(Matlab) Take an image, downsample and convert to black and white with the follwoing code:

image_BW=rgb2gray(image);

image_DS=downsample(image_BW,3);

The simplest interpolation would be reconstruction with a square pulse which produces a zero-order hold. Here is a method that works for a one-dimensional signal (i.e., one row or one column of the image), assuming that we start with a row vector xr1, and the result is the row vector xr1hold.

xr1 = (-2).(0:6);

L = length(xr1);

nn = ceil((0.999:1:4*L)/4); %<-- Round up to the integer part

xr1hold = xr1(nn);

Use this method to up sample the down sampled gray scale image by a factor of 3 and try to restore the orignal image. Interpolate both on rows and columns. Display the new image.