Chaotic Sensing: Using Fractals and Turbulence to Accelerate Imaging

Recently, the speaker was fortunate enough to discover a new class of fractals within the discrete Fourier transform (DFT). The DFT is an important transform that is used as a mechanism for solving many inverse problems, such as those found in magnetic resonance imaging (MRI). The speaker recently showed that fractal sampling, specifically those of the DFT, can be used to speed up MRI acquisition up to four times without any significant loss of image information or artefacts [1].

In this talk, the speaker will firstly introduce the newly discovered class of fractals within the finite geometry of the DFT. These fractals have the remarkable properties that they are invariant to the DFT, exist equivalently in the set of Gaussian integers and map exactly to a discrete Radon transform. Lastly, the speaker will show how these fractals have been used to create a chaotic theory of sampling and measurement called Chaotic Sensing. In this theory, fractal sampling is used to induce a chaotic mixing of image information within the recovered image. Since the original object remains consistent within any measurements made, any artefacts caused by sparse sampling become turbulent in nature, ensuring they are uncorrelated to the imaged object. These artefacts can then be dampened out using computational algorithms to recover the original representation of the object being imaged, but with significantly smaller number of samples or measurements. This work was also recently announced by UQ News and Phys.org.

[1] S. S. Chandra et al., “Chaotic Sensing,” IEEE Transactions on Image Processing, vol. 27, no. 12, pp. 6079–6092, Dec. 2018. https://doi.org/10.1109/TIP.2018.2864918