## From Discrete Measurements to Bounded Gradient Estimates: A Look at Some Regularizing Structures

journal contribution

posted on 04.09.2013 by Gene A. Bunin, Grégory François, Dominique Bonvin#### journal contribution

Any type of content formally published in an academic journal, usually following a peer-review process.

Obtaining
a reliable gradient estimate for an unknown function when given only
its discrete measurements is a common problem in many engineering
disciplines. While there are many approaches to obtaining an estimate
of a gradient, obtaining lower and upper bounds on this estimate is
an issue that is often overlooked, as rigorous bounds that are not
overly conservative usually require additional assumptions on the
function that may either be too restrictive or impossible to verify.
In this work, we try to make some progress in this direction by considering
four general structural assumptions as a means of bounding the function
gradient in a rigorous likelihood sense. After proposing an algorithm
for computing these bounds, we compare their accuracy and precision
across different scenarios in an extensive numerical study.