Valentin Emiya

Multipitch Estimation of Piano Sounds Using a New Probabilistic Spectral Smoothness Principle

A new method for the estimation of multiple concurrent pitches in piano recordings is presented. It addresses the issue of overlapping overtones by modeling the spectral envelope of the overtones of each note with a smooth autoregressive model. For the background noise, a moving-average model is used and the combination of both tends to eliminate harmonic and sub-harmonic erroneous pitch estimations. This leads to a complete generative spectral model for simultaneous piano notes, which also explicitly includes the typical deviation from exact harmonicity in a piano overtone series. The pitch set which maximizes an approximate likelihood is selected from among a restricted number of possible pitch combinations as the one. Tests have been conducted on a large homemade database called MAPS, composed of piano recordings from a real upright piano and from high-quality samples.

Subjective and Objective Quality Assessment of Audio Source Separation

We aim to assess the perceived quality of estimated source signals in the context of audio source separation. These signals may involve one or more kinds of distortions, including distortion of the target source, interference from the other sources or musical noise artifacts. We propose a subjective test protocol to assess the perceived quality with respect to each kind of distortion and collect the scores of 20 subjects over 80 sounds. We then propose a family of objective measures aiming to predict these subjective scores based on the decomposition of the estimation error into several distortion components and on the use of the PEMO-Q perceptual salience measure to provide multiple features that are then combined. These measures increase correlation with subjective scores up to 0.5 compared to nonlinear mapping of individual state-of-the-art source separation measures. Finally, we released the data and code presented in this paper in a freely available toolkit called PEASS.

Audio Inpainting

We propose the audio inpainting framework that recovers portions of audio data distorted due to impairments such as impulsive noise, clipping, and packet loss. In this framework, the distorted data are treated as missing and their location is assumed to be known. The signal is decomposed into overlapping time-domain frames and the restoration problem is then formulated as an inverse problem per audio frame. Sparse representation modeling is employed per frame, and each inverse problem is solved using the Orthogonal Matching Pursuit algorithm together with a discrete cosine or a Gabor dictionary. The Signal-to-Noise Ratio performance of this algorithm is shown to be comparable or better than state-of-the-art methods when blocks of samples of variable durations are missing. We also demonstrate that the size of the block of missing samples, rather than the overall number of missing samples, is a crucial parameter for high quality signal restoration. We further introduce a constrained Matching Pursuit approach for the special case of audio declipping that exploits the sign pattern of clipped audio samples and their maximal absolute value, as well as allowing the user to specify the maximum amplitude of the signal. This approach is shown to outperform state-of-the-art and commercially available methods for audio declipping in terms of Signal-to-Noise Ratio.

A constrained matching pursuit approach to audio declipping

We present a novel sparse representation based approach for the restoration of clipped audio signals. In the proposed approach, the clipped signal is decomposed into overlapping frames and the declipping problem is formulated as an inverse problem, per audio frame. This problem is further solved by a constrained matching pursuit algorithm, that exploits the sign pattern of the clipped samples and their maximal absolute value. Performance evaluation with a collection of music and speech signals demonstrate superior results compared to existing algorithms, over a wide range of clipping levels.

A Parametric Method for Pitch Estimation of Piano Tones

The efficiency of most pitch estimation methods declines when the analyzed frame is shortened and/or when a wide fundamental frequency (Fo) range is targeted. The technique proposed herein jointly uses a periodicity analysis and a spectral matching process to improve the fo estimation performance in such an adverse context: a 60 ms-long data frame together with the whole, 71/4-octaves, piano tessitura. The enhancements are obtained thanks to a parametric approach which, among other things, models the inharmonicity of piano tones. The performance of the algorithm is assessed, is compared to the results obtained from other estimators and is discussed in order to characterize their behavior and typical misestimations.

Expectation-maximization algorithm for multi-pitch estimation and separation of overlapping harmonic spectra

This paper addresses the problem of multi-pitch estimation, which consists in estimating the fundamental frequencies of multiple harmonic sources, with possibly overlapping partials, from their mixture. The proposed approach is based on the expectation-maximization algorithm, which aims at maximizing the likelihood of the observed spectrum, by performing successive single-pitch and spectral envelope estimations. This algorithm is illustrated in the context of musical chord identification.

Compressed sensing with unknown sensor permutation

Compressed sensing is the ability to retrieve a sparse vector from a set of linear measurements. The task gets more difficult when the sensing process is not perfectly known. We address such a problem in the case where the sensors have been permuted, i.e., the order of the measurements is unknown. We propose a branch-and-bound algorithm that converges to the solution. The experimental study shows that our approach always retrieves the unknown permutation, while a simple convex relaxation strategy almost always fails. In terms of its time complexity, we show that the proposed algorithm converges quickly with respect to the combinatorial nature of the problem.

Dynamic Screening: Accelerating First-Order Algorithms for the Lasso and Group-Lasso

Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some small computational effort to locate inactive atoms and remove them from the dictionary in a preprocessing stage so that the regression algorithm working with a smaller dictionary will then converge faster to the solution of the initial problem. We believe that there is an even more efficient way to screen the dictionary and obtain a greater acceleration: inside each iteration of the regression algorithm, one may take advantage of the algorithm computations to obtain a new screening test for free with increasing screening effects along the iterations. The dictionary is henceforth dynamically screened instead of being screened statically, once and for all, before the first iteration. We formalize this dynamic screening principle in a general algorithmic scheme and apply it by embedding inside a number of first-order algorithms adapted existing screening tests to solve the Lasso or new screening tests to solve the Group-Lasso. Computational gains are assessed in a large set of experiments on synthetic data as well as real-world sounds and images. They show both the screening efficiency and the gain in terms of running times.

Sparse underwater acoustic imaging: A case study

Underwater acoustic imaging is traditionally performed with beamforming: beams are formed at emission to insonify limited angular regions; beams are (synthetically) formed at reception to form the image. We propose to exploit a natural sparsity prior to perform 3D underwater imaging using a newly built flexible-configuration sonar device. The computational challenges raised by the high-dimensionality of the problem are highlighted, and we describe a strategy to overcome them. As a proof of concept, the proposed approach is used on real data acquired with the new sonar to obtain an image of an underwater target. We discuss the merits of the obtained image in comparison with standard beamforming, as well as the main challenges lying ahead, and the bottlenecks that will need to be solved before sparse methods can be fully exploited in the context of underwater compressed 3D sonar imaging.

Convex nonnegative matrix factorization with missing data

Convex nonnegative matrix factorization (CNMF) is a variant of nonnegative matrix factorization (NMF) in which the components are a convex combination of atoms of a known dictionary. In this contribution, we propose to extend CNMF to the case where the data matrix and the dictionary have missing entries. After a formulation of the problem in this context of missing data, we propose a majorization-minimization algorithm for the solving of the optimization problem incurred. Experimental results with synthetic data and audio spectrograms highlight an improvement of the performance of reconstruction with respect to standard NMF. The performance gap is particularly significant when the task of reconstruction becomes arduous, e.g. when the ratio of missing data is high, the noise is steep, or the complexity of data is high.