44,909 research outputs found
Sampling from a system-theoretic viewpoint: Part I - Concepts and tools
This paper is first in a series of papers studying a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. In this paper we present the paradigm and revise underlying technical tools, such as the lifting technique and some topics of the operator theory. This material facilitates a systematic and unified treatment of a wide range of sampling and reconstruction problems, recovering many hitherto considered different solutions and leading to new results. Some of these applications are discussed in the second part
Auto-encoders: reconstruction versus compression
We discuss the similarities and differences between training an auto-encoder
to minimize the reconstruction error, and training the same auto-encoder to
compress the data via a generative model. Minimizing a codelength for the data
using an auto-encoder is equivalent to minimizing the reconstruction error plus
some correcting terms which have an interpretation as either a denoising or
contractive property of the decoding function. These terms are related but not
identical to those used in denoising or contractive auto-encoders [Vincent et
al. 2010, Rifai et al. 2011]. In particular, the codelength viewpoint fully
determines an optimal noise level for the denoising criterion
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