How to interpolate across a missing pixel?

I am quite lost at the moment i had a supervisor who was working on this project but he left unexpected and now im left without any support or someone who really understands what im trying to do and that i can ask questions to so these may seem very trivial:

The code i have done below the main thing i want to achieve is for 64x64 bit image with the missing pixels i want to use the conv2 (or another method) to find the smallest difference in intensity surrounding the missing pixels and have this smallest difference to know which direction to interpolate. How would i word the coding the for for loop to do this? Image is attached.

Thanks!

    function FYPDCT_Image()

    lena=imread('lena.bmp');
    size(lena)
    [m n p]=size(lena)
    a=rgb2gray(lena);
    imshow(a);
    title('Original Grayscale Image');

    lena_c=zeros(m,n,p);

    lenad=a;

    for i=1:16:512
        for j=1:16:512
            lenad(i:i+7,j:j+7)=0;
        end
    end

    %%DCT

    subplot(2,2,1);
    imshow(lenad)
    [m n] = size(lenad)
    title([num2str(m) ' X ' num2str(n)]);

    subplot(2,2,2);
    lenad_ds1=DS_DCT(lenad,8);
    imshow(uint8(lenad_ds1));    
    [m n] = size(lenad_ds1)
    title([num2str(m) ' X ' num2str(n)]);

    subplot(2,2,3);
    lenad_ds2=DS_DCT(lenad_ds1,4);

    imshow(uint8(255*lenad_ds2/max(max(lenad_ds2))));      
    [m n] = size(lenad_ds2)
    title([num2str(m) ' X ' num2str(n)]);

    subplot(2,2,4);
    lenad_ds3=DS_DCT(lenad_ds2,2);

    imshow(uint8(255*lenad_ds3/max(max(lenad_ds3)))); 
    [m n] = size(lenad_ds3)
    title([num2str(m) ' X ' num2str(n)]);

    kernel = [-1 -1 -1;-1 8 -1; -1 -1 -1]/8;

    differenceImage = conv2(double(lenad_ds3), kernel, 'same');

    differenceImage

    %%Downsample by a factor of square(2) using DCT
    function ImageOut=DS_DCT(ImageIn,MBsize)

    [m n]=size(ImageIn);
    k=1;
    for i=1:MBsize:m-MBsize+1
        l=1;
        for j=1:MBsize:m-MBsize+1
            temp=ImageIn(i:i+MBsize-1,j:j+MBsize-1);
            tempDCT=dct2(temp);
            temp=idct2(tempDCT(1:MBsize/2,1:MBsize/2));
            ImageOut(k:k+MBsize/2-1,l:l+MBsize/2-1)=temp;
            l=l+MBsize/2;
        end
        k=k+MBsize/2;
    end

[Image Analyst]

What indicates whether a pixel is "missing" or not?