Introducing SPAIN (SParse Audio INpainter)

Abstract

A novel sparsity-based algorithm for audio inpainting is proposed. It is an adaptation of the SPADE algorithm by Kitić et al., originally developed for audio declipping, to the task of audio inpainting. The new SPAIN (SParse Audio INpainter) comes in synthesis and analysis variants. Experiments show that both A-SPAIN and S-SPAIN outperform other sparsity-based inpainting algorithms. Moreover, A-SPAIN performs on a par with the state-of-the-art method based on linear prediction in terms of the SNR, and, for larger gaps, SPAIN is even slightly better in terms of the PEMO-Q psychoacoustic criterion.

Dictionary Learning for Sparse Audio Inpainting

“…Our audio inpainting approach is inspired by the recently introduced algorithm SParse Audio INpainter (SPAIN) [17] and extends our work [34]. SPAIN is an adaptation of the so-called SParse Audio DEclipper (SPADE) algorithm [28] to the inpainting problem and exploits sparsity with respect to tight (Gabor) frames [35], [36].…”

“…SPAIN is an adaptation of the so-called SParse Audio DEclipper (SPADE) algorithm [28] to the inpainting problem and exploits sparsity with respect to tight (Gabor) frames [35], [36]. In [17], both synthesis and analysis models are discussed and an efficient implementation with segment-wise application of the algorithm is presented. More specifically, the time-domain signal is segmented using overlapping Hann windows, sparsity with respect to an overcomplete Discrete Fourier Transform (DFT) dictionary is exploited, and the restored blocks are combined using an overlap-add scheme.…”

“…For the audio inpainting specific notation we adopt most of the conventions from [17], [18]: Let x ∈ R N be the timedomain signal and assume that the indices of its missing (or unreliable) samples are known. This will be referred to as the gap.…”

“…In this section, we will briefly introduce the SPAIN algorithm presented in [17]. Being an adaptation of the SParse Audio DEclipper (SPADE) algorithm [28] to the inpainting problem, SPAIN differs from SPADE only in the definition of the set of feasible signals Γ x (see (1) for its SPAIN definition).…”

A New Generalized Projection and Its Application to Acceleration of Audio Declipping

“…Dequantization is another example: each quantized signal sample has its origin in one of the non-overlapping intervals and our lemma is suitable to find signal coefficients that are consistent with the quantized observation [58]. As the last example, we name the signal inpainting problem, where a portion of samples is completely missing, while the others are considered reliable [35,50,59]. In this problem, nothing is directly known about the missing samples, thus the set Γ is defined such that the lower and upper bounds are set to minus and plus infinity, respectively; with this definition, projection lemma can be used here as well.…”