Publications by Michaël Unser

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This work considers sampled data of continuous-domain Gaussian processes. We derive a maximum-likelihood estimator for identifying autoregressive moving average parameters while incorporating the sampling process into the problem formulation. The proposed ...

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 propose a wavefront-based method to estimate the PSF over the whole field of view. This method estimate the aberrations of all the mirrors of the telescope using only field stars. In this proof of concept paper, we described the method and present some ...

We perform elastic registration by an algorithm based on a pixelwise and regularized optimization criterion. We express the deformation field thanks to B-splines, which allows us to deal with a rich variety of deformations. The algorithm is able to handle soft landmark constraints, which is particularly useful when parts of the images contain very little information or when it is unevenly distributed. We solve the problem by minimizing a distance between the target image and the warped source. We regularize

We designed a complete acquisition-reconstruction framework to reduce the radiation dosage in 3D scanning transmission electron microscopy (STEM). Projection measurements are acquired by randomly scanning a subset of pixels at every tilt-view (i.e., random ...

We provide a short, self-contained introduction to deep neural networks that is aimed at mathematically inclined readers. We promote the use of a vect--matrix formalism that is well suited to the compositional structure of these networks and that facilitates the derivation/description of the backpropagation algorithm. We present a detailed analysis of supervised learning for the two most common scenarios, (i) multivariate regression and (ii) classification, which rely on the minimization of least squares an

We describe a texture classification system that identifies lung tissue patterns from high-resolution computed tomography (HRCT) images of patients affected with interstitial lung diseases (ILD). This pattern recognition task is part of an image-based diag ...

We present a new, robust, computational procedure for tracking fluorescent markers in time-lapse microscopy. The algorithm is optimized for finding the time-trajectory of single particles in very noisy dynamic (two- or three-dimensional) image sequences. I ...

We propose a framework for the detection of junctions in images. Although the detection of edges and key points is a well examined and described area, the multiscale detection of junction centers, especially for odd orders, poses a challenge in pattern ana ...

We introduce the multivariate fields of experts, a new framework for the learning of image priors. Our model generalizes existing fields of experts methods by incorporating multivariate potential functions constructed via Moreau envelopes of the

\ell_\infty

-norm. We demonstrate the effectiveness of our proposal across a range of inverse problems that include image denoising, deblurring, compressed-sensing magnetic-resonance imaging, and computed tomography. The proposed approach outperforms comparable uni

We present a simple, original method to improve piecewise linear interpolation with uniform knots: We shift the sampling knots by a fixed amount, while enforcing the interpolation property. Thanks to a theoretical analysis, we determine the optimal shift that maximizes the quality of our shifted linear interpolation. Surprisingly enough, this optimal value is nonzero and it is close to 1 ⁄ 5. We confirm our theoretical findings by performing a cumulative rotation experiment, which shows a significant increa

Mechanical properties of the adventitia are largely determined by the organization of collagen fibers. Measurements on the waviness and orientation of collagen, particularly at the zero-stress state, are necessary to relate the structural organization of c ...

We present a numerical two-step reconstruction procedure for digital off-axis Fresnel holograms. First, we retrieve the amplitude and phase of the object wave in the CCD plane. For each point we solve a weighted linear set of equations in the least-squares sense. The algorithm has O(N) complexity and gives great flexibility. Second, we numerically propagate the obtained wave to achieve proper focus. We apply the method to microscopy and demonstrate its suitability for the real time imaging of biological sam

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functional ...

We present a procedure for designing interpolation kernels that are adapted to time signals; i.e., they are causal, even though they do not have a finite support. The considered kernels are obtained by digital IIR filtering of a finite support function that has maximum approximation order. We show how to build these kernel starting from the all-pole digital filter and we give some practical design examples.

We propose a semi-automatic technique to segment corpus callosum (CC) using a two-stage snake formulation: A restricted affine transform (RAT) constrained snake followed by an unconstrained snake in an iterative fashion. A statistical model is developed to ...

We introduce a definition of the notion of compressibility for infinite deterministic and i.i.d. random sequences which is based on the asymptotic behavior of truncated subsequences. For this purpose, we use asymptotic results regarding the distribution of ...

In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise. More precisely, we describe new sample paths properties of a given noise in terms of weighted Besov spaces. In particular, we characterize the smoothness and integrab ...

State-of-the-art image reconstruction often relies on complex, abundantly parameterized deep architectures. We propose an alternative: a datadriven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively refines intermediate reconstructions by solving a sequence of quadratic problems. These updates have two key components: (i) learned filters to extract salient image features; and (ii) an attention mechanism that locally adjusts the penalty of the filter responses. Ou

Lensless inline holography can produce high-resolution images over a large field of view (FoV). In a previous work [Appl. Opt.60, B38 (2021)], we showed that (i) the actual FoV can be extrapolated outside of the camera FoV and (ii) the effective resolution ...

Michaël Unser

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Maximum-Likelihood Identification of Sampled Gaussian Processes

Deep Spline Networks With Control Of Lipschitz Regularity

Back-Propagating the Light of Field Stars to Probe Telescope Mirrors Aberrations

Algorithm for Spline-Based Elastic Registration in Application to Confocal Images of Gene Expression

Compressed Sensing for Dose Reduction in STEM Tomography

Formalizing Deep Neural Networks

Lung Tissue Classification Using Wavelet Frames

Automatic Tracking of Individual Fluorescence Particles: Application to the Study of Chromosome Dynamics

Design of Steerable Wavelets to Detect Multifold Junctions

Multivariate Fields of Experts for Convergent Image Reconstruction

How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation

Experimental investigation of collagen waviness and orientation in the arterial adventitia using confocal laser scanning microscopy

Local Amplitude and Phase Retrieval Method for Digital Holography Applied to Microscopy

Hessian-Based Regularization For 3-D Microscopy Image Restoration

High-Quality Causal Interpolation for Online Unidimensional Signal Processing

A Shape-Template Based Two-Stage Corpus Callosum Segmentation Technique for Sagittal Plane T1-Weighted Brain Magnetic Resonance Images

Compressibility of Deterministic and Random Infinite Sequences

Multidimensional Lévy White Noise in Weighted Besov Spaces

DEALing with Image Reconstruction: Deep Attentive Least Squares

A constrained method for lensless coherent imaging of thin samples