On Homotopy Continuation for Speech Restoration

Abstract

In this paper, a homotopy-based method is employed for the recovery of speech recordings from missing or corrupted samples taken in a noisy environment. The model for the acquisition device is a compressed sensing scenario using Gabor frames. To recover an approximation of the speech file, we used the basis pursuit denoising method with the homotopy continuation algorithm. We tested the proposed method with various speech recordings.

Detection of the mandibular canal in orthopantomography using a Gabor-filtered anisotropic generalized Hough transform

“…When discretized directly it results a highly redundant representation. Therefore, the proper sampling of position space and frequency space with step widths α = ( α 1 , α 2 ) and β = ( β 1 , β 2 ), chosen such that we obtain a Gabor frame [10] is necessary. The result is a set of Gabor coefficients which represent local waves contained in the image.…”

“…Gabor analysis [3,8,10] is a discrete version of the STFT and it is concerned with the representation of signals or images using a series consisting of time-frequency shifted copies of the given atom g . The Gabor system for analysis 𝒢( g , Λ) = { π ( λ ) g ; λ ∈ Λ} over the lattice Λ consists of the translated and modulated versions of g , and it forms a frame for the space L 2 (ℝ d ), if and only if there exist 0 < A ≤ B < ∞ ( frame bounds ) with A||f|false|2≤∑λ∈Λ|〈f,π(λ)g〉|2≤B||f||2foreveryf∈L2(ℝd), With the interpretation proposed in Section 3.1, we will use the direct Gabor transform for ranking in the accumulator space of the AGHT.…”