We apply a general procedure of the author to choose penalty parameters in total variation denoising.

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We derive a smoothing regularizer for recurrent network models by requiring robustness in prediction performance to perturbations of the training data. The regularizer can be viewed as a generalization of the first order Tikhonov stabilizer to dynamic models. The closed-form expression of the regularizer covers both time-lagged and simultaneous recurrent nets, with feedforward nets and onelayer...

Electrical capacitance tomography (ECT) is considered to be a competitive measurement method. The imaging objects in ECT measurements are often in a time-varying process, and exploiting the prior information related to the dynamic nature is important for reconstructing high-quality images. Different from existing reconstruction models, in this paper a new model that incorporates the spatial cor...

We propose a partially learned approach for the solution of ill posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularization theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularizing functional. Th...

Learning embeddings of words and knowledge base elements is a promising approach for open domain question answering. Based on the remark that relations and entities are distinct object types lying in the same embedding space, we analyze the benefit of adding a regularizer favoring the embeddings of entities to be orthogonal to those of relations. The main motivation comes from the observation t...

In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [6] in order to remove mixed Poisson-Gaussian (MPG) noise. existing splitting algorithm TV-IC, an inner loop by Newton method had be adopted one nonlinear optimization subproblem, which increased computation cost per outer loop. By introducing a bilinear constraint a...

The space-discrete Total Variation (TV) flow is analyzed using several mode decomposition techniques. In the one-dimensional case, we provide analytic formulations to Dynamic Mode Decomposition (DMD) and Koopman (KMD) of TV-flow compare obtained modes TV spectral decomposition. We propose a computationally efficient algorithm evolve TV-flow. A significant speedup by three orders magnitude obtai...