Minimum-energy multi-wavelets tight frames associated with two scaling functions

Minimum-Energy Multiwavelet Frame on the Interval[0,1]

“…An overcomplete frame also allows one to represent each element via it, but the representation is not unique. This property plays an important role in mathematics, signal analysis, timefrequency analysis, and so on [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In nearly thirty years, frame theory has been growing rapidly.…”

“…Huang and Li [18] studied the algorithms of constructing minimum-energy wavelet frames on the interval. Recently, Huang et al [19] and Liang and Zhao [20] have been concerned with the algorithms of constructing minimum-energy multiwavelet frames. In [19], the authors gave the definitions of multiwavelet frame multiresolution analysis for 2 (R) and minimum-energy multiwavelet frame.…”

Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

“…With well timefrequency localization and shift invariance, frames can be designed more easily than wavelets or multivariate wavelets. At present, frames theory has been widely used in theoretical and applicable domains [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], such as signal analysis, image processing, numerical calculation, Banach space theory, and Besov space theory.…”

“…Gao and Cao [8] researched the structure of the minimum-energy wavelet frames on the interval [0,1] and its application on signal denoising. Liang and Zhao [9] studied the minimum-energy multiwavelet frames with dilation factor 2 and multiplicity 2 and gave a characterization and a necessary condition of minimum-energy multiwavelets frames. Huang et al [10,11] studied minimum-energy multiwavelet frames and wavelet frames on the interval [0,1] with arbitrary dilation factor.…”