Content-Aware Image Restoration Techniques without Ground Truth and Novel Ideas to Image Reconstruction

In this thesis I will use state-of-the-art (SOTA) image denoising methods to denoise electron microscopy (EM) data. Then, I will present NoiseVoid a deep learning based self-supervised image denoising approach which is trained on single noisy observations. Eventually, I approach the missing wedge problem in tomography and introduce a novel image encoding, based on the Fourier transform which I am using to predict missing Fourier coefficients directly in Fourier space with Fourier Image Transformer (FIT). In the next paragraphs I will summarize the individual contributions briefly. Electron microscopy is the go to method for high-resolution images in biological research. Modern scanning electron microscopy (SEM) setups are used to obtain neural connectivity maps, allowing us to identify individual synapses. However, slow scanning speeds are required to obtain SEM images of sufficient quality. In (Weigert et al. 2018) the authors show, for fluorescence microscopy, how pairs of low- and high-quality images can be obtained from biological samples and use them to train content-aware image restoration (CARE) networks. Once such a network is trained, it can be applied to noisy data to restore high quality images. With SEM-CARE I present how this approach can be directly applied to SEM data, allowing us to scan the samples faster, resulting in $40$- to $50$-fold imaging speedups for SEM imaging. In structural biology cryo transmission electron microscopy (cryo TEM) is used to resolve protein structures and describe molecular interactions. However, missing contrast agents as well as beam induced sample damage (Knapek and Dubochet 1980) prevent acquisition of high quality projection images. Hence, reconstructed tomograms suffer from low signal-to-noise ratio (SNR) and low contrast, which makes post-processing of such data difficult and often has to be done manually. To facilitate down stream analysis and manual data browsing of cryo tomograms I present cryoCARE a Noise2Noise (Lehtinen et al. 2018) based denoising method which is able to restore high contrast, low noise tomograms from sparse-view low-dose tilt-series. An implementation of cryoCARE is publicly available as Scipion (de la Rosa-Trevín et al. 2016) plugin. Next, I will discuss the problem of self-supervised image denoising. With cryoCARE I exploited the fact that modern cryo TEM cameras acquire multiple low-dose images, hence the Noise2Noise (Lehtinen et al. 2018) training paradigm can be applied. However, acquiring multiple noisy observations is not always possible e.g. in live imaging, with old cryo TEM cameras or simply by lack of access to the used imaging system. In such cases we have to fall back to self-supervised denoising methods and with Noise2Void I present the first self-supervised neural network based image denoising approach. Noise2Void is also available as an open-source Python package and as a one-click solution in Fiji (Schindelin et al. 2012). In the last part of this thesis I present Fourier Image Transformer (FIT) a novel approach to image reconstruction with Transformer networks. I develop a novel 1D image encoding based on the Fourier transform where each prefix encodes the whole image at reduced resolution, which I call Fourier Domain Encoding (FDE). I use FIT with FDEs and present proof of concept for super-resolution and tomographic reconstruction with missing wedge correction. The missing wedge artefacts in tomographic imaging originate in sparse-view imaging. Sparse-view imaging is used to keep the total exposure of the imaged sample to a minimum, by only acquiring a limited number of projection images. However, tomographic reconstructions from sparse-view acquisitions are affected by missing wedge artefacts, characterized by missing wedges in the Fourier space and visible as streaking artefacts in real image space. I show that FITs can be applied to tomographic reconstruction and that they fill in missing Fourier coefficients. Hence, FIT for tomographic reconstruction solves the missing wedge problem at its source.:Contents Summary iii Acknowledgements v 1 Introduction 1 1.1 Scanning Electron Microscopy . . . . . . . . . . . . . . . . . . . . 3 1.2 Cryo Transmission Electron Microscopy . . . . . . . . . . . . . . . 4 1.2.1 Single Particle Analysis . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Cryo Tomography . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Tomographic Reconstruction . . . . . . . . . . . . . . . . . . . . . 8 1.4 Overview and Contributions . . . . . . . . . . . . . . . . . . . . . 11 2 Denoising in Electron Microscopy 15 2.1 Image Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Supervised Image Restoration . . . . . . . . . . . . . . . . . . . . 19 2.2.1 Training and Validation Loss . . . . . . . . . . . . . . . . 19 2.2.2 Neural Network Architectures . . . . . . . . . . . . . . . . 21 2.3 SEM-CARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.1 SEM-CARE Experiments . . . . . . . . . . . . . . . . . . 23 2.3.2 SEM-CARE Results . . . . . . . . . . . . . . . . . . . . . 25 2.4 Noise2Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 cryoCARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5.1 Restoration of cryo TEM Projections . . . . . . . . . . . . 27 2.5.2 Restoration of cryo TEM Tomograms . . . . . . . . . . . . 29 2.5.3 Automated Downstream Analysis . . . . . . . . . . . . . . 31 2.6 Implementations and Availability . . . . . . . . . . . . . . . . . . 32 2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.7.1 Tasks Facilitated through cryoCARE . . . . . . . . . . . 33 3 Noise2Void: Self-Supervised Denoising 35 3.1 Probabilistic Image Formation . . . . . . . . . . . . . . . . . . . . 37 3.2 Receptive Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3 Noise2Void Training . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3.1 Implementation Details . . . . . . . . . . . . . . . . . . . . 41 3.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4.1 Natural Images . . . . . . . . . . . . . . . . . . . . . . . . 43 3.4.2 Light Microscopy Data . . . . . . . . . . . . . . . . . . . . 44 3.4.3 Electron Microscopy Data . . . . . . . . . . . . . . . . . . 47 3.4.4 Errors and Limitations . . . . . . . . . . . . . . . . . . . . 48 3.5 Conclusion and Followup Work . . . . . . . . . . . . . . . . . . . 50 4 Fourier Image Transformer 53 4.1 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.1.1 Attention Is All You Need . . . . . . . . . . . . . . . . . . 55 4.1.2 Fast-Transformers . . . . . . . . . . . . . . . . . . . . . . . 56 4.1.3 Transformers in Computer Vision . . . . . . . . . . . . . . 57 4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2.1 Fourier Domain Encodings (FDEs) . . . . . . . . . . . . . 57 4.2.2 Fourier Coefficient Loss . . . . . . . . . . . . . . . . . . . . 59 4.3 FIT for Super-Resolution . . . . . . . . . . . . . . . . . . . . . . . 60 4.3.1 Super-Resolution Data . . . . . . . . . . . . . . . . . . . . 60 4.3.2 Super-Resolution Experiments . . . . . . . . . . . . . . . . 61 4.4 FIT for Tomography . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4.1 Computed Tomography Data . . . . . . . . . . . . . . . . 64 4.4.2 Computed Tomography Experiments . . . . . . . . . . . . 66 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Conclusions and Outlook 7

Diffuse Optical Imaging with Ultrasound Priors and Deep Learning

Diffuse Optical Imaging (DOI) techniques are an ever growing field of research as they are noninvasive, compact, cost-effective and can furnish functional information about human tissues. Among others, they include techniques such as Tomography, which solves an inverse reconstruction problem in a tissue volume, and Mapping which only seeks to find values on a tissue surface. Limitations in reliability and resolution, due to the ill-posedness of the underlying inverse problems, have hindered the clinical uptake of this medical imaging modality. Multimodal imaging and Deep Learning present themselves as two promising solutions to further research in DOI. In relation to the first idea, we implement and assess here a set of methods for SOLUS, a combined Ultrasound (US) and Diffuse Optical Tomography (DOT) probe for breast cancer diagnosis. An ad hoc morphological prior is extracted from US B-mode images and utilised for the regularisation of the inverse problem in DOT. Combination of the latter in reconstruction with a linearised forward model for DOT is assessed on specifically designed dual phantoms. The same reconstruction approach with the incorporation of a spectral model has been assessed on meat phantoms for reconstruction of functional properties. A simulation study with realistic digital phantoms is presented for an assessment of a non-linear model in reconstruction for the quantification of optical properties of breast lesions. A set of machine learning tools is presented for diagnosis breast lesions based on the reconstructed optical properties. A preliminary clinical study with the SOLUS probe is presented. Finally, a specifically designed deep learning architecture for diffusion is applied to mapping on the brain cortex or Diffuse Optical Cortical Mapping (DOCM). An assessment of its performances is presented on simulated and experimental data