Lucas Rencker

We address the problem of sparse signal reconstruction from a few noisy samples. Recently, a Covariance-Assisted Matching Pursuit (CAMP) algorithm has been proposed, improving the sparse coefficient update step of the classic Orthogonal Matching Pursuit (OMP) algorithm. CAMP allows the a-priori mean and covariance of the non-zero coefficients to be considered in the coefficient update step. In this paper, we analyze CAMP, which leads to a new interpretation of the update step as a maximum-a-posteriori (MAP) estimation of the non-zero coefficients at each step. We then propose to leverage this idea, by finding a MAP estimate of the sparse reconstruction problem, in a greedy OMP-like way. Our approach allows the statistical dependencies between sparse coefficients to be modelled, while keeping the practicality of OMP. Experiments show improved performance when reconstructing the signal from a few noisy samples.

Musical noise is a recurrent issue that appears in spectral techniques for denoising or blind source separation. Due to localised errors of estimation, isolated peaks may appear in the processed spectrograms, resulting in annoying tonal sounds after synthesis known as ?musical noise?. In this paper, we propose a method to assess the amount of musical noise in an audio signal, by characterising the impact of these artificial isolated peaks on the processed sound. It turns out that because of the constraints between STFT coefficients, the isolated peaks are described as time-frequency ?spots? in the spectrogram of the processed audio signal. The quantification of these ?spots?, achieved through the adaptation of a method for localisation of significant STFT regions, allows for an evaluation of the amount of musical noise. We believe that this will pave the way to an objective measure and a better understanding of this phenomenon.

We address the problem of decomposing several consecutive sparse signals, such as audio time frames or image patches. A typical approach is to process each signal sequentially and independently, with an arbitrary sparsity level fixed for each signal. Here, we propose to process several frames simultaneously, allowing for more flexible sparsity patterns to be considered. We propose a multivariate sparse coding approach, where sparsity is enforced on average across several frames. We propose a Multivariate Iterative Hard Thresholding to solve this problem. The usefulness of the proposed approach is demonstrated on audio coding and denoising tasks. Experiments show that the proposed approach leads to better results when the signal contains both transients and tonal components.

An OMP-like Covariance-Assisted Matching Pursuit (CAMP) method has recently been proposed. Given a priorknowledge of the covariance and mean of the sparse coefficients, CAMP balances the least squares estimator and the priorknowledge by leveraging the Gauss-Markov theorem. In this letter, we study the performance of CAMP in the framework of restricted isometry property (RIP). It is shown that under some conditions on RIP and the minimum magnitude of the nonzero elements of the sparse signal, CAMP with sparse level K can recover the exact support of the sparse signal from noisy measurements. l2 bounded noise and Gaussian noise are considered in our analysis.We also discuss the extreme conditions of noise (e.g. the noise power is infinite) to simply show the stability of CAMP.

Clipping, or saturation, is a common nonlinear distortion in signal processing. Recently, declipping techniques have been proposed based on sparse decomposition of the clipped signals on a fixed dictionary, with additional constraints on the amplitude of the clipped samples. Here we propose a dictionary learning approach, where the dictionary is directly learned from the clipped measurements. We propose a soft-consistency metric that minimizes the distance to a convex feasibility set, and takes into account our knowledge about the clipping process. We then propose a gradient descent-based dictionary learning algorithm that minimizes the proposed metric, and is thus consistent with the clipping measurement. Experiments show that the proposed algorithm outperforms other dictionary learning algorithms applied to clipped signals. We also show that learning the dictionary directly from the clipped signals outperforms consistent sparse coding with a fixed dictionary.

Non-negative Matrix Factorization (NMF) is a well established tool for audio analysis. However, it is not well suited for learning on weakly labeled data, i.e. data where the exact timestamp of the sound of interest is not known. In this paper we propose a novel extension to NMF, that allows it to extract meaningful representations from weakly labeled audio data. Recently, a constraint on the activation matrix was proposed to adapt for learning on weak labels. To further improve the method we propose to add an orthogonality regularizer of the dictionary in the cost function of NMF. In that way we obtain appropriate dictionaries for the sounds of interest and background sounds from weakly labeled data. We demonstrate that the proposed Orthogonality-Regularized Masked NMF (ORM-NMF) can be used for Audio Event Detection of rare events and evaluate the method on the development data from Task2 of DCASE2017 Challenge.

We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable cost function. We then propose a fast iterative shrinkage/thresholding algorithm that minimizes the proposed cost, which provides a fast and efficient algorithm to recover sparse signals from clipped and quantized measurements.