Question

Test the noise removal features of the Haar wavelets by adding random noise to one of the functions in Exercises 9.7.1 and 9.7.2, computing the wavelet series, and then setting the high "frequency" modes to zero. What do you observe? Is this a reasonable denoising algorithm when compared with a Fourier method?

    Test the noise removal features of the Haar wavelets by adding random noise to one of the functions in Exercises 9.7.1 and 9.7.2, computing the wavelet series, and then setting the high "frequency" modes to zero. What do you observe? Is this a reasonable denoising algorithm when compared with a Fourier method?

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Applied Linear Algebra (Undergraduate Texts in Mathematics)

Applied Linear Algebra (Undergraduate Texts in Mathematics)

Peter J. Olver,… 2nd Edition

Chapter 9, Problem 5

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Step 1

- Generate random noise, typically Gaussian noise, and add it to the function. For instance, if \( \eta(x) \) represents Gaussian noise, the noisy function becomes \( g(x) = f(x) + \eta(x) \). Show more…

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Test the noise removal features of the Haar wavelets by adding random noise to one of the functions in Exercises 9.7.1 and 9.7.2, computing the wavelet series, and then setting the high "frequency" modes to zero. What do you observe? Is this a reasonable denoising algorithm when compared with a Fourier method?

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