in this paper, we characterize multiresolution analysis(mra) parseval frame multiwavelets in l^2(r^d) with matrix dilations of the form (d f )(x) = sqrt{2}f (ax), where a is an arbitrary expanding dtimes d matrix with integer coefficients, such that |deta| =2. we study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of mra tight frame multiwav...

When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L = L(IR) with dilation integer factor M ≥ 2, the standard “matrix extension” approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notio...

Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we...

When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L2 = L2(IR) with dilation integer factor M ≥ 2, the standard “matrix extension” approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The not...

Wavelet families arise by scaling and translations of a prototype function, called the mother wavelet. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact...

Harten’s framework is a nonlinear generalization of the wavelet framework. Previously, the choice of discretization (scaling function) in Harten multiresolution schemes has been limited to point-value, cell-average, and hat-based discretization. This paper shows how to construct multiresolution schemes consistent with Harten’s framework for a variety of discretizations. The construction here be...

We describe a new family of scaling functions, the (α, τ)fractional splines, which generate valid multiresolution analyses. These functions are characterized by two real parameters: α, which controls the width of the scaling functions; and τ , which specifies their position with respect to the grid (shift parameter). This new family is complete in the sense that it is closed under convolutions ...

A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of ...