Quantitative Results Using Error Metric

Error Metric

I selected to use the mean squared error as the error metric to evaluate the effectiveness of the system. The benefit of using this metric is that it provides a method for calculating the error that gives a numerical value that can be used to compare errors from different reconstructions regardless of the size of the images in question.

Where

X – Original High resolution image

X’ – Reconstructed High resolution image

L – Number of pixels along each axis (assumes square image)

Quantitative Results

The image below shows the original high resolution image that was used in order to assess the performance of the super-resolution algorithm when applied to various low resolution sets.

20 Pixels Super-Resolved to 30

Original High Resolution Image

Low Resolution Input frames (Each one is 30 x 30)

Output Image

Rank of Model Matrix = 900 (Full Rank)

Mean Squared Error = 1.6491e-024

15 Pixels Super-Resolved to 30

I wont include images for this case as they look pretty similar to the images for the 20 pixel low resolution case.

Rank of Model Matrix = 900 (Full Rank)

Mean Squared Error = 9.0744e-023

10 Pixels Super-Resolved to 30

Rank of Model Matrix = 900 (Full Rank)

Mean Squared Error = 1.2279e-025

6 Pixels Super-Resolved to 30

6 Pixels was the lowest that could achieved whilst still having the model matrix have full rank.

Low Resolution Input frames (Each one is 6 x 6)

Reconstructed High Resolution Image

Rank of Model Matrix = 900 (Full Rank)

Mean Squared Error = 1.1463e-024

4 Pixels Super-Resolved to 30

Reconstructed High Resolution Image

Rank of Model Matrix = 400

Mean Squared Error = 0.0182