Johannes Leuschner

Riccardo Barbano, Javier Antorán, Johannes Leuschner et al. · cambridge

Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised learning methods, such as the deep image prior (DIP), naturally fill this gap, but bring a host of new issues: the susceptibility to overfitting due to a lack of robust early stopping strategies and unstable convergence. We present a novel approach to tackle these issues by restricting DIP optimisation to a sparse linear subspace of its parameters, employing a synergy of dimensionality reduction techniques and second order optimisation methods. The low-dimensionality of the subspace reduces DIP's tendency to fit noise and allows the use of stable second order optimisation methods, e.g., natural gradient descent or L-BFGS. Experiments across both image restoration and tomographic tasks of different geometry and ill-posedness show that second order optimisation within a low-dimensional subspace is favourable in terms of optimisation stability to reconstruction fidelity trade-off.

Riccardo Barbano, Johannes Leuschner, Javier Antorán et al.

We investigate adaptive design based on a single sparse pilot scan for generating effective scanning strategies for computed tomography reconstruction. We propose a novel approach using the linearised deep image prior. It allows incorporating information from the pilot measurements into the angle selection criteria, while maintaining the tractability of a conjugate Gaussian-linear model. On a synthetically generated dataset with preferential directions, linearised DIP design allows reducing the number of scans by up to 30% relative to an equidistant angle baseline.

Marco Nittscher, Michael Lameter, Riccardo Barbano et al.

The deep image prior (DIP) is a well-established unsupervised deep learning method for image reconstruction; yet it is far from being flawless. The DIP overfits to noise if not early stopped, or optimized via a regularized objective. We build on the regularized fine-tuning of a pretrained DIP, by adopting a novel strategy that restricts the learning to the adaptation of singular values. The proposed SVD-DIP uses ad hoc convolutional layers whose pretrained parameters are decomposed via the singular value decomposition. Optimizing the DIP then solely consists in the fine-tuning of the singular values, while keeping the left and right singular vectors fixed. We thoroughly validate the proposed method on real-measured $μ$CT data of a lotus root as well as two medical datasets (LoDoPaB and Mayo). We report significantly improved stability of the DIP optimization, by overcoming the overfitting to noise.

Javier Antorán, Riccardo Barbano, Johannes Leuschner et al.

Existing deep-learning based tomographic image reconstruction methods do not provide accurate estimates of reconstruction uncertainty, hindering their real-world deployment. This paper develops a method, termed as the linearised deep image prior (DIP), to estimate the uncertainty associated with reconstructions produced by the DIP with total variation regularisation (TV). Specifically, we endow the DIP with conjugate Gaussian-linear model type error-bars computed from a local linearisation of the neural network around its optimised parameters. To preserve conjugacy, we approximate the TV regulariser with a Gaussian surrogate. This approach provides pixel-wise uncertainty estimates and a marginal likelihood objective for hyperparameter optimisation. We demonstrate the method on synthetic data and real-measured high-resolution 2D $μ$CT data, and show that it provides superior calibration of uncertainty estimates relative to previous probabilistic formulations of the DIP. Our code is available at https://github.com/educating-dip/bayes_dip.

Riccardo Barbano, Johannes Leuschner, Maximilian Schmidt et al.

Deep image prior (DIP) was recently introduced as an effective unsupervised approach for image restoration tasks. DIP represents the image to be recovered as the output of a deep convolutional neural network, and learns the network's parameters such that the output matches the corrupted observation. Despite its impressive reconstructive properties, the approach is slow when compared to supervisedly learned, or traditional reconstruction techniques. To address the computational challenge, we bestow DIP with a two-stage learning paradigm: (i) perform a supervised pretraining of the network on a simulated dataset; (ii) fine-tune the network's parameters to adapt to the target reconstruction task. We provide a thorough empirical analysis to shed insights into the impacts of pretraining in the context of image reconstruction. We showcase that pretraining considerably speeds up and stabilizes the subsequent reconstruction task from real-measured 2D and 3D micro computed tomography data of biological specimens. The code and additional experimental materials are available at https://educateddip.github.io/docs.educated_deep_image_prior/.

Sören Schulze, Johannes Leuschner, Emily J. King

We propose a method for the blind separation of sounds of musical instruments in audio signals. We describe the individual tones via a parametric model, training a dictionary to capture the relative amplitudes of the harmonics. The model parameters are predicted via a U-Net, which is a type of deep neural network. The network is trained without ground truth information, based on the difference between the model prediction and the individual time frames of the short-time Fourier transform. Since some of the model parameters do not yield a useful backpropagation gradient, we model them stochastically and employ the policy gradient instead. To provide phase information and account for inaccuracies in the dictionary-based representation, we also let the network output a direct prediction, which we then use to resynthesize the audio signals for the individual instruments. Due to the flexibility of the neural network, inharmonicity can be incorporated seamlessly and no preprocessing of the input spectra is required. Our algorithm yields high-quality separation results with particularly low interference on a variety of different audio samples, both acoustic and synthetic, provided that the sample contains enough data for the training and that the spectral characteristics of the musical instruments are sufficiently stable to be approximated by the dictionary.

Daniel Otero Baguer, Johannes Leuschner, Maximilian Schmidt

In this work, we investigate the application of deep learning methods for computed tomography in the context of having a low-data regime. As motivation, we review some of the existing approaches and obtain quantitative results after training them with different amounts of data. We find that the learned primal-dual has an outstanding performance in terms of reconstruction quality and data efficiency. However, in general, end-to-end learned methods have two issues: a) lack of classical guarantees in inverse problems and b) lack of generalization when not trained with enough data. To overcome these issues, we bring in the deep image prior approach in combination with classical regularization. The proposed methods improve the state-of-the-art results in the low data-regime.

Johannes Leuschner, Maximilian Schmidt, Daniel Otero Baguer et al.

Deep Learning approaches for solving Inverse Problems in imaging have become very effective and are demonstrated to be quite competitive in the field. Comparing these approaches is a challenging task since they highly rely on the data and the setup that is used for training. We provide a public dataset of computed tomography images and simulated low-dose measurements suitable for training this kind of methods. With the LoDoPaB-CT Dataset we aim to create a benchmark that allows for a fair comparison. It contains over 40,000 scan slices from around 800 patients selected from the LIDC/IDRI Database. In this paper we describe how we processed the original slices and how we simulated the measurements. We also include first baseline results.