Analysis of regularized inversion of data corrupted by white Gaussian noise

Our aim is to provide new analytic insight to the relationship between the continuous and practical inversion models corrupted by white Gaussian noise. Let us consider an indirect noisy measurement M of a physical quantity u
M = Au + d*N
where A is linear smoothing operator and d > 0 is noise magnitude.

If N was an L2-function we could use the classical Tikhonov regularization to achieve an estimate. However, realizations of white Gaussian noise are almost never in L2. That is why we present a modification of Tikhonov regularization theory covering the case of white Gaussian measurement noise. We will also consider the question in which space does the estimate convergence to a correct solution when the noise amplitude tends to zero and what is the speed of the convergence.
This is joint work with Matti Lassas and Samuli Siltanen (University of Helsinki).

• Speaker: Hanne Kekonnen
• Friday 20 October 2017, 16:00–17:00
• Venue: MR12.
• Series: Statistics; organiser: Quentin Berthet.