Milana Gatarić
I am a research associate in the Centre for Mathematical Imaging in Healthcare based at the
Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge. Prior to this, I was an EPSRC Doctoral Prize Fellow at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
In 2016 I completed my PhD in Applied Mathematics at the University of Cambridge, where I was cosupervised by Ben Adcock and Anders Hansen. I also have a BSc and a MSc in Applied Mathematics, both from the University of Novi Sad, Serbia.
I provide consulting services at the Imaging and AI Clinic and the Statistical Clinic, which are open to all university members.
My research interests span across computational and statistical analysis motivated by image and signal processing applications. Specific topics include highdimensional clustering and principal component analysis; sparse models; image reconstruction; superresolution; inverse problems; sampling theory; Fourier analysis; multiscale approximations.
Here is my Google Scholar and my
LinkedIn profile.
Publications
Preprints
Reviewed Journal Papers

M. Gataric, G. S. D. Gordon, F. Renna, A. G. C. P. Ramos, M. P. Alcolea, S. E. Bohndiek
"Reconstruction of optical vectorfields with applications in endoscopic imaging"
IEEE Transactions on Medical Imaging, 2018.
[DOI:10.1109/TMI.2018.2875875] [arXiv] 

B. Adcock, M. Gataric, J. L. Romero
"Computing reconstructions from nonuniform Fourier samples:
Universality of stability barriers and stable sampling rates"
Elsevier Applied and Computational Harmonic Analysis, 2017.
[DOI:10.1016/j.acha.2017.05.004] [arXiv] 

M. Gataric, C. Poon
"A practical guide to the recovery of wavelet coefficients from Fourier measurements"
SIAM Journal on Scientific Computing, 2016.
[DOI:10.1137/15M1018630] [arXiv]
Code: [Matlab software] 

B. Adcock, M. Gataric, A. C. Hansen
"Density theorems for nonuniform sampling of bandlimited functions using derivatives or bunched measurements"
Springer Journal of Fourier Analysis and Applications, 2016.
[DOI:10.1007/s0004101695048] [arXiv] 

B. Adcock, M. Gataric, A. C. Hansen
"Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples"
Elsevier Applied and Computational Harmonic Analysis, 2015.
[DOI:10.1016/j.acha.2015.09.006] [arXiv] 

B. Adcock, M. Gataric, A. C. Hansen
"On stable reconstructions from nonuniform Fourier measurements"
SIAM Journal on Imaging Sciences, 2014.
[DOI:10.1137/130943431] [arXiv] 
Reviewed Conference Proceedings
Invited Discussion
 M. Gataric
"Invited Discussion of Random projection ensemble classification by Cannings and Samworth"
Journal of the Royal Statistical Society: Series B, 2017.
[Report]
[wiley.com]
Technical Report
 B. Adcock, M. Gataric, A. C. Hansen
"Nonuniform sampling and reconstruction of multivariate functions using derivatives"
Purdue Geomathematical Imaging Group Annual Project Review, 2014.
Theses
 PhD Thesis: "Nonuniform generalized sampling", Supervised by Ben Adcock & Anders Hansen, July 2015.
[DOI:10.17863/CAM.8433]
[Slides]
[Short summary]
My PhD thesis addresses the problem of function recovery from pointwise samples of its Fourier transform. This is a fundamental task in signal processing where the unknown function represents a signal or image that needs to be reconstructed from the data given by a sensing device. This basic problem arises in numerous applications such as medical imaging (MRI, CT), electron microscopy, as well as radar and geophysical imaging. The case when data is acquired nonuniformly, i.e. along a nonCartesian sampling pattern, is of a particular interest in these applications, and simultaneously, a particular focus of my PhD research.
In the joint work with Adcock and Hansen, we develop a novel approach to stable and accurate recovery of unknown compactly supported squareintegrable functions from nonuniform samples of their Fourier transform, socalled Nonuniform Generalized Sampling (NUGS). This new approach is based on a recently introduced framework, known as generalized sampling, which allows one to tailor the reconstruction system to the function to be approximated and thereby obtain sparse or rapidlyconvergent approximations. While preserving this important hallmark, NUGS describes sampling by the use of weighted Fourier frames, thus permitting for highly nonuniform sampling schemes common in the aforementioned applications. In particular, NUGS provides stable recovery in any desired reconstruction system subject to sufficiently wide sampling bandwidth and the universal sampling density, regardless of sampling clustering.
Additionally, the joint work with Poon demonstrates how NUGS can be implemented efficiently to obtain a wavelet representation of a signal or image from Fourier data. This work provides a publicly available Matlab software for such image recovery.
In the subsequent work with Adcock and Hansen, we address a related problem of nonuniform sampling of bandlimited functions using derivatives or bunched measurements, which present two different sampling scenarios that allow for a reduced sampling density.
Keywords: Nonuniform sampling, Generalized sampling, Fourier frames, Wavelets, Medical imaging (MRI, CT)
 Master Thesis: "New algorithm for combinatorial hypergraph partitioning", Supervised by Nebojsa Gvozdenovic, October 2010.
[Short summary]
My master thesis proposes a new idea for solving the problem of hypergraph partitioning with the objective function that minimizes the number of broken hyperedges subject to balance constraints on the size of each partitioning block. This problem is known to be equivalent to the problem of callgraph partitioning with the objective function that minimizes the number of interfaces subject to the same balance constraints. Both of these problems have practical use, for example, in VLSI design or for maintaining large software systems. Their significance also lies in the fact that they are NPcomplete. Although optimal solution can be found by integer linear programming, this takes a long computational time and faster techniques are required. We outline a new combinatorial algorithm that aims to solve the problem efficiently. This new algorithm is implemented in C++ and preliminary results are reported.
Keywords: Combinatorial optimization, Hypergraph, Callgraph, Integer linear programming
 Diploma Thesis: "On wedge method for nonlinear optimization", Supervised by Natasa Krejic, September 2009.
[Short summary]
My diploma thesis is about socalled wedge method for unconstrained derivativefree optimization [Marazzi & Nocedalz, 2002]. Under this framework, it is assumed that the objective function is nonlinear and Lipschitz continuous, its pointevaluations are expensive, and its derivatives are unavailable. The wedge method is an optimization technique which combines the trust region method with an interpolation model. Specifically, in each iteration, it solves a subproblem that optimizes a (quadratic) interpolation model in a small region around the current iteration, where it trusts the interpolation model to approximate the objective function well.
By imposing a simple geometric constraint, it ensures that each new iteration can be included in the interpolation model, thereby reducing the total number of function evaluations.
Keywords: Numerical nonlinear optimization, Trust region method, Interpolation model
CCA Essays
 Short Project: "Coupling of continuum and particle models", Supervised by Fehmi Cirak & Carola Schonlieb, January 2012.
[Report]
[Short summary]
Methods for coupling of continuum and particle models are used to reduce computational cost of simulations in molecular statics and dynamics, where material domain is decomposed into particle and continuum subdomains. Since particle models are more expensive, they are typically used only on small strategically chosen subdomains where some irregularities are expected, while most of the body is described by a numerical approximation to a continuum model, such as a finite element approximation. For this purpose, one can use ideas of a classical domain decomposition method for solving partial differential equations defined on overlapping subdomains, socalled alternating Schwarz method. In this report, we outline results on the existing error analysis of the alternating Schwartz in the particlecontinuum context, and moreover, we discuss its convergence. In order to further decrease computational time, a new onedimensional coupled model with nonmatching grids is implemented in Matlab and numerical results are reported.
Keywords: Domain decomposition method, Finite elements, PDEs, Atomistic modelling
 Long Project: "Concentrationcompactness in partial differential equations and orbital stability of galaxy configurations", Supervised by Clement Mouhot, June 2012.
[Report]
[Short summary]
In this miniproject, the VlasovPoisson system is studied in its form which is used to describe the time evolution of a galaxy. Its main properties are carefully revisited and results on nonlinear stability are given. The major part of the report is dedicated to the concentrationcompactness principle, which can be used in more general contexts in order to study stability of ground states in partial differential equations. Also, the concentrationcompactness principle is applied to the nonlinear Schrödinger equation. Finally, a selection of important recent results on the nonlinear stability of the VlasovPoisson system are summarized, which rely on the notion of rearrangements.
Keywords: VlasovPoisson system, Concentrationcompactness principle, Nonlinear Schrödinger equation, Kinetic theory, PDEs
Contacts
Email:
m.gataric [at] statslab.cam.ac.uk
m.gataric [at] maths.cam.ac.uk
mg617 [at] cam.ac.uk
milanagataric [at] gmail.com
Address:
DPMMS
Centre for Mathematical Sciences
Wilberforce Road
Cambridge CB3 0WB, UK
Office:
D0.16
Phone:
+44 1223 339791