#### Downsampling for Efficient Parameter Choice in Ill-Posed Deconvolution Problems

Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally…

Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.

**Contributors**

- Hansen, Jakob Kristian (Author)
- Renaut, Rosemary (Thesis director)
- Cochran, Douglas (Committee member)
- Barrett, The Honors College (Contributor)
- School of Music (Contributor)
- Economics Program in CLAS (Contributor)
- School of Mathematical and Statistical Sciences (Contributor)

**Created**