Abstract
In this paper, we propose a new technique for exact recovery of missing data due to impulsive noise in time-domain sampled acoustic waves, named as sketching and stacking with random fork (SSRF). Existing methods recover the original signal from the corrupted sequence based on the correlation between each element of the signal or between the bases constituting the signal such as in the field of interpolation or compressive sensing. In addition, a partially corrupted signal is retrieved through statistical approaches using a large amount of pre-measured data in the machine learning domain. As a new approach, we hypothesize that if there is a novel method of re-sampling and processing, which can extract the intrinsic information of a corrupted signal, then the original signal can be recovered without information loss. The mathematical backgrounds in our study are twofold; first, a signal made up of overlapped k damped sinusoidal waves can be represented as the superposition of 2k number of geometric sequences according to Euler's formula; second, this superposed signal can be decomposed into individual geometric sequences by well-transformed 2k+1 informative matrices. The proposed method is to extract the parameters of 2k geometric sequences by transforming the non-corrupted samples into 2k+1 informative matrices, and retrieve the corrupted samples by extrapolating the obtained parameters. We reveal the condition where SSRF perfectly fulfills the exact reconstruction, and verify the quality of reconstruction by comparing the results with conventional schemes.
Highlights
The scope of acoustic signal usage continuously broadens with advances in signal processing techniques
We hypothesized that if there is a novel method of re-sampling and processing, which can extract the intrinsic information of a corrupted signal, the original signal can be recovered without information loss
We utilized two mathematical backgrounds to support our hypothesis as follows: first, a signal made up of overlapped k damped sinusoidal waves can be represented as the superposition of 2k number of geometric sequences according to Euler’s formula; second, this superposed signal can be decomposed into individual geometric sequences by well-transformed 2k + 1 informative matrices
Summary
The scope of acoustic signal usage continuously broadens with advances in signal processing techniques. Park et al.: SSRF Based Exact Signal Recovery Under Sample Corruption accurately model the correlation between adjacent samples and extract the intrinsic parameters of signals. DEEP NEURAL NETWORK (DNN) With the soaring popularity of machine learning, there has been many approaches of combining machine learning methods with signal recovery [22]–[25] It contains the mechanism of training a neural network to make noisy samples as similar to the original signal as possible. It is based on statistical inference to learn how data is missing It is very effective in recovering the original signal, but it obviously requires pretraining with a huge number of data sets, which is highly challenging in practice. The acoustic signal from the source is the summation of k damped sinusoidal waves, v(t), which can be represented as follows:.
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