Computational bioimaging: How to further reduce exposure and/or increase image quality
We start our account of inverse problems in imaging with a brief review of first-generation reconstruction algorithms, which are linear and typically non-iterative (e.g., backprojection). We then highlight the emergence of the concept of sparsity, which opened the door to the resolution of more difficult image reconstruction problems, including compressed sensing. In particular, we demonstrate the global optimality of splines for solving problems with total-variation (TV) regularization constraints. Next, we introduce an alternative statistical formulation where signals are modeled as sparse stochastic processes. This allows us to establish a formal equivalence between non-Gaussian MAP estimation and sparsity-promoting techniques that are based on the minimization of a non-quadratic cost functional. We also show how to compute the solution efficiently via an alternating sequence of linear steps and pointwise nonlinearities (ADMM algorithm). This concludes our discussion of the second-generation methods that constitute the state-of-the-art in a variety of modalities.
In the final part of the presentation, we shall argue that learning techniques will play a central role in the future development of the field with the emergence of third-generation methods. A natural solution for improving image quality is to retain the linear part of the ADMM algorithm while optimizing its non-linear step (proximal operator) so as to minimize the reconstruction error. Another more extreme scenario is to replace the iterative part of the reconstruction by a deep convolutional network. The various approaches will be illustrated with the reconstruction of images in a variety of modalities including MRI, X-ray and cryo-electron tomography, and deconvolution microscopy.
Michael Unser is professor and director of EPFL’s Biomedical Imaging Group, Lausanne, Switzerland. His primary area of investigation is biomedical image processing. He is internationally recognized for his research contributions to sampling theory, wavelets, the use of splines for image processing, stochastic processes, and computational bioimaging. He has published over 250 journal papers on those topics. He is the author with P. Tafti of the book “An introduction to sparse stochastic processes”, Cambridge University Press 2014.
From 1985 to 1997, he was with the Biomedical Engineering and Instrumentation Program, National Institutes of Health, Bethesda USA, conducting research on bioimaging.
Dr. Unser has held the position of associate Editor-in-Chief (2003-2005) for the IEEE Transactions on Medical Imaging. He is currently member of the editorial boards of SIAM J. Imaging Sciences, IEEE J. Selected Topics in Signal Processing, and Foundations and Trends in Signal Processing. He co-organized the first IEEE International Symposium on Biomedical Imaging (ISBI’2002) and was the founding chair of the technical committee of the IEEE-SP Society on Bio Imaging and Signal Processing (BISP).
Prof. Unser is a fellow of the IEEE (1999), an EURASIP fellow (2009), and a member of the Swiss Academy of Engineering Sciences. He is the recipient of several international prizes including three IEEE-SPS Best Paper Awards and two Technical Achievement Awards from the IEEE (2008 SPS and EMBS 2010).