C. Vonesch

Princeton University, Princeton, NJ, United States

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Publications (29)34.08 Total impact

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    ABSTRACT: 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 temporal resolution which is a serious limitation when investigating live-cell dynamics. Here, we present an algorithm for high-density super-resolution microscopy which combines a sparsity-promoting formulation with a Taylor series approximation of the PSF. Our algorithm is designed to provide unbiased localization on continuous space and high recall rates for high-density imaging, and to have orders-of-magnitude shorter run times compared to previous high-density algorithms. We validated our algorithm on both simulated and experimental data, and demonstrated live-cell imaging with temporal resolution of 2.5 seconds by recovering fast ER dynamics.
    Scientific Reports 01/2014; 4:4577. · 5.08 Impact Factor
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    ABSTRACT: In this paper we introduce a new reconstruction algorithm for X-ray differential phase-contrast Imaging (DPCI). Our approach is based on 1) a variational formulation with a weighted data term and 2) a variable-splitting scheme that allows for fast convergence while reducing reconstruction artifacts. In order to improve the quality of the reconstruction we take advantage of higher-order total-variation regularization. In addition, the prior information on the support and positivity of the refractive index is considered, which yields significant improvement. We test our method in two reconstruction experiments involving real data; our results demonstrate its potential for in-vivo and medical imaging.
    Optics Express 12/2013; 21(26):32340-8. · 3.55 Impact Factor
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    ABSTRACT: Differential phase-contrast is a recent technique in the context of X-ray imaging. In order to reduce the specimen's exposure time, we propose a new iterative algorithm that can achieve the same quality as FBP-type methods, while using substantially fewer angular views. Our approach is based on 1) a novel spline-based discretization of the forward model and 2) an iterative reconstruction algorithm using the alternating direction method of multipliers. Our experimental results on real data suggest that the method allows to reduce the number of required views by at least a factor of four.
    Optics Express 03/2013; 21(5):5511-5528. · 3.55 Impact Factor
  • C. Vonesch, F. Stauber, M. Unser
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    ABSTRACT: This paper presents two contributions. We first introduce a continuous-domain version of Principal-Component Analysis (PCA) for designing steerable filters so that they best approximate a given set of image templates. We exploit the fact that steerability does not need to be enforced explicitly if one extends the set of templates by incorporating all their rotations. Our results extend previous work by Perona to multiple templates. We then apply our framework to the automatic detection and classification of micro-particles that carry biochemical probes for molecular diagnostics. Our continuous-domain PCA formalism is particularly well adapted in this context because the geometry of the carriers is known analytically. In addition, the steerable structure of our filters allows for a fast FFT-based recognition of the type of probe.
    Biomedical Imaging (ISBI), 2013 IEEE 10th International Symposium on; 01/2013
  • H. Kirshner, C. Vonesch, M. Unser
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    ABSTRACT: We introduce a general and computationally efficient approach to 3-D localization microscopy. The main idea is to construct a continuous-domain representation of the PSF by expanding it in a polynomial B-spline basis. This allows us to fit the PSF to the data with sub-pixel accuracy. Since the basis functions are compactly supported, the evaluation of the PSF is computationally efficient. Furthermore, our approach can accommodate for any 3-D PSF design, and it does not require a calibration curve for the axial position. We further introduce a computationally efficient implementation of the least-squares criterion and demonstrate its potential use for fast and accurate reconstruction of super-resolution data.
    Biomedical Imaging (ISBI), 2013 IEEE 10th International Symposium on; 01/2013
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    ABSTRACT: X-ray differential phase-contrast tomography is a recently-developed modality for the imaging of low-contrast biological samples. Its mathematical model is based on the first derivative of the Radon transform and the images, in practice, are reconstructed using a variant of filtered back-projection (FBP). In this paper, we develop an alternative reconstruction algorithm with the aim of reducing the number of required views, while maintaining image quality. To that end, we discretize the forward model based on polynomial B-spline functions. Then, we formulate the reconstruction as a regularized weighted-norm optimization problem with a penalty on the total variation (TV) of the solution. This leads to the derivation of a novel iterative algorithm that involves an alternation of gradient updates (FBP step) and shrinkage-thresholding (within the framework of the fast iterative shrinkage-thresholding algorithm). Experiments with real data suggest that the proposed method significantly improves upon FBP; it can handle a drastic reduction in the number of projections without noticeable degradation of the quality with respect to the standard procedure.
    Biomedical Imaging (ISBI), 2013 IEEE 10th International Symposium on; 01/2013
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    ABSTRACT: Super-resolution localization microscopy relies on sparse activation of photo-switchable probes. Such activation, however, introduces limited temporal resolution. High-density imaging overcomes this limitation by allowing several neighboring probes to be activated simultaneously. In this work, we propose an algorithm that incorporates a continuous-domain sparsity prior into the high-density localization problem. We use a Taylor approximation of the PSF, and rely on a fast proximal gradient optimization procedure. Unlike currently available methods that use discrete-domain sparsity priors, our approach does not restrict the estimated locations to a pre-defined sampling grid. Experimental results of simulated and real data demonstrate significant improvement over these methods in terms of accuracy, molecular identification and computational complexity.
    Biomedical Imaging (ISBI), 2013 IEEE 10th International Symposium on; 01/2013
  • Z. Puspoki, C. Vonesch, M. Unser
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    ABSTRACT: 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 micrographs. The analysis with 2-D steerable wavelets allows us to have detections at different scales and arbitrary orientations. Owing to the steering property of our wavelets the detection is fast and accurate. We provide experimental results on both synthetic images and biological micrographs to demonstrate the performance of the algorithm.
    Biomedical Imaging (ISBI), 2013 IEEE 10th International Symposium on; 01/2013
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    ABSTRACT: This paper presents a novel algorithm for the 3D tomographic inversion problem that arises in single-particle electron cryo-microscopy (Cryo-EM). It is based on two key components: 1) a variational formulation that promotes sparsity in the wavelet domain and 2) the Toeplitz structure of the combined projection/back-projection operator. The first idea has proven to be very effective for the recovery of piecewise-smooth signals, which is confirmed by our numerical experiments. The second idea allows for a computationally efficient implementation of the reconstruction procedure, using only one circulant convolution per iteration.
    Proceedings / IEEE International Symposium on Biomedical Imaging: from nano to macro. IEEE International Symposium on Biomedical Imaging 06/2011; 2011:1950-1953.
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    ABSTRACT: We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies with position within the Earth. Our procedure is numerically efficient and can be implemented with parallel computing. We discuss two possible types of discrete wavelet transforms in the angular dimension of the cubed sphere. We discuss benefits and drawbacks of these constructions and apply them to analyze the information present in two published seismic wavespeed models of the mantle, for the statistics and power of wavelet coefficients across scales. The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the $\ell_2$ norm of data fit and the $\ell_1$ norm on the wavelet coefficients. By validation with realistic synthetic experiments we illustrate the likely gains of our new approach in future inversions of finite-frequency seismic data and show its readiness for global seismic tomography.
    Geophysical Journal International 04/2011; 187. · 2.85 Impact Factor
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    ABSTRACT: The computation of finite frequency kernels using dynamic ray tracing, as originally proposed by Dahlen et al. (GJI, 2000) is very efficient, but the method has several disadvantages: it is prone to ambiguities and errors whenever the radius of curvature of a ray is smaller than the effective width of a kernel, and it breaks down completely for rays, such as PP or PKP that may reach as far as the antipode. Motivated by the development of a wavelet parameterization in a `cubed sphere', we have developed a new method for the fast computation of travel times and geometrical spreading factors. First, we confined our calculations to a finite set of discrete radii. The goal then is to find the travel time and spreading factors for an arbitrary location along one of these radii. We use a traditional method to compute a fine fan of rays through a spherically symmetric model. For each ray we obtain the travel time and its second derivative with respect to distance from the ray in the ray plane, and the geometrical spreading at a series of nodes, typically spaced 15 km apart. These values are then interpolated to obtain data along each of the radii, resulting in a finite set (for each radius) of closely sampled data. Different arrivals are recognized by non-monotonic behaviour of the time as function of distance. Travel times and geometrical spreading at arbitrary locations can be computed in two ways from this grid: either one interpolates from the times and spreading stored on the grid points, or one extrapolates a small distance from the nearest ray using dynamic ray tracing. We compare the two methods for efficiency and accuracy.
    05/2010;
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    ABSTRACT: Global seismic wavespeed models are routinely parameterized in terms of spherical harmonics, networks of tetrahedral nodes, rectangular voxels, or spherical splines. Up to now, Earth model parametrizations by wavelets on the three-dimensional ball remain uncommon. Here we propose such a procedure with the following three goals in mind: (1) The multiresolution character of a wavelet basis allows for the models to be represented with an effective spatial resolution that varies as a function of position within the Earth. (2) This property can be used to great advantage in the regularization of seismic inversion schemes by seeking the most sparse solution vector, in wavelet space, through iterative minimization of a combination of the ℓ2 (to fit the data) and ℓ1 norms (to promote sparsity in wavelet space). (3) With the continuing increase in high-quality seismic data, our focus is also on numerical efficiency and the ability to use parallel computing in reconstructing the model. In this presentation we propose a new wavelet basis to take advantage of these three properties. To form the numerical grid we begin with a surface tesselation known as the 'cubed sphere', a construction popular in fluid dynamics and computational seismology, coupled with an semi-regular radial subdivison that honors the major seismic discontinuities between the core-mantle boundary and the surface. This mapping first divides the volume of the mantle into six portions. In each 'chunk' two angular and one radial variable are used for parametrization. In the new variables standard 'cartesian' algorithms can more easily be used to perform the wavelet transform (or other common transforms). Edges between chunks are handled by special boundary filters. We highlight the benefits of this construction and use it to analyze the information present in several published seismic compressional-wavespeed models of the mantle, paying special attention to the statistics of wavelet and scaling coefficients across scales. We also focus on the likely gains of future inversions of finite-frequency seismic data using a sparsity promoting penalty in combination with our new wavelet approach.
    04/2010; 12:6033.
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    ABSTRACT: We present a fast algorithm for image restoration in the presence of Poisson noise. Our approach is based on (1) the minimization of an unbiased estimate of the MSE for Poisson noise, (2) a linear parametrization of the denoising process and (3) the preservation of Poisson statistics across scales within the Haar DWT. The minimization of the MSE estimate is performed independently in each wavelet subband, but this is equivalent to a global image-domain MSE minimization, thanks to the orthogonality of Haar wavelets. This is an important difference with standard Poisson noise-removal methods, in particular those that rely on a non-linear preprocessing of the data to stabilize the variance.Our non-redundant interscale wavelet thresholding outperforms standard variance-stabilizing schemes, even when the latter are applied in a translation-invariant setting (cycle-spinning). It also achieves a quality similar to a state-of-the-art multiscale method that was specially developed for Poisson data. Considering that the computational complexity of our method is orders of magnitude lower, it is a very competitive alternative.The proposed approach is particularly promising in the context of low signal intensities and/or large data sets. This is illustrated experimentally with the denoising of low-count fluorescence micrographs of a biological sample.
    Signal Processing 01/2010; · 1.85 Impact Factor
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    F. Luisier, C. Vonesch, T. Blu, M. Unser
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    ABSTRACT: We propose a novel denoising algorithm to reduce the Poisson noise that is typically dominant in fluorescence microscopy data. To process large datasets at a low computational cost, we use the unnormalized Haar wavelet transform. Thanks to some of its appealing properties, independent unbiased MSE estimates can be derived for each subband. Based on these Poisson unbiased MSE estimates, we then optimize linearly parametrized interscale thresholding. Correlations between adjacent images of the multidimensional data are accounted for through a sliding window approach. Experiments on simulated and real data show that the proposed solution is qualitatively similar to a state-of-the-art multiscale method, while being orders of magnitude faster.
    Biomedical Imaging: From Nano to Macro, 2009. ISBI '09. IEEE International Symposium on; 08/2009
  • Cédric Vonesch, Michael Unser
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    ABSTRACT: We present a multilevel extension of the popular "thresholded Landweber" algorithm for wavelet-regularized image restoration that yields an order of magnitude speed improvement over the standard fixed-scale implementation. The method is generic and targeted towards large-scale linear inverse problems, such as 3-D deconvolution microscopy. The algorithm is derived within the framework of bound optimization. The key idea is to successively update the coefficients in the various wavelet channels using fixed, subband-adapted iteration parameters (step sizes and threshold levels). The optimization problem is solved efficiently via a proper chaining of basic iteration modules. The higher level description of the algorithm is similar to that of a multigrid solver for PDEs, but there is one fundamental difference: the latter iterates though a sequence of multiresolution versions of the original problem, while, in our case, we cycle through the wavelet subspaces corresponding to the difference between successive approximations. This strategy is motivated by the special structure of the problem and the preconditioning properties of the wavelet representation. We establish that the solution of the restoration problem corresponds to a fixed point of our multilevel optimizer. We also provide experimental evidence that the improvement in convergence rate is essentially determined by the (unconstrained) linear part of the algorithm, irrespective of the type of wavelet. Finally, we illustrate the technique with some image deconvolution examples, including some real 3-D fluorescence microscopy data.
    IEEE Transactions on Image Processing 03/2009; 18(3):509-23. · 3.20 Impact Factor
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    ABSTRACT: We propose a reconstruction scheme adapted to MRI that takes advantage of a sparsity constraint in the wavelet domain. We show that artifacts are significantly reduced compared to conventional reconstruction methods. Our approach is also competitive with total variation regularization both in terms of MSE and computation time. We show that lscr<sup>1</sup> regularization allows partial recovery of the missing k-space regions. We also present a multi-level version that significantly reduces the computational cost.
    Proceedings of the 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Boston, MA, USA, June 28 - July 1, 2009; 01/2009
  • Approximation and Optimization in Image Restoration and Reconstruction (AOIRR'09); 01/2009
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    C. Vonesch, M. Unser
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    ABSTRACT: Wavelet-domain lscr<sub>1</sub>-regularization is a promising approach to deconvolution. The corresponding variational problem can be solved using a "thresholded Landweber" (TL) algorithm. While this iterative procedure is simple to implement, it is known to converge slowly. In this paper, we give the principle of a modified algorithm that is substantially faster. The method is applicable to arbitrary wavelet representations, thus generalizing our previous work which was restricted to the or- thonormal Shannon wavelet basis. Numerical experiments show that we can obtain up to a 10-fold speed-up with respect to the existing TL algorithm, while providing the same restoration quality. We also present an example with real data that demonstrates the feasibility of wavelet-domain regularization for 3D deconvolution microscopy.
    Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008
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    S. Ramani, C. Vonesch, M. Unser
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    ABSTRACT: We investigate the problem of automatic tuning of a deconvolution algorithm for three-dimensional (3D) fluorescence microscopy; specifically, the selection of the regularization parameter lambda. For this, we consider a realistic noise model for data obtained from a CCD detector: Poisson photon-counting noise plus Gaussian read-out noise. Based on this model, we develop a new risk measure which unbiasedly estimates the original mean-squared-error of the deconvolved signal estimate. We then show how to use this risk estimate to optimize the regularization parameter for Tikhonov-type deconvolution algorithms. We present experimental results on simulated data and numerically demonstrate the validity of the proposed risk measure. We also present results for real 3D microscopy data.
    Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008
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    C Vonesch, M Unser
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    ABSTRACT: We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the l(1)-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alternating between a Landweber iteration and a wavelet-domain soft-thresholding operation. While having the advantage of simplicity, they are known to converge slowly. By expressing the cost functional in a Shannon wavelet basis, we are able to decompose the problem into a series of subband-dependent minimizations. In particular, this allows for larger (subband-dependent) step sizes and threshold levels than the previous method. This improves the convergence properties of the algorithm significantly. We demonstrate a speed-up of one order of magnitude in practical situations. This makes wavelet-regularized deconvolution more widely accessible, even for applications with a strong limitation on computational complexity. We present promising results in 3-D deconvolution microscopy, where the size of typical data sets does not permit more than a few tens of iterations.
    IEEE Transactions on Image Processing 05/2008; 17(4):539-49. · 3.20 Impact Factor

Publication Stats

260 Citations
34.08 Total Impact Points

Institutions

  • 2011
    • Princeton University
      • Program in Applied and Computational Mathematics
      Princeton, NJ, United States
  • 2010
    • The Chinese University of Hong Kong
      • Department of Electronic Engineering
      Hong Kong, Hong Kong
  • 2005–2010
    • École Polytechnique Fédérale de Lausanne
      • Laboratoire d'optique biomédicale
      Lausanne, Vaud, Switzerland