We present a novel method for automatic transcription of polyphonic music based on a recently published algorithm for non-negative matrix factor 2-D deconvolution. The method works by simultaneously estimating a time-frequency model for an instrument and a pattern corresponding to the notes which are played based on a log-frequency spectrogram of the music.

Spectral factorization methods are used for the estimation of minimum phase time series from a given power spectrum. We present an efficient technique for spectral factorization, based on Newton’s method. We show how to apply the method to the factorization of both auto and cross-spectra, and present a simple example of 2-D deconvolution in the helical coordinate system.

tion techniques, such as predictive deconvolution or Radon transforms, fail in the presence of complex structures. A technique popularized by the Delphi consortium offers an attractive alternative in 2-D because it is theoretically independent of subsurface structure and can therefore attack all surface-related multiples regardless of their complexity. The Delphi approach can be summarized by t...

We address the problem of improving the spatial resolution of ultrasound images through blind deconvolution. The ultrasound image formation process in the RF domaim can be expressed as a spatio-temporal convolution between the tissue response and the ultrasonic system response, plus additive noise. Convolutional components of the dispersive attenuation and aberrations introduced by propagating ...

Seismic interferometry is a field of growing interest in exploration seismology. In this paper we provide the theoretical basis for performing interferometry by deconvolution. We argue that for general models, deconvolution interferometry gives only the causal scattering response between any two receivers, as opposed to cross-correlation which gives both causal and acausal scattering responses....

If the Navier-Stokes equations are averaged with a local, spacial convolution type filter, φ = gδ ∗ φ , the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which satisfies

Minimizing a convex function of measure with sparsity-inducing penalty is typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this can be solved by discretizing the and running non-convex gradient descent on positions weights particles. For measures d-dimensional manifold under some non-degeneracy assumptions, leads to global optimiz...

We develop a self-consistent automatic procedure to restore informations from astronomical observations. It relies on both a new deconvolution algorithm called LBCA (Lower Bound Constraint Algorithm) and the use of the Wiener filter. In order to explore its scientific potential for strong and weak gravitational lensing, we process a CFHT image of the galaxies cluster Abell 370 which exhibits sp...