Publications by Shayan Aziznejad

Linear inverse problems with Hessian-Schatten total variation

In this paper, we characterize the class of extremal points of the unit ball of the Hessian-Schatten total variation (HTV) functional. The underlying motivation for our work stems from a general representer theorem that characterizes the solution set of re ...

Springer Heidelberg2024

Measuring Complexity of Learning Schemes Using Hessian-Schatten Total Variation

Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos

2023

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos

We develop a novel 2D functional learning framework that employs a sparsity-promoting regularization based on second-order derivatives. Motivated by the nature of the regularizer, we restrict the search space to the span of piecewise-linear box splines shi ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Sparsest Univariate Learning Models Under Lipschitz Constraint

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

Beside the minimizationof the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we propose continuous-domain formulations for one-dimensional regression problems. I ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Optimization Over Banach Spaces: A Unified View on Supervised Learning and Inverse Problems

Shayan Aziznejad

In this thesis, we reveal that supervised learning and inverse problems share similar mathematical foundations. Consequently, we are able to present a unified variational view of these tasks that we formulate as optimization problems posed over infinite-di ...

EPFL2022

The Wavelet Compressibility of Compound Poisson Processes

Julien René Pierre Fageot, Shayan Aziznejad

In this paper, we precisely quantify the wavelet compressibility of compound Poisson processes. To that end, we expand the given random process over the Haar wavelet basis and we analyse its asymptotic approximation properties. By only considering the nonz ...

2022

Coupled Splines for Sparse Curve Fitting

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We prove that an op ...

2022

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Multikernel Regression with Sparsity Constraint

Michaël Unser, Shayan Aziznejad

In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...

2021

Graphic: Graph-Based Hierarchical Clustering For Single-Molecule Localization Microscopy

Michaël Unser, Daniel Sage, Shayan Aziznejad

We propose a novel method for the clustering of point-cloud data that originate from single-molecule localization microscopy (SMLM). Our scheme has the ability to infer a hierarchical structure from the data. It takes a particular relevance when quantitati ...

IEEE2021