Part 1. Noise reduction by image averaging

1.1 Have a read of related lecture notes and the following online material for information about noise reduction using image averaging. https://www.cambridgeincolour.com/tutorials/image-averaging-noise.htm

1.2 Download or take a clear picture I1, and convert the image into a grayscale image I2. Then add random Gaussian noise to image I2 and generate 30 noise-contaminated images N1 to N30.

1.3 Show noise reduction results by taking the average of any 2, 5, 20, and 30 images from N1 to N30. Briefly analyze your results based on your understanding.

1.4 Report: Your report should include a brief technical description of noise reduction by image averaging, image I1, I2, N1 to N4, the source code, the four averaged images, and a brief analysis of your results.

Part 2. Power-law transformation

2.1 Write down the equations for log and power-law transformations; state the effects of the two transformations.

2.2 Using the grayscale image I2 generated in Part 1, perform a power-law transformation on I2 with = 0.3 and = 3, and generate transformed images T1 and T2, respectively.

2.3 Report: Your report should include part 2.1, image I2, the transformed images T1 and T2, and a brief analysis of your results.

Part 3. Histogram equalization

3.1 State the basic principle of histogram equalization.

3.2 Compute the histogram of the three images: I2 from part 1, and T1 and T2 from part 2.

3.3 Perform histogram equalization on the three images I2, T1 and T2.

3.4 Report: Your report should include part 3.1, the three images and the corresponding histograms, the three histogram-equalized images and the corresponding histograms, as well as a brief analysis of your results.