Poisson noise removal in multivariate count data

J. M. Fadili; J.-L. Starck; B. Zhang; S. Digel

doi:10.1117/12.825063

3 September 2009 Poisson noise removal in multivariate count data

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

Proceedings Volume 7446, Wavelets XIII; 74461B (2009) https://doi.org/10.1117/12.825063
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

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.

Citation Download Citation

J. M. Fadili, J.-L. Starck, B. Zhang, and S. Digel "Poisson noise removal in multivariate count data", Proc. SPIE 7446, Wavelets XIII, 74461B (3 September 2009); https://doi.org/10.1117/12.825063

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
11 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Wavelets

Denoising

Wavelet transforms

Linear filtering

Reconstruction algorithms

Gamma radiation

Photons

Show All Keywords

Keywords/Phrases

Search In:

Publication Years