Dr. Bo Zhang Profile

Dr. Bo Zhang

at Institut Pasteur

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Publications (2)

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Proceedings Article | 3 September 2009 Paper

Poisson noise removal in multivariate count data

J. Fadili, J.-L. Starck, B. Zhang, S. Digel

Proceedings Volume 7446, 74461B (2009) https://doi.org/10.1117/12.825063

KEYWORDS: Wavelets, Denoising, Wavelet transforms, Linear filtering, Reconstruction algorithms, Gamma radiation, Photons, Hyperspectral imaging, Astronomy, Binary data

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The Multi-scale Variance Stabilization Transform (MSVST) has recently been proposed for 2D Poisson data denoising.¹ In this work, we present an extension of the MSVST with the wavelet transform to multivariate data-each pixel is vector-valued-, where the vector field dimension may be the wavelength, the energy, or the time. Such data can be viewed naively as 3D data where the third dimension may be time, wavelength or energy (e.g. hyperspectral imaging). But this naive analysis using a 3D MSVST would be awkward as the data dimensions have different physical meanings. A more appropriate approach would be to use a wavelet transform, where the time or energy scale is not connected to the spatial scale. We show that our multivalued extension of MSVST can be used advantageously for approximately Gaussianizing and stabilizing the variance of a sequence of independent Poisson random vectors. This approach is shown to be fast and very well adapted to extremely low-count situations. We use a hypothesis testing framework in the wavelet domain to denoise the Gaussianized and stabilized coefficients, and then apply an iterative reconstruction algorithm to recover the estimated vector field of intensities underlying the Poisson data. Our approach is illustrated for the detection and characterization of astrophysical sources of high-energy gamma rays, using realistic simulated observations. We show that the multivariate MSVST permits efficient estimation across the time/energy dimension and immediate recovery of spectral properties.

Proceedings Article | 23 February 2006 Paper

A study of Gaussian approximations of fluorescence microscopy PSF models

Bo Zhang, Josiane Zerubia, Jean-Christophe Olivo-Marin

Proceedings Volume 6090, 60900K (2006) https://doi.org/10.1117/12.645650

KEYWORDS: Point spread functions, Microscopy, Luminescence, Confocal microscopy, 3D modeling, Data modeling, Objectives, Data processing, Expectation maximization algorithms, Deconvolution

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Despite the availability of rigorous physical models of microscopy point spread functions (PSFs), approximative PSFs, particularly separable Gaussian approximations are widely used in practical microscopic data processing. In fact, compared with a physical PSF model, which usually involves non-trivial terms such as integrals and infinite series, a Gaussian function has the advantage that it is much simpler and can be computed much faster. Moreover, due to its special analytical form, a Gaussian PSF is often preferred to facilitate the analysis of theoretical models such as Fluorescence Recovery After Photobleaching (FRAP) process and of processing algorithms such as EM deconvolution. However, in these works, the selection of Gaussian parameters and the approximation accuracy were rarely investigated. In this paper, we present a comprehensive study of Gaussian approximations for diffraction-limited 2D/3D paraxial/non-paraxial PSFs of Wide Field Fluorescence Microscopy (WFFM), Laser Scanning Confocal Microscopy (LSCM) and Disk Scanning Confocal Microscopy (DSCM) described using the Debye integral. Besides providing an optimal Gaussian parameter for the 2D paraxial WFFM PSF case, we further derive nearly optimal parameters in explicit forms for each of the other cases, based on Maclaurin series matching. Numerical results show that the accuracy of the 2D approximations is very high (Relative Squared Error (RSE) < 2% in WFFM, < 0.3% in LSCM and < 4% in DSCM). For the 3D PSFs, the approximations are average in WFFM (RSE ≃ 16-20%), accurate in DSCM (RSE≃ 3-6%) and nearly perfect in LSCM (RSE ≃ 0.3-0.5%).

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