Noise complaints: how statistical innovations are cleaning up noisy data

Scientific data are rarely clean and clear. Often, they are blurred or distorted by ‘noise’ – random disturbances that get mixed in with real data and make them difficult to interpret. Thankfully, statisticians like Dr Catia Scricciolo from the University of Verona in Italy are developing methods to counteract the problem, drawing on mathematical optimisation and probability to remove this noise and reveal the signals it was hiding.

When scientists record data – whether astronomers are measuring stars, medical personnel are taking MRI scans, or physicists are measuring subatomic particles – their results are rarely squeaky clean. This makes it difficult to see the true signal through the blur. “In science, ‘blur’ comes from equipment limitations, physical effects or interference, as well as random noise,” says Catia. “To counter this, scientists use deconvolution – a process that mathematically recovers the original clear signal from the blurred measurement.”

When astronomers look up at the night sky using telescopes here on Earth, the atmosphere bends light randomly, which is why stars appear to twinkle. When biologists look at cells under the microscope, all the parts of the three-dimensional cell that are not in the targeted two-dimensional plane show up as out-of-focus haze. “We can use deconvolution to turn blurry, hard-to-interpret data like these into sharper, more useful information,” says Catia. “Mathematically speaking, this involves estimating the original signal by undoing the effects of an unknown or partially known blurring process.”

Noise: the enemy of deconvolution

But deconvolution becomes trickier when the blurring is caused by random, unpredictable effects. “This type of unwanted, random disturbance is called noise,” explains Catia. “Noise makes deconvolution much harder, and sometimes impossible.” The more noise there is, the harder it is to decide what is signal and what is just random, limiting what can be recovered. Ideally, noise is minimised when the measurements are taken, but this is not always possible. “Because noise is random, you can never be completely sure which parts of your observation are the original signal and which are just noise,” says Catia. “So, deconvolution can give you an estimate of the truth, but not the exact truth.”

Thankfully, statisticians have some nifty tricks up their sleeves to help with deconvolution for noisy data. “The Wasserstein metric defines a distance between probability distributions,” says Catia. “In plainer language, it’s a way to focus on the overall shape of a distribution of data, rather than getting caught up in the ‘bumps’ caused by noise.” Catia studies Wasserstein deconvolution through a mix of mathematics and probability. “I use mathematical optimisation to find the original distribution that best explains the noisy data,” she says. “The Wasserstein metric then acts as a score that measures how far my guess is from the truth.” Catia also adds in a regularisation term that forces a recovered distribution to smooth out any wiggles that are likely to be due to noise rather than actual quirks in the data. “All together, these methods turn messy, noisy data into a clean estimate of the original distribution,” she says.

Helping out scientists

Catia’s research is improving the reliability of Wasserstein deconvolution methods, which other scientists can then use to clean up their own datasets. “Scientists in other fields can apply my deconvolution method without needing to be experts in the mathematics behind it,” she says. “For example, doctors can use it to sharpen MRI scans, helping them see tumours more clearly.” Going back to astronomers, they can use Catia’s method to clean up blurry images of distant galaxies, uncovering details that were previously hidden by the noise of the atmosphere. Space telescopes can also benefit – when the Hubble Telescope was first launched, there was an error in its mirror array which introduced blur into the data it recorded. Using deconvolution, astronomers recovered stunning images of space from the blurry data.

Catia hopes that her research can help accelerate scientific discovery by taking the burden off scientists to develop their own data cleaning methods. “Instead of struggling to invent their own mathematical solutions, they can use the Wasserstein deconvolution techniques I helped develop,” she says. “In short, my work removes a barrier so other scientists can focus on their own research – whether that is curing a disease, discovering a new planet or understanding human behaviour.”

Dr Catia Scricciolo
Associate Professor, Department of Economics, University of Verona, Italy

Field of research: Statistics

Research paper: Adaptive minimax-optimal Wasserstein deconvolution with unknown error distributions. Scricciolo, C., (2026) doi: 110.1016/j.spl.2025.110589

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While Catia is developing methods to remove noise from data, some computer scientists are adding noise to data to improve online privacy:

futurumcareers.com/make-some-noise-the-mathematical-theories-behind-data-privacy