Abstract

In this thesis, we develop various methods for the purpose of data denoising. We propose a method for Mean Square Error (MSE) estimation in Soft Thresholding. The MSE estimator is based on Minimum Noiseless Data Length (MNDL). Our simulation results show that this MSE estimate is a valuable comparison measure for different soft thresholding methods. Two denoising methods are proposed for analog domain: Mean Square Error EstiMation (MSEEM) which minimizes the worst case MSE estimate, and Noise Invalidation Denoising (NIDe) method which is based on the newly prosposed idea of noise signature. While MSEEM shown to be the optimum denoising method for non-sparse signals, NIDe approach outperforms the other well known denoising methods in presence of colored noise. In digital domain we address two interesting problems: 1) simultaneous denoising and quantization method, 2) denoising a digital signal in digital domain. For problem one, we propose a new method that generalizes the idea of dead zone estimation to a multi-level noise removal. An example of this method is shown for hyperspectral image denoising and compression. A digital domain denoising approach pioneers in answering the second problem with only one prior knowledge on the desired signal, that it is digital. The method provides the optimum reconstruction levels in the MSE sense. One of the critical steps of denoising process is the noise variance estimation. As a part of this thesis, we propose a novel noise variance estimation method for BayesShrink that outperforms conventional MAD-based noise variance estimation. Although BayesShrink is one of the most efficient denoising methods, no analytical analysis is available for it. Here, we study Bayes estimators for General Gaussian Distribued (GGD) data and provide the theoretical justification for BayesShrink. This study enables us to generalize the BayesShrink threshold to Generalized BayesShrink which outperforms the BayesShrink itself.

Highlights

  • A fundamental problem in statistical signal processing is estimating signal from its noisy version

  • In this chapter we propose a method called Residual Autocorrelation Power (RAP), which is an adaptive method for noise variance estimation to improve the BayesShrink denoising [10, 9]

  • We can make a hybrid method which is very fast and accurate, a first estimation is made by Median Abolute absolute Deviation (MAD) an interval from a little less and a little more than

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Summary

Introduction

A fundamental problem in statistical signal processing is estimating signal from its noisy version. It is typical to assume the signal is low-pass and the noise is not. The noise can be reduced with a low-pass linear filter. Low-pass filtering is extensively studied in many classical signal processing textbook, [1, 2, 3]. Many signals have useful high-pass features like edges in the images which are removed or blurred by using low-pass filters. Wiener filtering is another classical method used for denoising the signal corrupted by noise. Wavelet denoising can provide low-pass filtering to reduce noise, while the useful high-pass features of the signal can be preserved. The edges and the useful high-pass features have significant coefficients

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