Framelets: MRA-based constructions of wavelet frames☆☆☆

By Ingrid Daubechies, Bin Han, Amos Ron, Zuowei Shen. 2003

817 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/26b830024c79cae200c3e962db9fab75289ac563

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Interpolation and denoising of high-dimensional seismic data by learning a tight frame (2015, methodology): “We use the tensor linear spline framelet (Daubechies et al., 2003) as initial wavelet, as shown in Figure 3 (b) (20 out of 343 filters are shown).”
On Multivariate Compactly Supported Bi-Frames (2007, methodology): “In the present work, we apply the mixed oblique extension principle (MOEP) as discussed in [10] for the construction of bi–frames.”
Split Bregman Methods and Frame Based Image Restoration (2009, methodology): “While it is known that framelets of [39,59], curvelets of [17] and translation invariant wavelets [34] can represent the cartoon part sparsely, it is hard to say which system can represent the texture part sparsely.”
Nonlinear Approximation with Dictionaries I. Direct Estimates (2004, background): “Consider D a (bi)orthogonal wavelet basis [5, 6, 30] or a (tight) wavelet frame [35, 34, 8 ] for L 2 (R d )”
Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix (2003, background): “However, as in Gr¨ochnig and Ron [13], the number of elements in “ in Theorem 1.1 may be significantly greater than jdetMji1 and may even increase exponentially with respect to r. Using recent results in [3, 10 ], based on a simple observation, we shall be able to further improve Theorem 1.1 such t”
Compactly supported tight and sibling frames with maximum vanishing moments (2001, result): “Related work concerning wavelet frames with higher vanishing moments has been carried out independently in parallel to our development by Daubechies et al. [14].”
The double-density dual-tree DWT (2004, background): “In addition, the double-density DWT is an example of an affine frame; see [3], [4], [7], [18], [19], [21], and [22].”
Medical image processing on the GPU - Past, present and future (2013, methodology): “Tight frame regularization (Daubechies et al., 2003), based on wavelets, is another alternative to TV but is also computationally demanding (Jia et al., 2011).”
Dual Wavelet Frames and Riesz Bases in Sobolev Spaces (2009, methodology): “Principle) in [11, 21 ] (also see [20] for a comprehensive study of dual wavelet frames obtained by OEP) can easily be generalized from L2(R d ) to Sobolev spaces.”
Seismic data restoration via data-driven tight frame (2014, methodology): “In this section, we first briefly introduce the concept of the wavelet TF (Daubechies et al., 2003; Dong and Shen, 2010; Shen, 2010), and we then introduce the newly developed data-driven TF technique for denoising (Cai et al., 2013).”
Dynamic Steerable Blocks in Deep Residual Networks (2017, methodology): “Secondly, we replace the pixel-basis with widely-used frames that take natural image statistics into account, namely non-orthogonal, overcomplete Gaussian derivatives [13] and non-orthogonal framelets [10] in an alternating fashion, yielding superior performance compared to the pixel-basis by replac”
Pairs of frequency-based nonhomogeneous dual wavelet frames in the distribution space (2009, background): “16) also appeared in the study of homogeneous dual wavelet frames in L2(R) and their frame approximation properties, for example, see [12, 17, 18].”
PSEUDO-SPLINES, WAVELETS AND FRAMELETS (2007, methodology): “Furthermore, this short support wavelet is one of the tight framelets constructed from the same pseudo-spline derived from the methods provided in both [ DHRS ] and our currant paper.”
Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems (2017, methodology): “Then, a frame-based denoising algorithm [18, 13, 12] recovers the unknown signal by substituting g for f in the right side of (81) and applies a shrinkage operator Sτ to the framelet coefficients to eliminate the small magnitude noise signals:”