Bring on the noise

Now I am fully aware that the big physics story of the moment is the imminent announcement from CERN that the elusive Higgs Boson may have been detected. Susan Watts covered it last night on Newsnight, and I am every bit as excited as she about the potential discovery. But there is more in science, and physics in particular, than all this God, the Universe and Everything stuff. And it is every bit as exciting.

As an undergraduate student I was particularly captivated by such areas of classical physics as thermodynamics – the science of engines, energy and entropy – and information theory. The latter I went on to make extensive use of as a space science researcher. My measurements tools at the time were ground-based radar and optical systems, and through this work I acquired a detailed knowledge of radio antennas and camera lenses.

In geophysical research we are dealing with messy, real-world systems rather than clean laboratory conditions, and the data collected tend to be rather noisy. Making sense of these data requires the use of sophisticated signal processing and statistical analysis techniques, and the challenge is to extract the signal of interest from a mass of noise contributed by interfering physical processes and instrumental effects.

So imagine my surprise to learn as a student that one way of improving the quality of a geophysical data stream is to add more noise to it. Specifically white, or random, noise. The process involved is known as stochastic resonance, and it occurs in non-linear systems, where the input signal does not lead to a directly proportional response. Examples of nonlinear systems in geophysics include turbulent atmospheric flow and unstable space plasmas (ionised gases). We also see nonlinear processes at work in the economy.

Adding noise to an already noisy signal as a means of strengthening that signal may seem counterintuitive, but the effect is real. When observing the ionosphere over northern Scandinavia with the EISCAT system, I would add small amounts of artificially generated noise to particular radar receiver channels, and the result was to improve the clarity of the backscattered radar signal from the upper atmosphere in frequency bands affected by natural or instrumental interference.

Stochastic resonance is an established part of information science, but some of the details remain little understood. For example, under what specific energy conditions will the addition of random noise boost a signal? This question has been addressed by scientists in Orissa, India. In a paper recently published in the European Physical Journal, PhD students Shubhashis Rana and Sourabh Lahiri, together with their supervisor Arun Jayannavar, show with the aid of a model consisting of a particle allowed to move freely within an energy well divided by a central wall, that the steepness of the well walls is critical to the process of stochastic resonance. The researchers were able to quantify the effect, and found that resonance occurs only when the so-called bistable potential is ‘hard’, meaning that is has sufficiently steep walls. Otherwise, the resonance effect breaks down.

The theoretical discussion presented by Rana and his colleagues is somewhat abstract and mathematical, but the improved understanding it provides could lead to a deeper understanding of fuzzy image processing and biological and neurological systems analysis, as well as the geophysical phenomena with which I am most familiar.

For a graphical illustration of the power of stochastic resonance, take the following video clip of a dry fingerprint enhanced by the gradual addition of white noise…

See what I mean? This is stochastic resonance at work in a very practical world.

Further reading

Rana et al. – “The role of soft versus hard bistable systems on stochastic resonance using average cycle energy as a quantifier”, Eur. J. Phys. B 84, 323 (2011)