# Soft Smoothness for Audio Inpainting Using a Latent Matrix Model in Delay-embedded Space

arXiv: https://arxiv.org/abs/2203.09746 · HTML: https://mlsanity.com/paper/2203.09746/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 53 references that are in the map.
- First posted on arXiv 18 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting](https://mlsanity.com/paper/2002.12135/) (2020)
- [Simultaneous Tensor Completion and Denoising by Noise Inequality Constrained Convex Optimization](https://mlsanity.com/paper/1801.03299/) (2018)

## Abstract (arXiv)

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.