Tensor networks are used in quantum many-body physics to efficiently describe quantum wavefunctions: in essence they serve as a form of data compression for wavefunctions. Recent investigations have shown that certain multi-scale tensor networks are closely related to discrete wavelet transformations (DWTs) and other forms of multi-resolution analysis used in signal/image processing.
In this talk I will show how tools and ideas borrowed from multi-scale tensor networks can be used to construct new families of discrete wavelet transformations with desirable properties and superior performance in practical applications, such as image compression. In particular, I will demonstrate several new (compact, orthogonal, symmetric) wavelets which, tested over a large range of photographic images, consistently outperform the widely adopted CDF 9/7 wavelets used in the JPEG 2000 standard, offering approximately 10% improved compression efficiency for the same quality factor.
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