Terahertz (THz) sensing is a promising imaging technology for a wide variety of different applications. Extracting the interpretable and physically meaningful parameters for such applications, however, requires solving an inverse problem in which a model function determined by these parameters needs to be fitted to the measured data. Since the underlying optimization problem is nonconvex and very costly to solve, we propose learning the prediction of suitable parameters from the measured data directly. More precisely, we develop a model-based autoencoder in which the encoder network predicts suitable parameters and the decoder is fixed to a physically meaningful model function, such that we can train the encoding network in an unsupervised way. We illustrate numerically that the resulting network is more than 140 times faster than classical optimization techniques while making predictions with only slightly higher objective values. Using such predictions as starting points of local optimization techniques allows us to converge to better local minima about twice as fast as optimization without the network-based initialization.
Due to the revolutionary success (convolutional) neural networks have had on computer vision problems over the last decade, researchers have extended the fields of applications of neural networks significantly. A particularly interesting concept is to learn the solution of complex, possibly nonconvex, optimization problems. Different lines of research have considered directly learning the optimizer itself, e.g. modelled as a recurrent neural network @cite_12 , or rolling out optimization algorithms and learning the incremental steps, e.g. in the form of parameterized proximal operators in @cite_10 . Further hybrid approaches include optimization problems in the networks' architecture, e.g. @cite_29 , or combining optimizers with networks that have been trained individually @cite_25 @cite_2 . The recent work of @cite_19 trains a network to predict descent directions to a given energy in order to give provable convergence results on the learned optimizer.
@cite_29 @cite_19 @cite_2 @cite_10 @cite_25 @cite_12
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Learning Convolutional Neural Networks (CNN) is commonly carried out by plain supervised gradient descent. With sufficient training data, this leads to very competitive results for visual recognition tasks when starting from a random initialization. When the amount of labeled data is limited, CNNs reveal their strong dependence on large amounts of training data. However, recent results have shown that a well chosen optimization starting point can be beneficial for convergence to a good generalizing minimum. This starting point was mostly found using unsupervised feature learning techniques such as sparse coding or transfer learning from related recognition tasks. In this work, we compare these two approaches against a simple patch based initialization scheme and a random initialization of the weights. We show that pre-training helps to train CNNs from few samples and that the correct choice of the initialization scheme can push the network's performance by up to 41 compared to random initialization. In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise non-linearity) when the normal operator ( @math , where @math is the adjoint of the forward imaging operator, @math ) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a @math image on the GPU. In recent years, state-of-the-art methods in computer vision have utilized increasingly deep convolutional neural network architectures (CNNs), with some of the most successful models employing hundreds or even thousands of layers. A variety of pathologies such as vanishing exploding gradients make training such deep networks challenging. While residual connections and batch normalization do enable training at these depths, it has remained unclear whether such specialized architecture designs are truly necessary to train deep CNNs. In this work, we demonstrate that it is possible to train vanilla CNNs with ten thousand layers or more simply by using an appropriate initialization scheme. We derive this initialization scheme theoretically by developing a mean field theory for signal propagation and by characterizing the conditions for dynamical isometry, the equilibration of singular values of the input-output Jacobian matrix. These conditions require that the convolution operator be an orthogonal transformation in the sense that it is norm-preserving. We present an algorithm for generating such random initial orthogonal convolution kernels and demonstrate empirically that they enable efficient training of extremely deep architectures. Deep neural network is difficult to train and this predicament becomes worse as the depth increases. The essence of this problem exists in the magnitude of backpropagated errors that will result in gradient vanishing or exploding phenomenon. We show that a variant of regularizer which utilizes orthonormality among different filter banks can alleviate this problem. Moreover, we design a backward error modulation mechanism based on the quasi-isometry assumption between two consecutive parametric layers. Equipped with these two ingredients, we propose several novel optimization solutions that can be utilized for training a specific-structured (repetitively triple modules of Conv-BNReLU) extremely deep convolutional neural network (CNN) WITHOUT any shortcuts identity mappings from scratch. Experiments show that our proposed solutions can achieve distinct improvements for a 44-layer and a 110-layer plain networks on both the CIFAR-10 and ImageNet datasets. Moreover, we can successfully train plain CNNs to match the performance of the residual counterparts. Besides, we propose new principles for designing network structure from the insights evoked by orthonormality. Combined with residual structure, we achieve comparative performance on the ImageNet dataset.