**CIS115-6 Signals and Electronic Systems**

AssignmentTutorOnline

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**Signal Processing Assignment**

**(50% of total assignment marks)**

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__Hand-in Date: Friday, ____7 ^{th} May 2022, 10.00am__

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**You MUST submit an electronic copy of your INDIVIDUAL report through the BREO site for this unit**

__Aim__

- Gain experience of designing systems for image approximation using signal transforms

__Task__

You are designing an image compression method as a component of a new face recognition photography system. Your task is to design and optimise the image compression algorithm using the wavelet transform. Write a ** detailed individual report** following the points below. For each task below, you need to provide a detailed justification for each choice you make.

- Using only the operator symbols for filtering and downsampling, show and explain a detailed schematic diagram of the
__forward wavelet transform__applied to images with only 1 decomposition level. Recall that the wavelet transform needs to be applied along horizontal and vertical directions when applied to images. (5%)

**Operator symbol**

**For filtering, and down-sampling**

**Need to show (figure), and explain a schematic diagram of FORWARD WAVELET TRANSFORM**

**Decomposition level (iteration level) with 1**

**Recall that WAVELET TRANSFORM required to be apply on horizontal and vertical direction applied to image.**

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- Using only the operator symbols for filtering and upsampling, show and explain a detailed schematic diagram of the
__inverse wavelet transform__used for reconstruction of images with only 1 synthesis level. (5%)

**Operator symbol**

**For filtering, and up-sampling**

**Need to show (figure), and explain a schematic diagram of INVERSE WAVELET TRANSFORM**

**Decomposition level (iteration level) with 1.**

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- Using the schematic diagram derived in A. as a building block, show and explain in detail the schematic diagram for deploying the
__forward wavelet transform with 3 iterations__(decomposition levels) to images. Use the schematic diagram from A. as a box with input(s) and output(s) – there is no need to show again the content of the box. (10%)

**Schematic diagram in question A / deploying forward wavelet transform with 3 iteration (decomposition level) to image.**

**Schematic diagram from A , as a box with input (s) and output (s) , no need to show content of the box.**

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- Using the schematic diagram derived in B. as a building block, show and explain in detail the schematic diagram for the
__inverse wavelet transform using 3 iterations__(decomposition levels). (10%)

**Schematic diagram in question B / show and explain inverse wavelet transform with 3 iteration (decomposition level) to image.**

- Show a schematic diagram that combines the ones derived in C and D to apply image approximation. Assume that in the approximation process, all transform coefficients that
__do not belong__to the lowest pass subband are set to zero. (20%)

**Question C, and D, schematic diagram / apply image approximation.**

**Assume that in approximation process **

**All transform coefficient that do not belong to lowest pass subband are set to zero**

- Calculate how many operations (additions and multiplications) are required to be carried out for approximation (forward, then inverse wavelet transform with the modification as in E, that is zeroing out all the coefficients except the ones from the lowest pass subband) of an image of the size 512 x 512 pixels. Assume that the wavelet filters used in the process consist of 4 coefficients. Show and explain every step of the calculations. Show how the downsampling operator can reduce the number of operations. (30%)

**Required to be carried out the operations ( additions, and multiplications) for approximation ( forward then inverse wavelet transform with the modification as in E, that zeroing out all the coefficient except the ones from the lowest pass subband ) of image size 512×512.**

**Assume that the wavelet filters used in the process consist of 4 coefficient.**

**Show and explain every step of calculations.**

**Show how the downswampling operator can reduce the number of operation.**

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- Using the exercises and Matlab source code carried out in practicals, apply the approximation defined in F using one of the test images provided in Breo and calculate the mean-square error (MSE). (20%)

**Refer in practical 6 **

**Apply the approximation defined in question F, using one of the test image provided in BREO, and calculate the MEAN-SQUARE ERROR (MSE).**

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