Publications by Michaël Unser

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We construct parametric active contours (snakes) for outlining cells in histology images. These snakes are defined in terms of cubic B-spline basis functions. We use a steerable ridge detector for obtaining a reliable map of the cell boundaries. Using the ...

Wavelets and radial basis functions (RBF) are two rather distinct ways of representing signals in terms of shifted basis functions. An essential aspect of RBF, which makes the method applicable to non-uniform grids, is that the basis functions, unlike wavelets, are non-local—in addition, they do not involve any scaling at all. Despite these fundamental differences, we show that the two types of representation are closely connected. We use the linear splines as motivating example. These can be constructed by

We present a new family of 2D orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order α, which may be non-integer. The wavelets have good isotropy properties. We can also prove that they yield wavelet bases of

L _{ 2 }

(\Re ^{ 2 }

) for any α > 0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like

O(a ^{ \alpha }

); they also essential

We present a functional framework for the design of tight steerable wavelet frames in any number of dimensions. The 2-D version of the method can be viewed as a generalization of Simoncelli's steerable pyramid that gives access to a larger palette of steer ...

We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible ...

Background. We describe a set of image processing algorithms and mathematical models that can be advantageously used in schemes for the segmentation of thallium-201-single photon emission computed tomography (SPECT) images and for computation of left ventricular ejection fraction (EF). Methods. The system consists of two independent blocs for image segmentation and computation of function. The former is based on a multiresolution elliptical coordinate transformation and dynamic contour tracking. Computation

High resolution multidimensional image data yield huge datasets. For compression and analysis, 2D approaches are often used, neglecting the information coherence in higher dimensions, which can be exploited for improved compression. We designed a wavelet compression algorithm suited for data of arbitrary dimensions, and assessed its ability for compression of 4D medical images. Basically, separable wavelet transforms are done in each dimension, followed by quantization and standard coding. Results were comp

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an

\ell_{ 1 }

-regularization constraint, which favors sparse solutions in the wavelet dom ...

Localization microscopy such as STORM/PALM can achieve a nanometer scale spatial resolution by iteratively localizing fluorescence molecules. It was shown that imaging of densely activated molecules can accelerate temporal resolution which was considered a ...

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000) and offer a signal ...

We propose a new global registration method for estimating the cardiac displacement field in 2D sequences of ultrasound images of the heart. The basic idea is to select a reference frame (e.g., the first image of a cycle) and to map each image in the sequence to it using elastic deformation. What makes our method specific is the use of a semi-local parametric model of the deformation (spatio-temporal spline), and the reformulation of the registration task as a global spatio-temporal optimization problem. Th

We present an automatic sub-pixel registration algorithm that minimizes the mean square difference of intensities between a reference and a test data set, which can be either tri-dimensional (3-D) volumes or bi-dimensional (2-D) images. It uses spline processing, is based on a coarse-to-fine strategy (pyramid approach), and performs minimization according to a new variation of the iterative Marquardt-Levenberg algorithm for non-linear least-square optimization (MLA). The geometric deformation model is a glo

Optical projection tomography (OPT) is a powerful tool for three-dimensional (3D) imaging of mesoscopic samples. While it is able to achieve resolution of a few tens of microns over a sample volume of several cubic centimeters, the reconstructed images oft ...

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curv ...

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characteriz ...

In computational phase imaging with a microscope equipped with an array of light emitting diodes as the illumination unit, conventional Fourier ptychographic microscopy achieves high resolution and wide-field reconstructions but is constrained by a lengthy acquisition time. Conversely, differential phase contrast (DPC) offers fast imaging but is limited in resolution. Here, we introduce perturbative Fourier ptychographic microscopy (pFPM). pFPM is an extension of DPC that incorporates dark-field illuminatio

We propose a Riesz transform approach to the demodulation of digital holograms. The Riesz transform is a higher-dimensional extension of the Hilbert transform and is steerable to a desired orientation. Accurate demodulation of the hologram requires a relia ...

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems". The corresponding scripts can be accessed on GitHub (https://github.com/axgoujon/convex_ridge_regularizers). The data is organized as follows: - ct_data_sets.tar.gz: contains prepr ...

Microscopy imaging, including fluorescence microscopy and electron microscopy, has a prominent role in life science and medical research. During the past two decades, biological imaging has undergone a revolution by way of the development of new microscopy ...

In the field of image segmentation, most of level-set-based active contour approaches are based on a discrete representation of the associated implicit function. We present in this paper a different formulation where the level-set is modelled as a continuo ...

Michaël Unser

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Parametric B-Spline Snakes on Distance Maps—Application to Segmentation of Histology Images

Wavelets and Radial Basis Functions: A Unifying Perspective

Orthogonal Quincunx Wavelets with Fractional Orders

Steerable Pyramids and Tight Wavelet Frames in L_2(R^d)

3D Steerable Wavelets in Practice

Segmentation of Gated Tl-SPECT Images and Computation of Ejection Fraction: A Different Approach

Extension of Wavelet Compression Algorithms to 3D and 4D Image Data: Exploitation of Data Coherence in Higher Dimensions Allows Very High Compression Ratios

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Fast live cell imaging at nanometer scale using annihilating filter based low rank Hankel matrix approach

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

Cardiac Ultrasound Motion Detection by Elastic Registration Exploiting Temporal Coherence

A Pyramid Approach to Subpixel Registration Based on Intensity

Artifacts in optical projection tomography due to refractive-index mismatch: model and correction

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Perturbative Fourier ptychographic microscopy for fast quantitative phase imaging

Local demodulation of holograms using the Riesz transform with application to microscopy

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems"

Introduction to the Issue on Advanced Signal Processing in Microscopy and Cell Imaging

Variational B-Spline Level-Set Method for Fast Image Segmentation