Publications by Michaël Unser

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We address the problem of tomogram reconstruction in frequency-domain optical-coherence tomography. We propose a new technique for suppressing the autocorrelation artifacts that are commonly encountered with the conventional Fourier-transform-based approac ...

We present a 3D iterative reconstruction method for microtomography, where iterative methods have previously been limited by their high computational cost. Our preliminary results show that it improves reconstruction quality over the traditional slice-by-s ...

Single-molecule localization microscopy (SMLM) is a fluorescence microscopy technique that achieves super-resolution imaging by sequentially activating and localizing random sparse subsets of fluorophores. Each activated fluorophore emits light that then s ...

We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9⁄7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynom ...

We propose a novel active contour for the analysis of filament-like structures and boundaries—features that traditional snakes based on closed curves have difficulties to delineate. Our method relies on a parametric representation of an open curve involvin ...

We present a unifying framework for the development of state-of-the-art reconstruction algorithms in computational optics with a clear separation between the physical (forward model) and signal-related (regularization, incorporation of prior constraints) a ...

We address the problem of zero-order-free image reconstruction in digital holographic microscopy. We show how the goal can be achieved by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave inte ...

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

We introduce Flower, a solver for linear inverse problems. It leverages a pretrained flow model to produce reconstructions that are consistent with the observed measurements. Flower operates through an iterative procedure over three steps: (i) a flow-consistent destination estimation, where the velocity network predicts a denoised target; (ii) a refinement step that projects the estimated destination onto a feasible set defined by the forward operator; and (iii) a timeprogression step that re-projects the r

One of the main applications of electrophoretic 2-D gels is the analysis of differential responses between different conditions. For this reason, specific spots are present in one of the images, but not in the other. In some other occasions, the same exper ...

B-splines are attractive basis functions for the continuous-domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their ...

Most bioimaging modalities rely on indirect measurements of the quantity under investigation. The image is obtained as the result of an optimization problem involving a physical model of the measurement system. Due to the ill-posedness of the above problem ...

We propose the use of polyharmonic B-splines to build non-separable two-dimensional wavelet bases. The central idea is to base our design on the isotropic polyharmonic B-splines, a new type of polyharmonic B-splines that do converge to a Gaussian as the order increases. We opt for the quincunx subsampling scheme which allows us to characterize the wavelet spaces with a single wavelet: the isotropic-polyharmonic B-spline wavelet. Interestingly, this wavelet converges to a combination of four Gabor atoms, whi

We use cryo-electron microscopy to compare 3D shapes of 158 bp long DNA minicircles that differ only in the sequence within an 18 bp block containing either a TATA box or a catabolite activator protein binding site. We present a sorting algorithm that corr ...

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. Whi ...

We study 1D continuous-domain inverse problems for multicomponent signals. The prior assumption on these signals is that each component is sparse in a different dictionary specified by a regularization operators. We introduce a hybrid regularization functi ...

We consider the class of continuous-time autoregressive (CAR) processes driven by (possibly non-Gaussian) Lévy white noises. When the excitation is an impulsive noise, also known as compound Poisson noise, the associated CAR process is a random non-uniform ...

In this paper, we propose a novel second-order regularizer based on the maximum response of the second-order directional derivative, assuming that the image under consideration belongs to the class of piecewise-linear signals. Compared to total-variation r ...

CryoGAN uses ideas from deep generative adversarial learning to perform image reconstruction in single-particle cryo-electron microscopy (cryo-EM). In this chapter, we begin by introducing single-particle cryo-EM. We then formulate the associated image-reconstruction problem and discuss the main solutions found in the literature. Next, we describe the CryoGAN algorithm and show some representative results. Finally, we discuss what our experiences with Cryo-GAN suggest about the advantages and disadvantages

Michaël Unser

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Exact and Efficient Signal Reconstruction in Frequency-Domain Optical-Coherence Tomography

Slice-by-Slice versus Fully 3D Reconstruction for Parallel-Beam x-Ray Microtomography

Diffraction Tomography from Single-Molecule Localization Microscopy: Numerical Feasibility

Generalized Daubechies Wavelet Families

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

GlobalBioIm: A Unifying Computational Framework for Solving Inverse Problems

Self-Similarity: Part II—Optimal Estimation of Fractal Processes

Zero-Order-Free Image Reconstruction in Digital Holographic Microscopy

Shift-Invariant Spaces from Rotation-Covariant Functions

Flower: A Flow-Matching Solver for Inverse Problems

Elastic Image Registration of 2-D Gels for Differential and Repeatability Studies

A Box Spline Calculus for Computed Tomography

Efficient Image Reconstruction Under Sparsity Constraints With Application To Mri And Bioluminescence Tomography

Isotropic-Polyharmonic B-Splines and Wavelets

3D Reconstruction and Comparison of Shapes of DNA Minicircles Observed by Cryo-Electron Microscopy

Snakes With an Ellipse-Reproducing Property

Sparse Dictionaries for Continuous-Domain Inverse Problems

Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

A Second-Order Extension Of Tv Regularization For Image Deblurring

CryoGAN: A Deep Generative Adversarial Approach to Single-Particle Cryo-EM