Adaptative complex diffusion filtering
Problem Description
Optical coherence tomography (OCT) is a non-invasive imaging modality with an increasing number of applications and it is becoming an essential tool in ophthalmology allowing in vivo high-resolution cross-sectional imaging of the retinal tissue. However, as any imaging technique that bases its image formation on coherent waves, OCT images suffer from speckle noise, which reduces its quality. Speckle noise creates a grainy appearance that can mask diagnostically significant image features (small or low reflectivity features) and reduce the accuracy of segmentation and pattern recognition algorithms.
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Despeckling optical coherence tomograms from the human retina is a fundamental step to a better diagnosis and it is crucial as a preprocessing stage for retinal layer segmentation. Both of these applications are particularly important in monitoring the progression of retinal disorders.
Modelling & Computational Challenges
We aim to improve the process of speckle noise reduction and to improve the preservation of edge and image features using a new formulation for a well-known nonlinear complex diffusion filter (NCDF). We specifically aim to apply this filtering process to OCT data from the human eye fundus as a preprocessing step for layer segmentation, which explains the need to preserve the retinal tissue. Additionally, the process intends to be applied as a filter for visual inspection, as it preserves features within the tissue.
Research at LCM
Our goal is to explore both on the theoretical and the application aspects of nonlinear complex diffusion equations. We aim to implement and present a rigorous proofs for the stability and convergence of a class of finite difference schemes applied to this interesting type of equations. As a proof-of-concept, the proposed method will be compared with traditional NCDF methods from the literature by means of quantitative measures, such as the mean square error (MSE), contrast-to-noise ratio (CNR) and average effective number of looks (ENL).
Papers & Reports
- [1] A. Araújo, Sílvia Barbeiro & Pedro Serranho, Convergence of finite difference schemes for nonlinear complex reaction-diffusion processes, SIAM J. Numer. Anal. 53:1 (2015), pp. 228-250. DOI:10.1137/130933642
- [2] A. Araújo, Sílvia Barbeiro & Pedro Serranho, Stability of finite difference schemes for nonlinear complex reaction-diffusion processes, IMA Journal of Numerical Analysis 35(3) (2015), pp. 1381-1401. DOI: 10.1093/imanum/dru037
- [3] P. Rodrigues, P. Guimarães, A. Araújo, S. Barbeiro, R. Bernardes & P. Serranho, Explicit and Semi-Implicit Complex-Diffusion Schemes for Optical Coherence Tomography Despeckling, in Image Analysis and Recognition, ser. Lecture Notes in Computer Science, M. Kamel and A. Campilho, Eds. Springer Berlin Heidelberg, 2013, vol. 7950, pp. 282-289. DOI: 10.1007/978-3-642-39094-4_32
- [4] A. Araújo, S. Barbeiro and P. Serranho, Stability of finite difference schemes for complex diffusion processes, SIAM J. Numer. Anal., 50, 3 (2012), 1284-1296
- [5] P. Serranho, C. Maduro, T. Santos, J. Cunha-Vaz, R. Bernardes, A. Araújo, S. Barbeiro, Ocular fundus imaging: From structure to function. 1st Portuguese Meeting in Bioengineering (ENBENG), 2011. ENBENG 2011, IEEE, 2011, 1-4.
- [6] R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro, J. Cunha-Vaz, Improved adaptive complex diffusion despeckling filter, Optics Express, 18, 23 (2010) 24048-24059.
- [7] Maduro, C., Serranho, P., Santos, T., Rodrigues, P., Cunha-Vaz, J. & Bernardes, R. OCT Noise Despeckling Using 3D Nonlinear Complex Diffusion Filter. In: Technologies for Medical Sciences. Lecture Notes in Computational Vision and Biomechanics. Springer, 2012, 1, 141-157
Software
A new formulation for a well-known nonlinear complex diffusion filter is herewith proposed. A regularization factor is made to be dependent on data, and the process itself is an adaptive one.
http://www.mathworks.com/matlabcentral/fileexchange/29801-image-filtering
Project Team
- Adérito Araújo (LCM/CMUC)
- José Cunha-Vaz (IBILI/FMUC)
- Pedro Serranho (IBILI/UA)
- Rui Bernardes (IBILI/FMUC/AIBILI)
- Sílvia Barbeiro (LCM/CMUC)
- Torcato Santos (IBILI/FMUC/AIBILI)
