering is summarized and interpolation and accuracy issues are briefly discussed. We review the implementation of the fast wavelet transform in the frequency domain. The wavelet X-ray transform is derived, and the corresponding Fourier-wave...

A novel construction of compactly supported orthogonal scaling functions and wavelets with spline functions is presented in this paper. Let [Formula: see text] be the center B-spline of order n, except for the case of order one, we know [Formula: see text] is not orthogonal. But by the formula of orthonormalization procedure, we can construct an orthogonal scaling function corresponding to [For...

We investigate mutually orthogonal spline wavelet spaces on non-uniform partitions of a bounded interval, addressing the existence, uniqueness and construction of bases of minimally supported spline wavelets. The relevant algorithms for decomposition and reconstruction are considered as well as some stability-related questions. In addition, we briefly review the bivariate case for tensor produc...

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

Neural fields are spatially continuous state variables described by integro-differential equations, which are well suited to describe the spatiotemporal evolution of cortical activations on multiple scales. Here we develop a multi-resolution approximation (MRA) framework for the integro-difference equation (IDE) neural field model based on semi-orthogonal cardinal B-spline wavelets. In this way...

This paper introduces a novel framework for single-pixel imaging via compressive sensing (CS) in shift-invariant (SI) spaces by exploiting the sparsity property of wavelet representation. We reinterpret acquisition procedure camera as filtering observed signal with continuous-domain functions that lie an SI subspace spanned integer shifts box function. The is modeled arbitrary generator whose s...