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


About Applied and computational maths seminars

Our seminars bring together UQ's applied and computational mathematics communities.

UQ and invited scientists deliver the presentations, which are informal and promote discussion.

We welcome suggestions for speakers and topics from staff, students and visitors, and encourage students to share their work.

Our seminars are held on Thursdays from 3pm to 4pm in the Priestley Building (Building 67), Room 442.

To suggest a topic or speaker, and for more information, contact Dr Dietmar Oelz or Dr Fred Roosta-Khoransani.

Venue

Priestley Building #67
Room: 
442