The high complexity of various inverse problems poses a significant challenge to modelbased reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based methodologies such as deep learning. However, in the context of inverse problems, deep neural networks mostly act as black box routines, used for instance for a somewhat unspecified removal of artifacts in classical image reconstructions. In this paper, we will focus on the severely ill-posed inverse problem of limited angle computed tomography, in which entire boundary sections are not captured in the measurements. We will develop a hybrid reconstruction framework that fuses model-based sparse regularization with data-driven deep learning. Our method is reliable in the sense that we only learn the part that can provably not be handled by model-based methods, while applying the theoretically controllable sparse regularization technique to the remaining parts. Such a decomposition into visible and invisible segments is achieved by means of the shearlet transform that allows to resolve wavefront sets in the phase space. Furthermore, this split enables us to assign the clear task of inferring unknown shearlet coefficients to the neural network and thereby offering an interpretation of its performance in the context of limited angle computed tomography.Our numerical experiments show that our algorithm significantly surpasses both pure model-and more data-based reconstruction methods.

Providing force feedback as relevant information in current Robot-Assisted Minimally Invasive Surgery systems constitutes a technological challenge due to the constraints imposed by the surgical environment. In this context, Sensorless Force Estimation techniques represent a potential solution, enabling to sense the interaction forces between the surgical instruments and soft-tissues. Specifically, if visual feedback is available for observing soft-tissues' deformation, this feedback can be used to estimate the forces applied to these tissues. To this end, a force estimation model, based on Convolutional Neural Networks and Long-Short Term Memory networks, is proposed in this work. This model is designed to process both, the spatiotemporal information present in video sequences and the temporal structure of tool data (the surgical tool-tip trajectory and its grasping status). A series of analyses are carried out to reveal the advantages of the proposal and the challenges that remain for real applications. This research work focuses on two surgical task scenarios, referred to as pushing and pulling tissue. For these two scenarios, different input data modalities and their effect on the force estimation quality are investigated. These input data modalities are tool data, video sequences and a combination of both. The results suggest that the force estimation quality is better when both, the tool data and video sequences, are processed by the neural network model. Moreover, this study reveals the need for a loss function, designed to promote the modeling of smooth and sharp details found in force signals. Finally, the results show that the modeling of forces due to pulling tasks is more challenging than for the simplest pushing actions.

In low light or short-exposure photography the image is often corrupted by noise. While longer exposure helps reduce the noise, it can produce blurry results due to the object and camera motion. The reconstruction of a noise-less image is an ill posed problem. Recent approaches for image denoising aim to predict kernels which are convolved with a set of successively taken images (burst) to obtain a clear image. We propose a deep neural network based approach called Multi-Kernel Prediction Networks (MKPN) for burst image denoising. MKPN predicts kernels of not just one size but of varying sizes and performs fusion of these different kernels resulting in one kernel per pixel. The advantages of our method are two fold: (a) the different sized kernels help in extracting different information from the image which results in better reconstruction and (b) kernel fusion assures retaining of the extracted information while maintaining computational efficiency. Experimental results reveal that MKPN outperforms state-of-the-art on our synthetic datasets with different noise levels.

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