Publications by Michaël Unser

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In this paper, we propose a new technique for high-quality reconstruction from single digital holographic acquisitions. The unknown complex object field is found as the solution of a nonlinear inverse problem that consists in the minimization of an energy ...

We propose a new, cost-efficient method for computing back projections in parallel-ray X-ray CT. Forward and back projections are the basis of almost all X-ray CT reconstruction methods, but computing these accurately is costly. In the special case of para ...

The commonality between splines and Gaussian or sparse stochastic processes is that they are ruled by the same type of differential equations. Our purpose here is to demonstrate that this has profound implications for the three primary forms of sampling: u ...

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

We demonstrate that it is possible to filter an image with an elliptic window of varying size, elongation and orientation with a fixed computational cost per pixel. Our method involves the application of a suitable global pre-integrator followed by a point ...

We introduce a general and computationally efficient approach to 3-D localization microscopy. The main idea is to construct a continuous-domain representation of the PSF by expanding it in a polynomial B-spline basis. This allows us to fit the PSF to the d ...

We investigate the learning of a convex patch-based synthesis model for the reconstruction of images. In essence, we propose to learn a dictionary via bilevel optimization for denoising. Using implicit differentiation, we find a closed-form formula of the ...

We introduce a new semi-orthogonal complex wavelet basis of L-2(R-2). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single-generator wavelet that is shi ...

To study biological signalling, great effort goes into designing sensors whose fluorescence follows the concentration of chemical messengers as closely as possible. However, the binding kinetics of the sensors are often overlooked when interpreting cell si ...

We propose a robust autofocus method for reconstructing digital Fresnel holograms. The numerical reconstruction involves simulating the propagation of a complex wave front to the appropriate distance. Since the latter value is difficult to determine manually, it is desirable to rely on an automatic procedure for finding the optimal distance to achieve high-quality reconstructions. Our algorithm maximizes a sharpness metric related to the sparsity of the signal's expansion in distance-dependent waveletlike F

We propose an active contour (a.k.a. snake) that takes the shape of an ellipse. Its evolution is driven by surface terms made of two contributions: the integral of the data over an inner ellipse, counterbalanced by the integral of the data over an outer el ...

A fast computational method is given for the Fourier transform of the polyharmonic B-spline autocorrelation sequence in d dimensions. The approximation error is exponentially decaying with the number of terms taken into account. The algorithm improves spee ...

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

We introduce an exponential-based consistent approach to image scaling. Our model stems from Sobolev reproducing kernels, motivated by their role in continuous-domain stochastic autoregressive processes. The proposed approach imposes consistency and applie ...

In this paper we propose a new, interactive technique for the segmentation of elongated structures in images. It is based on the so-called live-wire segmentation paradigm and uses a newly developed steerable filter for computing local ridge strength and orientation. We describe the principles of our segmentation technique and present the results of preliminary experiments demonstrating its potential for the tracing of neurites in fluorescence microscopy images.

We investigate the approximation error of functions with continuous and piecewise-linear (CPWL) representations. We focus on the CPWL search spaces generated by translates of box splines on two-dimensional regular lattices. We compute the approximation error in terms of the stepsize, length ratio, and angle that define the lattice. Our results show that hexagonal lattices are optimal, in the sense that they minimize the asymptotic approximation error.

A broad class of imaging modalities involve the resolution of an inverse-scattering problem. Among them, three-dimensional optical diffraction tomography (ODT) comes with its own challenges. These include a limited range of views, a large size of the sampl ...

We present a new trigonometric basis function that is capable of perfectly reproducing circles, spheres and ellipsoids while at the same time being interpolatory. Such basis functions have the advantage that they allow to construct shapes through a sequenc ...

Michaël Unser

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A Practical Inverse-Problem Approach to Digital Holographic Reconstruction

High-Quality Parallel-Ray x-Ray CT Back Projection Using Optimized Interpolation

Sampling and (Sparse) Stochastic Processes: A Tale of Splines and Innovation

Dictionary Learning for Two-Dimensional Kendall Shapes

Fast Adaptive Elliptical Filtering Using Box Splines

Can Localization Microscopy Benefit From Approximation Theory?

Learning a Convex Patch-Based Synthesis Model via Deep Equilibrium

Unsupervised Image Classification of Medical Ultrasound Data by Multiresolution Elastic Registration

The Marr Wavelet Pyramid

Deep-prior ODEs augment fluorescence imaging with chemical sensors

Autofocus for Digital Fresnel Holograms by Use of a Fresnelet-Sparsity Criterion

The Ovuscule

Vision-Based System for the Control and Measurement of Wastewater Flow Rate in Sewer Systems

Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

A Stochastic Minimum-Norm Approach to Image and Texture Interpolation

A Novel Approach to Neurite Tracing in Fluorescence Microscopy Images

Comparison of 2D Regular Lattices for the CPWL Approximation of Functions

Three-Dimensional Optical Diffraction Tomography With Lippmann-Schwinger Model

Trigonometric Interpolation Kernel to Construct Deformable Shapes for User-Interactive Applications