Using results on syzygy modules over a multivariate polynomial ring, we are able to construct compactly supported wavelet bi-frames with few generators from almost any pair of compactly supported multivariate refinable functions. In our examples, we focus on wavelet bi-frames whose primal and dual wavelets are both derived from one box spline function. Our wavelet bi-frames have fewer generator...

Gabor frames, especially digital Gabor filters, have long been known as indispensable tools for local time-frequency analysis of discrete signals. With strong orientation selectivity, tensor products discrete (tight) Gabor frames also see their applications in image analysis and restoration. However, the lack of multi-scale structures existing in MRA-based wavelet (tight) frames makes discrete ...

Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function φ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function φ is compactly supported conjugate symmetric, then we prove that there exists a compactly s...

Abstract: Drawing inspiration from the construction of tight wavelet frames generated by the Walsh polynomials, we introduce the notion of minimum-energy wavelet frames generated by the Walsh polynomials on positive half-line R using unitary extension principles and present its equivalent characterizations in terms of their framelet symbols. Moreover, based on polyphase components of the Walsh ...

This paper proposes a new video denoising technique where spatially adaptive noise filtering in wavelet (transform) domain is combined with temporal filtering in signal domain. AWGN is being considered which behaves as Gaussian random variable. In this paper, spatial filtering of individual frames is done in the wavelet domain, and the filtering between the frames is done by recursive temporal ...

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

We propose a simple method to constructing step mask and corresponding wavelet functions that generate tight frames on the field Qp of p-adic numbers. To construct this we use three new ideas. First, consider only an additive group Qp. Second, special tree. Thirdly, do not principle unitary extension, Pontryagin's duality instead. Using method, obtain all refinable functions.

One of the major driven forces in the area of applied and computational harmonic analysis over the last decade or longer is the development of redundant systems that have sparse approximations of various classes of functions. Such redundant systems include framelet (tight wavelet frame), ridgelet, curvelet, shearlet and so on. This paper mainly focuses on a special class of such redundant syste...