Daniel Kessler is a BS/MS student expected to graduate May 2019. He works with Dr. Weihong Guo under the REU NSF project conducting work on High Dimensional Tensor Deblurring. The work focuses on factors such as motion, out of focus and air turbulence often cause blur in digital images, and recovering a sharp and clean image out of a noisy and blurred one is a difficult inverse problem. It becomes more challenging for high dimensional images. Dr. Guo and Daniel uses tensors to represent high dimensional images and propose a novel method based on Tensor Nuclear Norm (TNN) and high dimensional Total Variation (TV) regularity. Numerical results on degraded color images, hyperspectral images, and videos demonstrate the effectiveness of the proposed method.

Daniel joined CWRU in the Fall of 2015, coming from Leawood, Kansas to study Applied Math. He entered the BS/MS program Fall 2018. Check out the presentation’s abstract below.

**Abstract**

Blurs occur in images due to a variety of causes. Even if the details of the blur are known, recovering the original sharp image is a difficult inverse problem due to noise. Multidimensional images, represented as multidimensional tensors, suffer from blurring problems as well. These require special treatment, as they have multiple dimensions. Some results indicate that the Tensor Nuclear Norm regularity is a good condition for multidimensional tensor recovery. We propose a novel method to deblur multidimensional tensors, based on minimizing the TNN and imposing Total Variation (TV) regularity. Preliminary results show some promise for the recovery of these higher dimensional structures.