Publications by Michaël Unser

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A method for performing H-spline compatible isogeometric analysis (IGA) on a geometric object, the method being performed on a computer device having a memory, the method including the steps of creating an analysis suitable geometry (ASG) using H-splines f ...

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

Most state-of-the-art algorithms for filament detection in 3-D image-stacks rely on computing the Hessian matrix around individual pixels and labeling these pixels according to its eigenvalues. This approach, while very effective for clean data, hi which linear structures are nearly cylindrical, loses its effectiveness in the presence of noisy data and irregular structures.

We address the problem of exact signal recovery in frequency-domain optical-coherence tomography (FDOCT). The standard technique for tomogram reconstruction is the inverse Fourier transform. However, the inverse Fourier transform is known to yield autocorrelation artifacts which interfere with the desired signal. We propose a new transformation for computing an artifact-free tomogram from intensity measurements. Our technique relies on the fact that, in the FDOCT measurements, the intensity of the total sig

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theoretically. In cont ...

We present a new approach for the design of optimal steerable 2-D templates for feature detection. As opposed to classical schemes where the optimal 1-D template is derived and extended to 2-D, we directly obtain the 2-D template. We choose the template from a class of steerable functions based on the analytic optimization of a Canny-like criterion. Our approach gives more orientation selective templates that have simple closed form expression. We illustrate the method with the design of operators for edge

We present a generalization of the Daubechies wavelet family. The context is that of a non-stationary multiresolution analysis—i.e., a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. ...

Three-dimensional information about an object, such as its depth, may be captured and stored digitally in a single, two-dimensional, real-valued hologram acquired in an off-axis geometry. Digital reconstruction of the hologram permits the quantitative retr ...

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second- ...

We study the issue of localization in the context of isotropic wavelet frames. We define a variance-type measure of localization and propose an algorithm based on calculus of variations to minimize this criterion under the constraint of a tight wavelet fra ...

We present experimental investigation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object auto-correlation, commonly called the zero-order term, from holographic measurements, thereby suppressing the artifacts generated by the intensities of the two beams employed for interference from complex wavefield reconstruction. The algorithm is based on non-linear filtering, and can be applied to standard DHM setups, with realistic recording

The classical assumption in sampling and spline theories is that the input signal is square-integrable, which prevents us from applying such techniques to signals that do not decay or even grow at infinity. In this paper, we develop a sampling theory for m ...

We define and investigate the Local Rotation Invariance (LRI) and Directional Sensitivity (DS) of radiomics features. Most of the classical features cannot combine the two properties, which are antagonist in simple designs. We propose texture operators bas ...

In this paper, we focus on the problem of interpolating a continuous-time AR(1) process with stable innovations using minimum average error criterion. Stable innovations can be either Gaussian or non-Gaussian. In the former case, the optimality of the expo ...

Patient-Derived Xenografts (PDXs) are the preclinical models which best recapitulate inter- and intra-patient complexity of human breast malignancies, and are also emerging as useful tools to study the normal breast epithelium. However, data analysis gener ...

We propose new soft-prior approach for incorporating structural a priori in FDOT reconstruction. The technique is a non-linear regularization scheme based on the penalization of the (2, 1)-mixed norm. We solve the numerical reconstruction problem with an i ...

We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gra ...

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-ba ...

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9⁄7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by ...

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. We determine the theoretical optimal shift that maximizes the quality of our shifted linear interpolation. Surprisingly enough, this optimal value is nonzero and close to 1⁄5. We confirm our theoretical findings by performing several experiments: a cumulative rotation experiment and a zoom experiment. Both show a signifi

Michaël Unser

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System and method for performing isogeometric analysis and finite element analysis using h-splines

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Steerable Features for Statistical 3D Dendrite Detection

Logarithmic transformation technique for exact signal recovery in frequency-domain optical-coherence tomography - art. no. 662714

Iteratively Refined Image Reconstruction with Learned Attentive Regularizers

Optimal Steerable Filters for Feature Detection

Generalized Daubechies Wavelets

Comparing Algorithms for Reconstructing Digital Off-Axis Fresnel Holograms

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

VOW: Variance-Optimal Wavelets for the Steerable Pyramid

Artifact-free reconstruction from off-axis digital holograms through nonlinear filtering

A Sampling Theory for Non-Decaying Signals

Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

Optimal Interpolation Laws for Stable AR(1) Processes

Deep Learning Enables Individual Xenograft Cell Classification in Histological Images by Analysis of Contextual Features

A Priori Guided Reconstruction For Fdot Using Mixed Norms

Generalized Total Variation Denoising Via Augmented Lagrangian Cycle Spinning With Haar Wavelets

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Generalized Biorthogonal Daubechies Wavelets

Linear Interpolation Revitalized