Multi-pitch estimation exploiting block sparsity

An adaptive penalty approach to multi-pitch estimation

“…In some estimation scenarios, e.g., when estimating chroma using the approach in [8], this would simplify the tuning procedure significantly. Furthermore, we show that the proposed method performs comparably to that of [5], albeit with the notable improvement of requiring fewer tuning parameters. The method operates by solving a series of convex optimization problems, and so solve these we present an efficient algorithm based on the alternating directions method of multipliers (ADMM) [9].…”

“…We extend on these works by exploiting the harmonic structure of the signals in a block sparse framework, where each block represents a candidate pitch. A similar method was introduced in [5], where block sparsity was enforced using block-norms, penalizing the number of active pitches. As the block-norm penalty, under some circumstances, cannot distinguish a true pitch from its suboctave, i.e., the pitch with half of the true fundamental frequency, the method is also complemented by a total variation penalty, which is shown to solve such issues.…”

“…In this paper, we show that a total variation penalty, in itself, is enough to enforce a block sparse solution, if utilized efficiently. More specifically, by making the penalty function adaptive, we may improve upon the convex approximation used in [5], allowing us to drop the block-norm penalty altogether, and so reduce the number of tuning parameters. In some estimation scenarios, e.g., when estimating chroma using the approach in [8], this would simplify the tuning procedure significantly.…”

Online group-sparse estimation using the covariance fitting criterion

“…Estimating a sparse parameter support for a high-dimensional regression problem has been the focus of much scientific attention during the last two decades, as this methodology has shown its usefulness in many applications, ranging from spectral analysis [1][2][3], array- [4][5][6] and audio processing [7][8][9], to biomedical modeling [10], and magnetic resonance imaging [11,12]. In its vanguard, notable contributions were done by, among others, Donoho et al [13] and Tibshirani et al [14].…”

Sparse chroma estimation for harmonic non-stationary audio

“…The same chroma is then cyclically defined to each doubling of fundamental frequency, for all twelve chromas [2]. Methods for multi-pitch estimation in audio have been thoroughly examined in the literature (see e.g., [3][4][5], and the references therein). Typically, trouble arises when the complexity of the audio signal increases, such that there are simultaneously two or more pitches present, played by more than one instrument.…”