The development of environmental transmission electron microscopes (ETEM) as well as the environmental cells opens the way towards operando electron microscopy. In this respect, following the genesis of a catalyst or a chemical reaction in real time under gaseous environment and at high temperature becomes a possibly achievable goal. Performing such experiments in 2D has already been successful but reaching the 3D information in environmental mode is a challenge as it needs to acquire 2D projections fast enough in order to neglect the morphological evolution of the object during the chemical reaction, a required condition to reconstruct a ‘correct’ 3D object. Under environmental conditions, the motion and evolution of the objects might produce images corrupted by motion which will then exhibit possibly significant blurred features. These defaults might even be enhanced if one intends to acquire the image series rapidly. This contribution will address the possibility of using deconvolution methods to un-blur such environmental microscopy images. Here we mainly focus on the motion blur correction of corrupted images: g(x,y)=(f*h)(x,y)+n(x,y)

where * denotes the convolution product, f is the ground truth image, g is the observed corrupted image, h is the degradation function of the acquisition system and n is the noise.

The Minimum Square Error (MSE) and the Constrained Least Square (CLS) filtering are used as image restauration processes as shown in figure 1. Both of them require the degradation function h as input and the parameter k related to the noise level which has to be optimized. Denoting G the Fourier transform of the corruptedimage, the Fourier transform of the reconstructed image is then given by one of the following relations:

    F_MSE(u,v)= G(u,v).H(u,v)^c / (|H(u,v)|²+k) and   F_CLS(u,v)= G(u,v).H(u,v)^c / (|H(u,v)|²+k.|P(u,v)|²),

where H is the Fourier transform of the convolution filter h, H^c is its complex conjugate, P is the Fourier transform of the Laplacian filter and |.| denotes the complex modulus. However, the degradation function is not known in practice and has to be estimated from the experimental images. The estimation of a parametric degradation function h is performed by image comparison: so far we manually determine the unknown parameters by comparing the blurred image with a similar one not affected by the motion blur. We will present perspectives of this work in terms of running an automatic estimation of the convolution kernel for in-situ image processing of experimental micrographs.

Acknowledgements

Thanks are due to CLYM (Consortium Lyon – St-Etienne de Microscopie, www.clym.fr) for the access to the microscope funded by the Region Rhône-Alpes, the CNRS and the ‘GrandLyon’. This work was supported by the BQR SPEE3D granted by INSA Lyon, ANR project 3D-CLEAN, Labex iMUST and IFP Energies nouvelles.

Figures:

Fig. 1: Results of convolution and deconvolution. a) Original non-blurred image, b) blurred image created by convolution between a) and a known degradation function. Results of MSE and CLS inverse filtering are respectively shown in c) and d).

« Back to The 16th European Microscopy Congress 2016

EMC Abstracts - https://emc-proceedings.com/abstract/image-deconvolution-for-fast-tomography-in-environmental-transmission-electron-microscopy/