dessertation ppt

7/30/2019 dessertation ppt

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Image Denoisingusing

Wavelet Transform


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Contents

What is a transform?

Wavelet transform(WT)

Application of DWT in Signal Denoising

Noise

Denoising Process

Results

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What is a Transform?

Transform: A mathematical operation that takes a function or

sequence and maps it into another one

Transforms are good things because it may give additional /hidden information about the original

function.

With transform of an equation,it may be easier to solve than

the original equation The transform of a function/sequence may require less

storage.

An operation may be easier to apply on the transformed

function.

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What is a wavelet Transform? It is the representation of a function by wavelets.

The wavelets are scaled and translated copies

(known as "daughter wavelets") of a finite-lengthoscillating waveform. Basis functions of thewavelet transform (WT) aresmall waves locatedin different times.

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dts

ttxs

ssxx

*1,,CWT

Translation

(The location of

the window)

ScaleWindow function


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They are obtained using scaling and translation of ascaling function and wavelet function.

Therefore, the WT is localized in both time and frequency

Analysis windows of different lengths are used fordifferent frequencies:

Analysis of high frequencies Use narrower windows

for better time resolution

Analysis of low frequencies

Use wider windows forbetter frequency resolution


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We can construct discrete WT via filter banks The analysis section is illustrated below


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Two-Channel Filter Banks

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Applicationof

Wavelet Transform

in

Image denoising

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Denoising

Denosing is the process with which wereconstruct a signal from a noisy one.

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Denoising process

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Block Diagram


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Steps for removing noise1. Decompose signal using DWT;

Choose wavelet and number of decompositionlevels.

ComputeY=Wy

2. Perform thresholding in the Wavelet domain.

Shrink coefficients by thresholding (hard /soft)

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3. Reconstruct the signal from thresholded DWT

coefficients

Compute


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2-D WT

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Boats image WT in 3 levels


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Results

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Boats image Noisy image (additive Gaussian noise)

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Boats image Denoised image using DWT

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Thank you

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