Quantum Inspired Wavelet Transformations for Image Compression

Methods involving coarse-graining transformations and the real-space renormalization group (RG) have proved essential in our understanding of phase transitions and the physics of systems at different length scales. The multi-scale entanglement renormalization ansatz (MERA), a modern realization of the RG formulated in terms of quantum circuits, has been developed to efficiently describe scale-invariant critical systems and lattice conformal field theories. Recently, a precise connection has been established between MERA quantum circuits and various multiresolution analysis (MRA) techniques used in signal and image processing, such as discrete wavelet transforms (DWTs).

We describe how the connection between MERA quantum circuits and DWTs can be exploited to develop new classes of wavelets; in particular, how the standard tools and optimization methods used in designing quantum circuits can be applied to build DWTs which are optimized for certain tasks. We propose a new class of circuit derived DWTs for applications in image compression, which are argued to possess numerous advantages over the state-of-the-art CDF 9/7 wavelets used in established image compression algorithms (such as JPEG2000), including achieving a higher average compression ratio on a test bank of >1,000 images.