The orthonormal basis generated by a wavelet of L(R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L(R) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized...

We resolve a long-standing question on L completeness of the timescale (or wavelet) system generated by the Mexican hat function, when p ≥ 2. Our main result concerns frequency-scale systems generated by modulation and dilation of a single function. The mixed frame operator (analysis followed by synthesis) is shown to be bijective from L(R) to itself, for 1 ≤ q < ∞, so that the frequency-scale ...

The rate control problem can be greatly simpli ed by using a wavelet coder, since the desired bit rate for a particular frame can be easily reached by using its embedding property. We convert the rate control problem to a bit allocation problem for each frame, and solve it with two models. Frames are assumed to be independent in the basic model while their dependency is taken into account in th...

In this paper, we propose two algorithms, namely extrapolated proximal iterative hard thresholding (EPIHT) algorithm and EPIHT algorithm with line-search (EPIHT-LS), for solving `0 norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of KurdykaLojasiewicz property, we show that the sequences generated by the two algorithms converge to a local m...

In this note, we show that one can derive from any B-spline function of order m (m ∈ N) an MRA tight wavelet frame in L2(R) that is generated by the dyadic dilates and integer shifts of three compactly supported real-valued symmetric wavelet functions with vanishing moments of the highest possible order m.

We proved that for any matrix dilation and for any positive integer n, there exists a compactly supported tight wavelet frame with approximation order n. Explicit methods for construction of dual and tight wavelet frames with a given number of vanishing moments are suggested.