Evolution Nonlinear Diffusion‐Convection PDE Models for Spectrogram Enhancement

Dugnol, B.; Fernández, Carlos; Galiano, Gonzalo; Velasco, Julián

doi:10.1063/1.2990882

Cited by 1 publication

(4 citation statements)

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“…For instance, for Gaussian windows, S ∈ C ∞ (Ω). First attempts to denoising and enhancing of spectrogram images were made via local differential filters [6,7,9] based on corresponding well established methods, see [1,5,16], in which the filtering process of a intensity image S : Ω → [0, 1] at x ∈ Ω is based only on the intensities in a neighborhood of x. Although the resulting denoised spectrogram greatly improves the IF estimation of the signal, both computational time and low energy harmonic removing were drawbacks which motivated different approaches, see [8].…”

Section: Mathematical Frameworkmentioning

confidence: 99%

“…The discretization of ( 13)-( 15) follows the standard Finite Element methodology for the total variation denoising problem, see [9]. We consider a time semi-implicit Euler scheme and a P 1 continuous finite element approximation in space.…”

Section: Discretizationmentioning

confidence: 99%

“…In [6,7,9], we used nonlinear diffusion image denoising techniques applied to the spectrogram of a sound signal, a wolf chorus. Although, as above mentioned, execution time is not a relevant issue for this type of problems, we found that nonlinear diffusion algorithms require a high computational time, making their use not operative in many situations.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3, we introduce the discrete problem and deduce the corresponding formulas for algorithm implementation. Apart from the Neighborhood filter, we consider the Yaroslavsky-SUSAN [23,19] filter and a nonlinear diffusion filter based in the Total Variation norm [16,9], for comparison porpouses. Then, we demonstrate the performance of these filters by applying them to three noisy signals (synthetic, wolf chorus and ECG) and give quantitative comparisons based on the Mean Square Error (MSE), and the visual inspection of the processed spectrograms and other related magnitudes.…”

Section: Introductionmentioning

confidence: 99%

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On a nonlocal spectrogram for denoising one-dimensional signals

Galiano

Velasco

2014

Applied Mathematics and Computation

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In previous works, we investigated the use of local filters based on partial differential equations (PDE) to denoise one-dimensional signals through the image processing of timefrequency representations, such as the spectrogram. In this image denoising algorithms, the particularity of the image was hardly taken into account. We turn, in this paper, to study the performance of non-local filters, like Neighborhood or Yaroslavsky filters, in the same problem. We show that, for certain iterative schemes involving the Neighborhood filter, the computational time is drastically reduced with respect to Yaroslavsky or nonlinear PDE based filters, while the outputs of the filtering processes are similar. This is heuristically justified by the connection between the (fast) Neighborhood filter applied to a spectrogram and the corresponding Nonlocal Means filter (accurate) applied to the Wigner-Ville distribution of the signal. This correspondence holds only for time-frequency representations of one-dimensional signals, not to usual images, and in this sense the particularity of the image is exploited. We compare though a series of experiments on synthetic and biomedical signals the performance of local and non-local filters.

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