Publications by Shayan Aziznejad

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Generalized sampling consists in the recovery of a function f, from the samples of the responses of a collection of linear shift-invariant systems to the input f . The reconstructed function is typically a member of a finitely generated integer-shift invar ...

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, ...

We study one-dimensional continuous-domain inverse problems with multiple generalized total-variation regularization, which involves the joint use of several regularization operators. Our starting point is a new representer theorem that states that such in ...

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 ...

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 ...

In this paper, we fully characterize the duality mapping over the space of matrices that are equipped with Schatten norms. Our approach is based on the analysis of the saturation of the Holder inequality for Schatten norms. We prove in our main result that ...

We develop an efficient computational solution to train deep neural networks (DNN) with free-form activation functions. To make the problem well-posed, we augment the cost functional of the DNN by adding an appropriate shape regularization: the sum of the ...

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 ...

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 ...

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a cont ...

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 ...

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 ...

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions ...

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 ...

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Levy white noises. A recent paper showed that these processes are limits in law of generalized compound-P ...

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 ...

The motivation for this work is to improve the performance of deep neural networks through the optimization of the individual activation functions. Since the latter results in an infinite-dimensional optimization problem, we resolve the ambiguity by search ...

We consider a new stochastic formulation of sparse representations that is based on the family of symmetric alpha-stable (S alpha S) distributions. Within this framework, we develop a novel dictionary-learning algorithm that involves a new estimation techn ...

Shayan Aziznejad

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Shortest-support multi-spline bases for generalized sampling

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

Multikernel Regression with Sparsity Constraint

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

Duality Mapping for Schatten Matrix Norms

Learning Activation Functions in Deep (Spline) Neural Networks

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

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

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

Coupled Splines for Sparse Curve Fitting

Convex optimization in sums of Banach spaces

Support and approximation properties of Hermite splines

Optimal Spline Generators for Derivative Sampling

The Wavelet Compressibility of Compound Poisson Processes

Generating Sparse Stochastic Processes Using Matched Splines

Sparsest Univariate Learning Models Under Lipschitz Constraint

Deep Spline Networks With Control Of Lipschitz Regularity

Dictionary Learning with Statistical Sparsity in the Presence of Noise

Measuring Complexity of Learning Schemes Using Hessian-Schatten Total Variation