Windows are designed to smooth out the transition between the content and the zero-padded region, so apply them just to the data itself before zero-padding. I've tweaked your code to use that instead and a Kaiser window (experiment with beta values between zero and, say, four).
Maybe something like:
load penny;
sHR = -del2(P);
subplot(1,2,1);
imagesc(sHR);
colormap copper
shading flat
axis equal
% sHR: HR reference image
n = size(sHR,1);
kspHR = fftshift(fft(sHR,n,1),1)/n; % HR image in k-space
% Generating LR image (LR in row-direction)
kspLR = kspHR((n/2)-(n/4)+1:(n/2)+(n/4),:);
% ZP'd lr
beta = 4; % roughly equivalent to Hann
w = kaiser(size(kspLR,1),beta);
% wKspLR = w .* kspLR; % may work directly if you have R2016b or later.
wKspLR = bsxfun(@times, w, kspLR);
% continue onwards...
a = floor(size(wKspLR,1)/2);
wKspZP = padarray(wKspLR, a ,'both');
wsZP = real(ifft(ifftshift(wKspZP,1),n,1))*n;
subplot(1,2,2);
imagesc(wsZP);
shading flat
axis equal
As for the negative intensity question... a lot depends on how you want to process the image afterwards. Maybe someone else in the community can comment on that.
