Dictionary Learning for Sparse Audio Inpainting

Audio Inpainting via $\ell_1$-Minimization and Dictionary Learning

“…Motivated by these observations, we propose to slightly modify a selected weighted ℓ 1 -method from [5] as well as to incorporate the dictionary learning technique presented in [4]. As we will demonstrate, this modified weighted ℓ 1 -method exhibits significantly improved reconstruction performance compared with the original setting and achieves comparable results as the (currently) state-of-the-art SPAIN-LEARNED algorithm.…”

“…This work is inspired by two model-based optimization approaches for audio inpainting: SParse Audio INpainter (SPAIN) with dictionary learning [4], see also [13], and (weighted) ℓ 1 -minimization based audio inpainting [5]. Note that both methods use the Gabor transform (see Section III) to obtain a sparse representation of the original audio signal.…”

“…The optimization based inpainting methods are quite efficient in filling short gaps, but as the gaps tend to get longer, they suffer from energy loss within the gap after restoration. As a means to tackle this problem, remaining in the framework of sparse audio inpainting, in [5], various weighting methods were combined with ℓ 1 -minimization, whereas in [4], a dictionary learning method was proposed and combined with a modified version of the SPAIN algorithm, i.e., SPAIN-MOD [4]. This combination of dictionary learning and SPAIN-MOD will be referred to as SPAIN-LEARNED henceforth.…”

“…Over the years, several audio inpainting methods have been proposed, based on various approaches like auto regression by Janssen [2], Bayesian estimation [3], convex optimization [4]- [6], sinusoidal modeling [7], similarity graphs [8], and deep neural networks [9]- [11]. Whereas auto regression, Bayesian estimation and convex optimization are applicable to short gaps (less than 100 ms), sinusoidal modeling, similarity graphs and deep neural networks work well for longer gaps (more than 100 ms).…”

“…In this paper, we focus on audio inpainting approaches which are motivated by the observation that real-world audio signals may be sparsely represented in some overcomplete dictionary [1], [4], [5]. The cited methods exploit sparsity to fill the gap by employing optimization techniques while utilizing the information present around the gap.…”