  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.
