Evaluation metrics

1. Peak signal-to-noise ratio:

One of the more traditional approaches to compare the quality of regeneration of a high-resolution image from a low-resolution image that we can use in single-image super-resolution

1. PSNR is calculated by minimizing the mean squared error between the original image and a low-resolution image.

2. a high PSNR number generally indicates that the Reconstruction is of a higher quality but it is valid only when used to compare results from the same codec and content.

3. The validity of the PSNR-

   1. Considered a high-resolution image when compress using a lossy format converting from one lossy format to another creates a situation where a second codec is exposed to distortions made by the previous codec leading to a biased PSNR

   2. It is a solution to maximize speed and efficiency, for example, JPEG encoders allow chroma subsampling which will again lead to a biased PSNR

   3. Disclaimer- most tools for codec quality measurements approximate human perception but human perception may be biased in. Quality is subjective. A way to prevent this is by using two images that are exactly the same file size and compare which compression better retains the properties of the original image better.

2. Structural similarity index

Unlike the PSNR, the SSIM measures the visual impact of luminance contrast and structure of an image against a reference.

1. SSIM considers luminance masking and contrast masking incorporating important perceptual phenomena.

2. In luminance masking, distortions are less visible in bright regions of the image and in contrast masking distortions are less visible in textured regions of the image

3. A structural similarity closer to 1 indicates a better quality of reconstruction

2.1 Method for calculating SSIM-

1. The SSIM quality assessment index is based on the computation of luminance contrast and structure.

2. the standard deviation of an isotropic gaussian function is used for weighting the neighborhood pixels around the pixel to estimate local statistics

3. Luminance, contrast, and structure are multiplicatively combined and we use regularization constants to avoid instability for image regions where the local mean or standard deviation is close to zero.

where μx, μy, σx,σy, and σxy are the local means, standard deviations, and cross-covariance for images x, y

2.2 Method for image comparison with SSIM-

1. Calculate global SSIM value for the image and local SSIM values for each pixel

2. Create a local SSIM map and display small values of local SSIM as dark pixels in the map

3. small values indicate regions where the blurred image differs from the reference image

4. Likewise, bright pixels, i.e., higher values indicate regions where the blurred image is very similar to the reference.