Publications by Michaël Unser

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Shannon's sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some “shift-invariant” space, which may or may not be bandlimited. In this paper, we present some further justification for ...

Frequency domain optical coherence tomography (FDOCT) is a new technique that is well-suited for fast imaging of biological specimens, as well as non-biological objects. The measurements are in the frequency domain, and the objective is to retrieve an arti ...

Summary The continuous wavelet transform (CWT) is a common signal-processing tool for the analysis of nonstationary signals. We propose here a new B-spline-based method that allows the CWT computation at any scale. A nice property of the algorithm is that the computational cost is independent of the scale value. Its complexity is of the same order as that of the fastest published methods, without being restricted to dyadic or integer scales. The method reduces to the filtering of an auxiliary (pre-integrate

New phase-shifting techniques have recently been proposed to suppress the complex-conjugate ambiguity in frequency-domain optical-coherence tomography. A phase shift is introduced, in an elegant fashion, by incorporating a small beam offset at the scanning ...

In this paper, we propose an algorithm for automated segmentation of midsagittal brain MR images. First, we apply thresholding to obtain binary images. From the binary images, we locate some landmarks. Based on the landmarks and anatomical information, we preprocess the binary images, which substantially simplifies the subsequent operations. To separate regions that are incorrectly merged after this initial segmentation, a new connectivity-based threshold algorithm is proposed. Assuming that some prior info

In this chapter, we provide an overview of a recent image-reconstruction method that uses a deep generative algorithm for dynamic magnetic resonance-imaging (dMRI). We begin by briefly introducing the imaging modality of dMRI, the associated image-reconstruction problem, and existing reconstruction approaches. Next, we introduce the time-dependent deep image prior (TD-DIP), which exploits the structure of convolutional neural networks (CNNs) as a regularizing prior. We show some representative results and d

This paper presents an interpolation method based on shifted versions of two piecewise linear generators, which provides approximation order 2 like usual piecewise-linear interpolation; i.e., this method is able to represent the constant and the ramp exactly. Our interpolation is characterized by two real parameters: τ, the location of the generators, and α, related to their dissymmetry. By varying these parameters, we show that it is possible to optimize the quality of the approximation, independently of t

The identification and accurate location of centers of brain activity are vital both in neuro-surgery and brain research. This study aimed to provide a non-invasive, non-contact, accurate, rapid and user-friendly means of producing functional images intrao ...

Magnetic resonance spectroscopy imaging (MRSI) is an attractive tool for medical imaging. However, its practical use is often limited by the intrinsic low spatial resolution and long acquisition time. Spectral localization by imaging (SLIM) has been propos ...

We present an algorithm for fast elastic multidimensional intensity-based image registration with a parametric model of the deformation. It is fully automatic in its default mode of operation. In the case of hard real-world problems, it is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. Particular attention has been paid to the factors influencing the speed of this algorithm.

We define a new wavelet transform that is based on a recently defined family of scaling functions: the fractional B-splines. The interest of this family is that they interpolate between the integer degrees of polynomial B-splines and that they allow a fractional order of approximation. The orthogonal fractional spline wavelets essentially behave as a fractional differentiators. This property seems promising for the analysis of

1/f ^{ \alpha }

; noise that can be whitened by an appropriate choice of the

In this article, we review recent uses of convolutional neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding performance on object clas ...

Optical projection tomography (OPT) is a powerful tool for biomedical studies. It achieves 3D visualization of mesoscopic biological samples with high spatial resolution using conventional tomographic-reconstruction algorithms. However, various artifacts d ...

The paper provides a short introduction to wavelets and discusses their main applications in microscopy and biological imaging. ...

We formulate computed-tomography reconstruction as a continuous-domain optimization problem with Hessian total variation (HTV) as the regularizer. HTV is a sparsity-promoting regularizer that favors continuous and piecewise-linear functions with few affine ...

We propose a novel method for image reconstruction from nonuniform samples with no constraints on their locations. We adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the ...

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear coun ...

We introduce a new approach for the implementation of minimum mean-square error (MMSE) denoising for signals with decoupled derivatives. Our method casts the problem as a penalized least-squares regression in the redundant wavelet domain. It exploits the l ...

The field of biological imaging has evolved considerably during the past decade as a result of recent (r)evolutions in fluorescence labeling and optical microscopy. Bioimage informatics has been identified as a top priority to cope with the ever-increasing ...

Ill-posed inverse problems are often constrained by imposing a bound on the total variation of the solution. Here, we consider a generalized version of total-variation regularization that is tied to some differential operator L. We then show that the gener ...

Michaël Unser

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Nonideal Sampling and Regularization Theory

A new technique for high-resolution frequency domain optical coherence tomography

Continuous Wavelet Transform with Arbitrary Scales and O(N) Complexity

Theoretical analysis of complex-conjugate-ambiguity suppression in frequency-domain optical-coherence tomography

Unsupervised Connectivity-Based Thresholding Segmentation of Midsagittal Brain MR Images

Regularizing Deep-Neural-Network Paradigm for the Reconstruction of Dynamic Magnetic Resonance Images

Interpolation of Signals by Generalized Piecewise-Linear Multiple Generators

Laser Doppler imaging for intraoperative human brain mapping

BSLIM: Spectral Localization by Imaging with Explicit $ B _{ 0 } $ Field Inhomogeneity Compensation

Fast Parametric Elastic Image Registration

The Fractional Spline Wavelet Transform: Definition and Implementation

Convolutional Neural Networks for Inverse Problems in Imaging—A Review

Mechanical artifacts in optical projection tomography: classification and automatic calibration

Wavelets: on the virtues and applications of the mathematical microscope

A Continuous-Domain Solution for Computed Tomography with Hessian Total-Variation Regularization

Variational Image Reconstruction from Arbitrarily Spaced Samples: A Fast Multiresolution Spline Solution

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

Advanced Image Processing for Biology, and the Open Bio Image Alliance (OBIA)

Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization