Publications by Michaël Unser

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The stiffness of cells and of their nuclei is a biomarker of several pathological conditions. Current measurement methods rely on invasive physical probes that yield one or two stiffness values for the whole cell. However, the internal distribution of cell ...

Single-molecule localization microscopy (SMLM) is a popular microscopic technique that achieves super resolution imaging by localizing individual blinking molecules in thousands of frames. Therefore, the reconstructed high-resolution image is a combination ...

Although Lipschitz-constrained neural networks have many applications in machine learning, the design and training of expressive Lipschitz-constrained networks is very challenging. Since the popular rectified linear-unit networks have provable disadvantage ...

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

The Bio Image and Signal Processing (BISP) Technical Committee (TC) of the IEEE Signal Processing Society (SPS) promotes activities within the broad technical field of biomedical image and signal processing. Areas of interest include medical and biological ...

We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis elements have nice properties in Hilbert space such as smoothness of fractional order α ∈

R ^{ + }

. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.

Aging affects elastin, a key component of the arterial wall integrity and functionality. Elastin degradation in cerebral vessels is associated with cerebrovascular disease. The goal of this study is to assess the biomechanical properties of human cerebral ...

Hex-splines are a novel family of bivariate splines, which are well suited to handle hexagonally sampled data. Similar to classical 1D B-splines, the spline coefficients need to be computed by a prefilter. Unfortunately, the elegant implementation of this prefilter by causal and anti-causal recursive filtering is not applicable for the (non-separable) hex-splines. Therefore, in this paper we introduce a novel approach from the viewpoint of approximation theory. We propose three different recursive filters a

We present a numerical framework for Fluorescence Diffuse Optical Tomography (fDOT) that combines a forward model together with an iterative reconstruction procedure. Using rapid linear solvers, we derived an efficient reconstruction strategy for quadratic ...

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 ...

We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthog ...

We consider the estimation of an independent and identically distributed (i.i.d.) (possibly non-Gaussian) vector x is an element of R-n from measurements y is an element of R-m obtained by a general cascade model consisting of a known linear transform foll ...

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our ...

We propose two minimum-mean-square-error (MMSE) estimation methods for denoising non-Gaussian first-order autoregressive (AR(1)) processes. The first one is based on the message passing framework and gives the exact theoretic MMSE estimator. The second is ...

We provide an extension of the L-2-spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyha ...

We propose a complex generalization of Schoenberg's cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated po ...

A method for generating a data structure to digitally represent a geometrical object based on H-splines, the method being performed on a computer device having a data processor and memory, the method including the steps of creating a first data structure a ...

Assembling partial views is an attractive means to extend the field of view of microscope images. In this paper, we propose a semi-automated solution to achieve this goal. Its intended audience is the microscopist who desires to scan a large area while acq ...

Recently, we have proposed a novel family of bivariate, non-separable splines. These splines, called "hexsplines" have been designed to deal with hexagonally sampled data. Incorporating the shape of the Voronoi cell of a hexagonal lattice, they preserve the twelve-fold symmetry of the hexagon tiling cell. Similar to B-splines, we can use them to provide a link between the discrete and the continuous domain, which is required for many fundamental operations such as interpolation and resampling. The question

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and ...

Michaël Unser

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Estimation of Stiffness Maps in Deforming Cells Through Optical Flow With Bounded Curvature

Closed-Form Expression of the Fourier Ring-Correlation for Single-Molecule Localization Microscopy

Approximation of Lipschitz Functions Using Deep Spline Neural Networks

Explicit representations for Banach subspaces of Lizorkin distributions

From Nano to Macro An overview of the IEEE Bio Image and Signal Processing Technical Committee

A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D

Effect of aging on elastin functionality in human cerebral arteries

Recursive Filtering for Splines on Hexagonal Lattices

Integrated Modeling And Reconstruction With Sparsity Constraints For fDOT

Dictionary Learning with Statistical Sparsity in the Presence of Noise

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

Approximate Message Passing With Consistent Parameter Estimation and Applications to Sparse Learning

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

MMSE Denoising of Sparse and Non-Gaussian AR(1) Processes

Fractional Laplacian Pyramids

Complex B-Splines

Method and system for the creation of an h-spline based data structure, data storage, and data representation

A Strategy Based on Maximum Spanning Trees to Stitch Together Microscope Images

On the Approximation Power of Splines: Orthogonal Versus Hexagonal Lattices

Multiresolution Subdivision Snakes