Fourier transform on image - problem with sharpening filter

I implemented DFT and inverse DFT for images. So now I want to apply some filters in frequency space. Blur went easy. I simply do a fall off function on the frequencies as they go farther away from the center frequency. Now I wanted to do a sharpening filter by altering the high frequencies. I found this website http://www.cs.unm.edu/~brayer/vision/fourier.html that discusses sharpening filter and proses a simple piecewise linear function. So I used it and even used the very same Lena picture (size 256x256). In theory, I'm doing the same thing as the author of the website but my results are way different, which I enclose in the attachment. The image indeed seems to be sharper, but where does this white mess come from? I noticed similar problems when I tried to do an edge detection filter (by removing low frequencies). Basically, it looks that if I cut the high frequencies my results are predictable, but when I try to leave high and get rid off low frequencues, I get a lot of that white messy stuff. Any suggestions?

For the sake of clarity, here are my source codes (I think they are easy to follow):

DFT:

void discreteFourierTransform(CImageByte& input, CImageFloat& output)
{
for (int y = 0; y < input.getHeight(); y++)
{
for (int x = 0; x < input.getWidth(); x++)
{
for (int j = 0; j < input.getHeight(); j++)
{
for (int i = 0; i < input.getWidth(); i++)
{
float p = -PI_mul_2 * ((float)(x*i)/(float)input.getWidth() + (float)(y*j)/(float)input.getHeight());

float R = (float)input(i, j);
float I = 0.0f;

output(x, y, 0) += R*cosf(p) - I*sinf(p);
output(x, y, 1) += R*sinf(p) + I*cosf(p);
}
}
}
}
}


Inverse DFT:

void inverseDiscreteFourierTransform(CImageFloat& input, CImageFloat& output)
{
for (int y = 0; y < input.getHeight(); y++)
{
for (int x = 0; x < input.getWidth(); x++)
{
for (int j = 0; j < input.getHeight(); j++)
{
for (int i = 0; i < input.getWidth(); i++)
{
float p = PI_mul_2 * ((float)(x*i)/(float)input.getWidth() + (float)(y*j)/(float)input.getHeight());

float& R = input(i, j, 0);
float& I = input(i, j, 1);

output(x, y, 0) += R*cosf(p) - I*sinf(p);
output(x, y, 1) += R*sinf(p) + I*cosf(p);
}
}

output(x, y, 0) /= (float)(input.getWidth() * input.getHeight());
output(x, y, 1) /= (float)(input.getWidth() * input.getHeight());
}
}
}


Sharpening filter:

void sharpenFilter_frequencySpace(CImageFloat& dft)
{
float r1 = 0.0f;
float r2 = 96.0f;

vec2 coeffs = solve2x2(vec2(r1, 0.5f), vec2(r2, 4.0f));

for (int j = 0; j < dft.getHeight(); j++)
{
for (int i = 0; i < dft.getWidth(); i++)
{
float dx = (float)(dft.getWidth()/2 - i);
float dy = (float)(dft.getHeight()/2 - j);
float d = sqrtf(dx*dx + dy*dy);

if (d <= r1)
{
dft(i, j, 0) *= 0.5f;
dft(i, j, 1) *= 0.5f;
}
else if (d > r1 && d <= r2)
{
float s = coeffs.x*d + coeffs.y;
dft(i, j, 0) *= s;
dft(i, j, 1) *= s;
}
else if (d > r2)
{
dft(i, j, 0) *= 4.0f;
dft(i, j, 1) *= 4.0f;
}
}
}
}