Soft Smoothness for Audio Inpainting Using a Latent Matrix Model in Delay-embedded Space
This work addresses audio signal processing challenges like inpainting and declipping, but it appears incremental as it generalizes existing quadratic variation regularization.
The authors tackled the problem of reconstructing smooth time-series signals, specifically in audio inpainting and declipping, by proposing a new method that models signals in delay-embedded space with rank-1 matrix constraints and smooth factor vectors, achieving advantages over existing interpolation methods and sparse modeling.
Here, we propose a new reconstruction method of smooth time-series signals. A key concept of this study is not considering the model in signal space, but in delay-embedded space. In other words, we indirectly represent a time-series signal as an output of inverse delay-embedding of a matrix, and the matrix is constrained. Based on the model under inverse delay-embedding, we propose to constrain the matrix to be rank-1 with smooth factor vectors. The proposed model is closely related to the convolutional model, and quadratic variation (QV) regularization. Especially, the proposed method can be characterized as a generalization of QV regularization. In addition, we show that the proposed method provides the softer smoothness than QV regularization. Experiments of audio inpainting and declipping are conducted to show its advantages in comparison with several existing interpolation methods and sparse modeling.