BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Multidimensional Wavelets and Invariance Principles for the Analysis of Bioimages

M. Unser

Plenary talk, BioImage Informatics (BII'14), Leuven, Kingdom of Belgium, October 8-10, 2014.

In this talk, we shall advocate the use of wavelets for the processing and analysis of images in biomicroscopy. We start with a short tutorial on wavelet bases, emphasizing the fact that they provide a concise multiresolution representation of signals and that they can be computed efficiently using filterbanks. We then show how they can be extended to multiple dimensions, either, by using tensor-product-basis functions, or by allowing for some level of redundancy to achieve better invariance with respect to coordinate transformations. In particular, we present a parameric family of multidimensional wavelet transforms that are translation- and rotation-invariant and perfectly reversible (tight frame property). The underlying wavelet templates are steerable—meaning that they can be spatially rotated in any direction—and tunable to some extent, which makes them ideally suited for pattern analysis and key-point detection in 2-D or 3-D. The concepts are illustrated with applications in biological imaging. These include the denoising and deconvolution of fluorescence micrographs, model-based extraction of features (detection of edges, tracing of filaments, localization of junctions), and morphological component analysis.

References

  1. M. Unser, "Wavelets: On the Virtues and Applications of the Mathematical Microscope," Journal of Microscopy, vol. 255, no. 3, pp. 123-127, September 2014.

  2. M. Unser, N. Chenouard, "A Unifying Parametric Framework for 2D Steerable Wavelet Transforms," SIAM Journal on Imaging Sciences, vol. 6, no. 1, pp. 102-135, 2013.

  3. F. Luisier, T. Blu, M. Unser, "Image Denoising in Mixed Poisson-Gaussian Noise," IEEE Transactions on Image Processing, vol. 20, no. 3, pp. 696-708, March 2011. 

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