Interpolation Techniques with Matlab

Objective 

Objective of this project is to compare interpolation techniques by using Matlab. In the first part of the project we eliminated half of the columns of random data(eliminating 50 percent of the data), in the second part we eliminated half of the columns and rows of an image (eliminating 75 percent of the data) and applied the interpolation techniques to be able to obtain original data or image.

Interpolation Techniques for a Random Data

Firstly 64x64 size random data generated. To interpolate this data we eliminate half of the columns so that we have 64x32 size data.  In matlab there are 7 types of interpolation techniques (Nearest, Linear, Spline, Pchip, Cubic, V5cubic and FT). We applied all techniques one by one and found MSE (Mean Square Error)

Results

MSE of Nearest 19.606252

MSE of Linear 17.557691

MSE of Spline 19.606252

MSE of Pchip 17.738441

MSE of Cubic 17.738441

MSE of V5cubic 18.177292

MSE of FT 19.550018

For random data we obtained the best results with Linear method.

Interpolation Techniques for an Image

For this part, we used saturn.png image of matlab, and resized this image as 256x256. To interpolate this data we eliminated half of the columns and rows so that we have 64x64 size data. After elimination we added 3 types of noises (Gaussian, Poisson and Salt & Pepper). For this part we applied 4 methods (Nearest, Cubic, Spline and FT)to the remaining noisy data . We applied these 4 techniques and found MSE and PSNR.

Results

After Interpolation

Cubic Method

 Linear Method 

 Spline Method

FT Method

S&P Noise

MSE of Salt&Pepper   382.142734  and PSNR 22.308548 with Linear

MSE of Salt&Pepper   456.388458  and PSNR 21.537457 with Spline

MSE of Salt&Pepper   381.532439  and PSNR 22.315489 with Cubic

MSE of  Salt&Pepper  543.335752  and PSNR 20.814116  with FT

minmseSP =381.5324

maxpsnrSP =22.3155

Best results obtained with Cubic method for S&P noise.  

Gaussian Noise

MSE of  Gaussian   328.542685  and PSNR 22.964886 with Linear

MSE of  Gaussian   380.948627  and PSNR 22.322139 with Spline

MSE of  Gaussian   337.898027  and PSNR 22.842947 with Cubic

MSE of Gaussian   437.834990  and PSNR 21.751695 with FT

minmseGaussian =328.5427

maxpsnrGaussian =22.9649

Best results obtained with Linear method for Gaussian noise. 

Poisson Noise

MSE of  Poisson   51.035730  and PSNR 31.052060 with Linear

MSE of  Poisson   55.175091  and PSNR 30.713373 with Spline

MSE of  Poisson   50.987560  and PSNR 31.056161 with Cubic

MSE of Poisson   54.333921  and PSNR 30.814089 with FT

minmsePoisson =50.9876

maxpsnrPoisson =31.0562

Best results obtained with Cubic method for Poisson noise. 

 For source code;

https://drive.google.com/folderview?id=0B2WG_0RRtnAnfkc3WGlIQUhHOUNoWVV3OFNtdVRoN056Slh2TmZiSklLQTRkNkJCYkE4c2c&usp=sharing