Algebraic Wavelet Transform via Quantics Tensor Train Decomposition

By Ivan V. Oseledets, E. E. Tyrtyshnikov. 2011

40 citations recorded by the source corpus.

Subfields: Computational Mathematics, Radiology, Nuclear Medicine and Imaging, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Sergey V. Dolgov
2. Dmitry V. Savostyanov
3. Boris N. Khoromskij
4. Ivan V. Oseledets
5. Vladimir A. Kazeev
6. Venera Khoromskaia
7. E. E. Tyrtyshnikov
8. V. Dolgov

In Radiology, Nuclear Medicine and Imaging

1. Dmitry V. Savostyanov
2. Boris N. Khoromskij
3. Sergey V. Dolgov

In Signal Processing

1. Sergey V. Dolgov
2. Boris N. Khoromskij
3. Dmitry V. Savostyanov
4. Wolfgang Hackbusch
5. V. Dolgov
6. Ivan P. Gavrilyuk

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “A connection between QTT and the wavelet transform is discussed in [215].”
• Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “For example: • If Ar are rank-1 tensors of size I1 ˆ I2 ˆ ̈ ̈ ̈ ˆ IN , and Br are scalars, @r, then (37) expresses the rank-R CP decomposition; • If Ar are rank-Lr tensors of size I1 ˆ I2 ˆ ̈ ̈ ̈ ˆ IR ˆ 1 ˆ ̈ ̈ ̈ ˆ 1, in the Kruskal (CP) format, and Br are rank-1 tensors of size 1ˆ ̈ ̈ ̈”
• Superfast Fourier Transform Using QTT Approximation (2012, methodology): “We hope that such algorithms can have an application to image and video processing, directly or with the use of WTT version of the format, following the ideas of [46].”