The presence of noise is common in signal processing independent of the signal type. Deep neural networks have shown good performance in removing signal noise, especially in the image domain. In this work, we consider deep neural networks as a denoising tool where our focus is on one dimensional signals. For that purpose, we introduce an encoder-decoder network architecture to denoise signals, represented by a sequence of measurements. Instead of relying only on the standard reconstruction error to train the encoder-decoder network, we treat the task of signal denoising as distribution alignment between the clean and noisy signals. Then, we propose to train the encoder-decoder with adversarial learning, where the goal is to align the clean and noisy signal latent representation. Unlike standard adversarial learning, we do not have access to the distribution of the clean signal's latent representation in advance. For that reason, we propose a new formulation where both clean and noisy signals pass through the encoder to produce the latent representation. Afterwards, a discriminator neural network has to detect whether the latent representation comes from the clean or noisy signal. At the end of training, aligning the two signal distributions results in removing the noise. In our experiments, we study two signal types with complex noise models. First, we evaluate on electrocardiography and later on motion signal denoising. We show better performance than the related learning-based and non-learning approaches, such as autoencoders, wavenet denoiser, recurrent neural networks and wavelets, demonstrating the benefits of adversarial learning for one dimensional signal denoising.
Analysing molecular profiles requires the selection of classification models that can cope with the high dimensionality and variability of these data. Also, improper reference point choice and scaling pose additional challenges. Often model selection is somewhat guided by ad hoc simulations rather than by sophisticated considerations on the properties of a categorization model. Here, we derive and report four linked linear concept classes/models with distinct invariance properties for high-dimensional molecular classification. We can further show that these concept classes also form a half-order of complexity classes in terms of Vapnik–Chervonenkis dimensions, which also implies increased generalization abilities. We implemented support vector machines with these properties. Surprisingly, we were able to attain comparable or even superior generalization abilities to the standard linear one on the 27 investigated RNA-Seq and microarray datasets. Our results indicate that a priori chosen invariant models can replace ad hoc robustness analysis by interpretable and theoretically guaranteed properties in molecular categorization.
We study the problem of learning-based denoising where the training set contains just a handful of clean and noisy samples. A solution to mitigate the small training set issue is to train a denoising model with pairs of clean and synthesized noisy signals, produced from empirical noise priors; and finally only fine-tune on the available small training set. While transfer learning suits well to this pipeline, it does not generalize with the limited amount of training data. In this work, we propose a new training approach, based on meta-learning, for few-shot learning-based denoising problems. Our model is meta-trained using known synthetic noise models, and then fine-tuned with the small training set, with the real noise, as a few-shot learning task. Learning from synthetic data during meta-training gives us the ability to generate an infinite number of training data. Our approach is empirically shown to produce more accurate denoising results than supervised learning and transfer learning in three denoising evaluations for images and 1-D signals. Interestingly, our study provides strong indications that meta-learning has the potential to become the main learning algorithm for the denoising.
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