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Methods based on sparse representation have found great use in the recovery of audio signals degraded by clipping. The state of the art in declipping within the sparsity-based approaches has been achieved by the SPADE algorithm by Kitić et. al. (LVA/ICA'15). Our recent study (LVA/ICA'18) has shown that although the original S-SPADE can be improved such that it converges faster than the A-SPADE, the restoration quality is significantly worse. In the present paper, we propose a new version of S-SPADE. Experiments show that the novel version of S-SPADE outperforms its old version in terms of restoration quality, and that it is comparable with the A-SPADE while being even slightly faster than A-SPADE.

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The state of the art in audio declipping has currently been achieved by SPADE (SParse Audio DEclipper) algorithm by Kitić et al. Until now, the synthesis/sparse variant, S-SPADE, has been considered significantly slower than its analysis/cosparse counterpart, A-SPADE. It turns out that the opposite is true: by exploiting a recent projection lemma, individual iterations of both algorithms can be made equally computationally expensive, while S-SPADE tends to require considerably fewer iterations to converge. In this paper, the two algorithms are compared across a range of parameters such as the window length, window overlap and redundancy of the transform. The experiments show that although S-SPADE typically converges faster, the average performance in terms of restoration quality is not superior to A-SPADE.

Featured Application: The proposed framework is highly suitable for audio applications that require analysis-synthesis systems with the following properties: stability, perfect reconstruction, and a flexible choice of redundancy.Abstract: Many audio applications rely on filter banks (FBs) to analyze, process, and re-synthesize sounds. For these applications, an important property of the analysis-synthesis system is the reconstruction error; it has to be minimized to avoid audible artifacts. Other advantageous properties include stability and low redundancy. To exploit some aspects of auditory perception in the signal chain, some applications rely on FBs that approximate the frequency analysis performed in the auditory periphery, the gammatone FB being a popular example. However, current gammatone FBs only allow partial reconstruction and stability at high redundancies. In this article, we construct an analysis-synthesis system for audio applications. The proposed system, referred to as Audlet, is an oversampled FB with filters distributed on auditory frequency scales. It allows perfect reconstruction for a wide range of FB settings (e.g., the shape and density of filters), efficient FB design, and adaptable redundancy. In particular, we show how to construct a gammatone FB with perfect reconstruction. Experiments demonstrate performance improvements of the proposed gammatone FB when compared to current gammatone FBs in terms of reconstruction error and stability, especially at low redundancies. An application of the framework to audio source separation illustrates its utility for audio processing.

A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function. The warping function is a C 1 -diffeomorphism that determines the frequency progression and can be chosen freely, apart from minor technical restrictions. The resulting functions are interpreted as filter frequency responses and, combined with appropriately chosen downsampling factors, give rise to a non-uniform analysis filter bank. Classical Gabor and wavelet filter banks are obtained as special cases. Beyond the state-of-the-art, we construct a filter bank adapted to the auditory ERB frequency scale and families of filter banks that can be interpreted as an interpolation between linear (Gabor) and logarithmic (wavelet, ERBlet) frequency scales, closely related to the α-transform. For any arbitrary warping function, we derive straightforward decay conditions on the prototype filter and bounds for the downsampling factors, such that the resulting warped filter bank forms a frame. In particular, we obtain a simple and constructive method for obtaining tight frames with bandlimited filters by invoking previous results on generalized shift-invariant systems.

We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only coefficients. The cornerstone of our analysis is an expression of the partial derivatives of the continuous WT, which results in phase-magnitude relationships similar to the short-time Fourier transform (STFT) setting and valid for the generalized family of Cauchy wavelets. We show that the existence of such relations is equivalent to analyticity of the WT up to a multiplicative weight and a scaling of the mother wavelet. The implementation of the new phaseless reconstruction method is considered in detail and compared to previous methods. It is shown that the proposed method provides significant performance gains and a great flexibility regarding accuracy versus complexity. Additionally, we discuss the relation between scalogram reassignment operators and the wavelet transform phase gradient and present an observation on the phase around zeros of the WT.