Publications by Michaël Unser

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Mutual information is an attractive registration criterion because it provides a meaningful comparison of images that represent different physical properties. In this paper, we review the shortcomings of three published methods for its computation. We identify the grid effect and the overlap problem as the most severe artifacts that these methods face, and propose a solution based on irregular sampling to solve for the grid effect. By implementing irregular sampling as stochastic sampling, we see that our s

We present a new method for estimating heart motion from two-dimensional echocardiographic sequences by exploiting two ultrasound modalities: B-mode and tissue Doppler. The algorithmestimates a two-dimensional velocity field locally by using a spatial affine velocity model inside a sliding window. Within each window, we minimize a local cost function that is composed of two quadratic terms: an optical flow constraint that involves the B-mode data and a constraint that enforces the agreement of the velocity

We investigate the functions of given approximation order L that have the smallest support. Those are shown to be linear combinations of the B-spline of degree L-1 and its L-1 first derivatives. We then show how to find the functions that minimize the asymptotic approximation constant among this finite dimension space; in particular, a tractable induction relation is worked out. Using these functions instead of splines, we observe that the approximation error is dramatically reduced, not only in the limit w

BACKGROUND: Identification of embryos with high implantation potential remains a challenge in in vitro fertilization (IVF). Subjective pronuclear (PN) zygote scoring systems have been developed for that purpose. The aim of this work was to provide a softwa ...

We adopt an innovation-driven framework and investigate the sparse/compressible distributions obtained by linearly measuring or expanding continuous-domain stochastic models. Starting from the first principles, we show that all such distributions are neces ...

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Levy white noises. A recent paper showed that these processes are limits in law of generalized compound-P ...

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the

\ell ^{ 1 }

-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alte ...

In this paper we introduce a 3D wavelet frame that has the key property of steerability. The proposed wavelet frame relies on the combination of a 3D isotropic wavelet transform with the 3D Riesz operator which brings steerability to the pyramid. The novel ...

We have developed an algorithm for the rigid-body registration of a 3D CT to a set of C-arm images by matching them to computed cone-beam projections of the CT (DRRs). We precomputed rescaled versions (pyramid) of the CT volume and of the C-arm images. We perform the registration of the CT to the C-arm images starting from their coarsest resolution until we reach some finer resolution that offers a good compromise between time and accuracy. To achieve precision, we use a cubic-spline data model to compute t

As the field of bioimage informatics matures, the issue of the validation of image reconstruction algorithms and the definition of proper performance criteria becomes more pressing. In this work, we discuss benchmarking aspects of fluorescence microscopy q ...

We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal, curvature-constrained snake is a cubic spline, irrespective of the form of the external energy field. Unfortunately, such regularized snakes suffer from slow convergence speed because of a large number of control points, as well as from difficulties in determining the weight

We consider the problem of sampling continuous-time auto-regressive processes on a uniform grid. We investigate whether a given sampled process originates from a single continuous-time model, and address this uniqueness problem by introducing an alternativ ...

We suggest a continuous-domain stochastic modeling of images that is invariant to spatial resolution. Specifically, we are proposing an estimator that is calibrated with respect to the sampling step, and that can potentially handle aliased data. Motivated ...

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform indepe ...

We present a modified version of the deconvolution algorithm introduced by Figueiredo and Nowak, which leads to a substantial acceleration. The algorithm essentially consists in alternating between a Landweber-type iteration and a wavelet-domain denoising ...

Super resolution microscopy such as STORM and (F) PALM is now a well known method for biological studies at the nanometer scale. However, conventional imaging schemes based on sparse activation of photo-switchable fluorescent probes have inherently slow te ...

We describe a new family of scaling functions, the (α, τ)-fractional splines, which generate valid multiresolution analyses. These functions are characterized by two real parameters: α, which controls the width of the scaling functions; and τ, which specifies their position with respect to the grid (shift parameter). This new family is complete in the sense that it is closed under convolutions and correlations. We give the explicit time and Fourier domain expressions of these fractional splines. We prove th

We present a method for designing steerable wavelets that can detect local centers of symmetry in images. Based on this design, we then propose an algorithm for estimating the locations and the orientations of M-fold symmetric junctions in biological micro ...

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...

We consider the reconstruction of multi-dimensional signals from noisy samples. The problem is formulated within the framework of the theory of continuous-domain sparse stochastic processes. In particular, we study the fractional Laplacian as the whitening ...

Michaël Unser

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Stochastic Sampling for Computing the Mutual Information of Two Images

Bimodal Myocardial Motion Analysis from B-Mode and Tissue Doppler Ultrasound

Minimum Support Interpolators with Optimum Approximation Properties

Quantitative Morphometrical Characterization of Human Pronuclear Zygotes

Sparsity and Infinite Divisibility

Generating Sparse Stochastic Processes Using Matched Splines

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

3D Steerable Wavelets And Monogenic Analysis For Bioimaging

Multiresolution-Based Registration of a Volume to a Set of Its Projections

Benchmarking Image-Processing Algorithms for Biomicroscopy: Reference Datasets and Perspectives

B-Spline Snakes: A Flexible Tool for Parametric Contour Detection

Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?

Resolution-Invariant Separable Arma Modeling Of Images

Optimized Kaiser-Bessel Window Functions for Computed Tomography

Fast wavelet regularized image deconvolution

FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data

A Complete Family of Scaling Functions: The (α, τ)-Fractional Splines

Detection Of Symmetric Junctions In Biological Images Using 2-D Steerable Wavelet Transforms

Stability of Image-Reconstruction Algorithms

MAP Estimators for Self-Similar Sparse Stochastic Models