You may never have heard of an "inverse problem", but as Roy Pike of King's College London explains in this video, it is a way of looking at many different questions within science. It refers to a method of estimating data that are not there. Or to be more precise, it refers to the process of estimating data that are not obtainable using direct measurements – perhaps because they are lost during an experiment, or perhaps because they were never measured accurately in the first place.

Pike gives the example of a pinhole camera used to produce an image of an object. A "direct problem" would be to work out how the image will appear, which can be done by using tools such as Maxwell's equations and propagation diffraction theory to calculate how the light will disperse. An "inverse problem", however, would be to calculate the nature of the object based on the data contained in the image you have produced, as some data are inevitably not present, particularly at the blurred edges of the image. "The direct problem is relatively easy, the inverse one is impossible," says Pike.

In order to make educated guesses at the missing data in these situations, researchers such as Pike have a range of mathematical tools at their disposal.

You can also watch this video about how an inverse approach is being applied within speech science.

Watch more from our 100 Second Science video series.