Finding the best K -sparse approximation of a signal in a redundant dictionary is an NP-hard problem. Suboptimal greedy matching pursuit algorithms are generally used for this task. In this work, we present an acceleration technique and an implementation of the matching pursuit algorithm acting on a multi-Gabor dictionary, i.e., a concatenation of several Gabor-type time-frequency dictionaries, each of which consists of translations and modulations of a possibly different window and time and frequency shift parameters. The technique is based on pre-computing and thresholding inner products between atoms and on updating the residual directly in the coefficient domain, i.e., without the round-trip to the signal domain. Since the proposed acceleration technique involves an approximate update step, we provide theoretical and experimental results illustrating the convergence of the resulting algorithm. The implementation is written in C (compatible with C99 and C++11), and we also provide Matlab and GNU Octave interfaces. For some settings, the implementation is up to 70 times faster than the standard Matching Pursuit Toolkit.

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.

An efficient algorithm for real-time signal reconstruction from the magnitude of the short-time Fourier transform (STFT) is introduced. The proposed approach combines the strengths of two previously published algorithms: the real-time phase gradient heap integration and the Gnann and Spiertz's real-time iterative spectrogram inversion with look-ahead. An extensive comparison with the state-of-the-art algorithms in a reproducible manner is presented.

A noniterative method for the reconstruction of the short-time fourier transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of the magnitude of the un-sampled STFT with respect to the Gaussian window. Although the theory holds in the continuous setting only, the experiments show that the algorithm performs well even in the discretized setting (discrete Gabor transform) with low redundancy using the sampled Gaussian window, the truncated Gaussian window and even other compactly supported windows such as the Hann window. Due to the noniterative nature, the algorithm is very fast and it is suitable for long audio signals. Moreover, solutions of iterative phase reconstruction algorithms can be improved considerably by initializing them with the phase estimate provided by the present algorithm. We present an extensive comparison with the state-of-the-art algorithms in a reproducible manner.

The discrete wavelet transform module is a recent addition to the Large Time-Frequency Analysis Toolbox (LTFAT). It provides implementations of various generalizations of Mallat's well-known algorithm (iterated filterbank) such that completely general filterbank trees, dual-tree complex wavelet transforms, and wavelet packets can be computed. The resulting transforms can be equivalently represented as filterbanks and analyzed as filterbank frames using fast algorithms.