Episode 18: Medical imaging and Fourier analysis

04.24.2015 - By Taking Maths Further Podcast

Download our free app to listen on your phone

This week the topic was Fourier analysis. We interviewed Heather Williams, who’s a medical physicist and works with Positron Emission Tomography (PET) scanners, as well as other medical scanning devices. We talked about her work and how maths is important in converting data from the scanner into images that can be used to diagnose patients. Interesting links:PET scanners on the NHS websiteBeing a Medical Physicist on the NHS careers websiteCentral Manchester University Hospitals, Heather's employerShape of the sine and cosine graphs at BBC BitesizeAn interactive guide to the Fourier transform at BetterExplained.com XKCD comic 'Fourier' Puzzle:If a function is made by adding sin(x) + cos(x), what’s the maximum value attained by this function? Solution: This is a periodic function, which repeats every 180 degrees (or π radians). Its maximum value is the square root of two, or √2 = 1.414213..., which it first reaches at a value of 45 degrees, or π/4. The function varies between √2 and -√2, and it looks like a sin curve. The function can also be written as √ 2 + sin(θ + π/4). For a graph of the function, and more detail, input it into Wolfram Alpha. Show/Hide

More episodes from Taking Maths Further Podcast