<blockquote>
  <p>but still has a blurred effect on it.</p>
</blockquote>

<p>Thats because you deleted high frequencies with your Notch filter.</p>

<blockquote>
  <p>I am trying to sharpen this image an return it to its original
  quality</p>
</blockquote>

<p>It is not possible to return the image to its original Moire free quality. Although you might be able to yield better results if you design your Notch filter more carefully.</p>

<p>Moire already destroyed information and removing those disturbing frequencies with the Notch filter destroyed even more.</p>

<p>You cannot get that information back. The only thing you can do is to apply some sharpening filters which usualy rely on increasing the <a href="https://en.wikipedia.org/wiki/Acutance" rel="nofollow noreferrer">acutance</a>. With such filters the image is actually not sharpened but edge transitions are manipulated in a way that makes them appear sharper.</p>

<p>There are other techniques than using Notch filters which in many cases perform better.</p>

<p>Read <a href="https://arxiv.org/ftp/arxiv/papers/1701/1701.09037.pdf" rel="nofollow noreferrer">A New Method for Removing the Moire' Pattern from
Images</a> for example. They use median filters.</p>
sharpening an image after removing a Moiré pattern
<p>I am attempting to remove a moire pattern from an image by blurring the image and then returning it to its original quality by enhancing and sharpening the image, however I can only seem to remove the pattern and leave it very blurry, which is not what I am trying to do. </p>

<p>I have tried to apply a filter to the image to blur the image and remove the checkerboard pattern however I cannot seem to return the image to its original quality without the checkerboard. </p>

<pre><code>imageFiles = {'radiograph_01.jpg', 'radiograph_02.jpg'};
medWinSize = [7 11];
notchCenters{1} = [269 80; 261 123; 245 216; 238 258];
sigmas{1} = [45 20 20 45];
notchCenters{2} = [277 442; 209 450];
sigmas{2} = [20 20];
for nImage = 1:length(imageFiles)
% Load image
 [pathStr, name, ext] = fileparts(imageFiles{nImage});
 img = imread(imageFiles{nImage});
 img = im2double(img);
 [height, width] = size(img);
 figure(1); clf;
 subplot(1,3,1);
 imshow(img);

 % Median filter
 imgMed = medfilt2(img, medWinSize(nImage)*[1 1]);
 subplot(1,3,2);
 imshow(imgMed);
 imwrite(imgMed, [name '-med-filtered.jpg']);

 % Compute DFT of original image
 imgDFT = fftshift(fft2(img));
 imgDFTMag = abs(imgDFT);
 figure(2); clf;
 subplot(1,3,1);
 imshow(log(imgDFTMag), [0 10]); colorbar;

 % Apply notch filter
 [omega_x, omega_y] = meshgrid(1:width, 1:height);
 filterDFT = ones(size(omega_x));
 for n = 1:size(notchCenters{nImage},1)
 rSq = (omega_x - notchCenters{nImage}(n,1)).^2 + ...
 (omega_y - notchCenters{nImage}(n,2)).^2;
 filterDFT = filterDFT .* (1 - exp(-rSq / sigmas{nImage}(n)^2));
 end % n
 imgFiltDFT = imgDFT .* filterDFT;
 imgFiltDFTMag = abs(imgFiltDFT);
 subplot(1,3,2);
 imshow(filterDFT, [0 1]); colorbar;
 subplot(1,3,3);
 imshow(log(imgFiltDFTMag), [0 10]); colorbar;
 % Reconstruct image
 imgFilt = real(ifft2(ifftshift(imgFiltDFT)));
 imgFilt = max(0, min(1, imgFilt));
 figure(1);
 subplot(1,3,3);
 imshow(imgFilt);
 imwrite(imgFilt, [name '-notch-filtered.jpg']);
end % nImage
</code></pre>

<p><img src="https://i.stack.imgur.com/c6r5D.png" alt="Original Image"></p>

<p>With this current code, the image is loaded in, the filter is applied and the image is returned without the moire pattern, but still has a blurred effect on it. I am trying to sharpen this image an return it to its original quality after having removed this pattern.</p>