Congratulations Jackie!

My MSc student Qinghong (Jackie) Xu successfully defended her Master’s thesis. Congratulations!

Jackies thesis is titled “Compressive Imaging with Total Variation Regularization and Application to Auto-calibration of Parallel Magnetic Resonance Imaging”. It contains a novel (and technical) theoretical analysis of TV regularization in compressed sensing, and a new method for auto-calibration in parallel MRI. Stand by for the paper later this year!

Optimal sampling in general domains

When approximating a multivariate function defined on an irregular domain, a good choice of sampling points is critical. In this paper, my PhD student Juan and I develop new, practical sampling strategies for which the sample complexity is near-optimal: specifically, it is linear (up to a log factor) in the degree of the approximation. This improves previous approaches which were at best quadratic in the degree. Here’s the paper:

Optimal sampling strategies for multivariate function approximation on general domains

New group members

I am pleased to announce the arrival of three new members to my group this fall:

  • Nick Dexter is a PIMS Postdoctoral Fellow, joining from the University of Tennessee in the USA.
  • Juan Manuel Cárdenas is a PhD student, joining from the University of Concepcion in Chile.  He previously visited my group in Spring 2017.
  • Matthew King-Roskamp is an NSERC MSc student, and a former undergraduate honours student at SFU.  He was previously an undergraduate researcher in my group.


Approximating high-dimensional functions on irregular domains

Multivariate polynomials are excellent means of approximating high-dimensional functions on tensor-product domains.  But what about approximations on irregular domains, as is quite common in applications?  In our new paper, Daan Huybrechs and I tackle this question using tools from frame theory and approximation theory:

Approximating smooth, multivariate functions on irregular domains

We establish a series of results on approximation rates and sample complexity, deriving bounds that scale well with dimension in a variety of cases.

Congratulations Casie!

My former undergraduate student Anyi (Casie) Bao was a winner of the SFU Department of Mathematics Undergraduate Research Prize. Her work involved the development and analysis of compressed sensing-based strategies for correcting for corrupted measurements in Uncertainty Quantification.  A draft version of the resulting paper can be found here:

Compressed sensing with sparse corruptions: Fault-tolerant sparse collocation approximations

Congratulations (again) Matt!

Matt King-Roskamp – an undergraduate student in my group co-supervised with Simone Brugiapaglia – was awarded runner-up in two poster competitions this summer:

His work, entitled Optimal Sampling Strategies for Compressive Imaging, presents new, theoretically optimal sampling techniques for imaging using compressed sensing.