Signal degradation is ubiquitous, and computational restoration of degraded signal has been investigated for many years. Recently, it is reported that the capability of signal restoration is fundamentally limited by the so-called perception-distortion tradeoff, i.e. the distortion and the perceptual difference between the restored signal and the ideal original signal cannot be made both minimal simultaneously. Distortion corresponds to signal fidelity and perceptual difference corresponds to perceptual naturalness, both of which are important metrics in practice. Besides, there is another dimension worthy of consideration--the semantic quality of the restored signal, i.e. the utility of the signal for recognition purpose.

Signal degradation is ubiquitous, and computational restoration of degraded signal has been investigated for many years. Recently, it is reported that the capability of signal restoration is fundamentally limited by the so-called perception-distortion tradeoff, i.e. the distortion and the perceptual difference between the restored signal and the ideal "original" signal cannot be made both minimal simultaneously. Distortion corresponds to signal fidelity and perceptual difference corresponds to perceptual naturalness, both of which are important metrics in practice. Besides, there is another dimension worthy of consideration--the semantic quality of the restored signal, i.e. the utility of the signal for recognition purpose. In particular, we consider the classification error rate achieved on the restored signal using a predefined classifier as a representative metric for semantic quality.

Signal degradation is ubiquitous, and computational restoration of degraded signal has been investigated for many years. Recently, it is reported that the capability of signal restoration is fundamentally limited by the so-called perception-distortion tradeoff, i.e. the distortion and the perceptual difference between the restored signal and the ideal "original" signal cannot be made both minimal simultaneously. Distortion corresponds to signal fidelity and perceptual difference corresponds to perceptual naturalness, both of which are important metrics in practice. Besides, there is another dimension worthy of consideration--the semantic quality of the restored signal, i.e. the utility of the signal for recognition purpose. In particular, we consider the classification error rate achieved on the restored signal using a predefined classifier as a representative metric for semantic quality.

For example, we might expect to encounter sensor malfunctions in a wireless sensor network at a rate proportional to the size of the network. Therefore, there is a growing need to develop machine learning techniques that enable satisfactory training and inference from incomplete data. Imputation, where missing data values are filled with suitable values inferred from observations, represents a promising technique for extending machine learning methods to handle missing data. Given their explicit representation of underlying data distributions, Restricted Boltzmann Machines (RBMs) are an appealing choice for imputing missing values. With a well trained RBM, the conditional probabilities of the missing values given the observed values remain accessible via either direct calculation (in a theoretical sense) or indirect Gibbs sampling. A variety of training and imputing procedures have been proposed to allow the application of RBMs to handle missing data, with various computational costs.