Block-matching and 3D filtering

<h2 id="method">Method</h2>
<h3>Grouping</h3>
<p>Image fragments are grouped together based on similarity, but unlike standard <a href="/facts/K-means_clustering/vxIcqHwN">k-means clustering</a> and such <a href="/facts/Cluster_analysis/HUeDnWPt">cluster analysis</a> methods, the image fragments are not necessarily <a href="/facts/Disjoint_sets/nLr8XRVd">disjoint</a>. This <a href="/facts/Block-matching_algorithm/UulHuNX6">block-matching algorithm</a> is less computationally demanding and is useful later on in the aggregation step. Fragments do however have the same size.
A fragment is grouped if its dissimilarity with a reference fragment falls below a specified threshold.
This grouping technique is called block-matching, it is typically used to group similar groups across different frames of a <a href="/facts/Digital_video/xsn9omqG">digital video</a>, BM3D on the other hand may group <a href="/facts/Macroblocks/L7XPoRNP">macroblocks</a> within a single frame.
All image fragments in a group are then stacked to form 3D cylinder-like shapes.
</p>
<h3>Collaborative filtering</h3>
<p>Filtering is done on every fragments group. A 
  
    
      
        d
        +
        1
      
    
    {\displaystyle d+1}
  
 dimensional linear transform is applied, followed by a transform-domain shrinkage such as <a href="/facts/Wiener_filtering/oGWdBTYa">Wiener filtering</a>, then the linear transform is inverted to reproduce all (filtered) fragments.
</p>
<h3>Aggregation</h3>
<p>The image is transformed back into its two-dimensional form. All overlapping image fragments are weight-averaged to ensure that they are filtered for noise yet retain their distinct signal.
</p>
<h2 id="extensions">Extensions</h2>
<h3>Color images</h3>
<p>RGB images can be processed much like grayscale ones. A luminance-chrominance transformation should be applied to the RGB image. The grouping is then completed on the luminance channel which contains most of the useful information and a higher SNR. This approach works because the noise in the chrominance channels is strongly correlated to that of the luminance channel, and it saves approximately one-third of the computing time because grouping takes up approximately half of the required computing time.
</p>
<h3>Deblurring</h3>
<p>The BM3D algorithm has been extended (IDD-BM3D) to perform decoupled deblurring and denoising using the <a href="/facts/Nash_equilibrium/l74xzIHd">Nash equilibrium</a> balance of the two objective functions.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>
</p>
<h3>Convolutional neural network</h3>
<p>An approach that integrates a <a href="/facts/Convolutional_neural_network/kHEdnmGU">convolutional neural network</a> has been proposed and shows better results (albeit with a slower runtime).<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> <a href="/facts/MATLAB/qPjLISCk">MATLAB</a> code has been released for research purpose.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a>
</p>
<h2 id="implementations">Implementations</h2>
<ul><li>Reference implementation in <a href="/facts/MATLAB/qPjLISCk">MATLAB</a> and <a href="/facts/Python_(programming_language)/YbuGqofa">Python</a> released under an <a href="/facts/Open-source_license/FlFTwHmd">open-source</a> <a href="/facts/Proprietary_software/9zcskxYL">proprietary</a> license:<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> <a href="http://www.cs.tut.fi/~foi/GCF-BM3D/">BM3D</a></li>
<li>Well documented<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> <a href="/facts/C_(programming_language)/Ky2No763">C</a>-based implementation released under the <a href="/facts/GPLv3/S75KhLSX">GPLv3</a>: <a href="https://github.com/gfacciol/bm3d">bm3d</a></li>
<li><a href="/facts/CUDA/fvPpolot">CUDA</a> and <a href="/facts/C%252B%252B/Et0F2qn9">C++</a> based implementation released under the <a href="/facts/GPLv3/S75KhLSX">GPLv3</a>: <a href="https://github.com/DawyD/bm3d-gpu">bm3d-gpu</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Dabov, Kostadin; Foi, Alessandro; Katkovnik, Vladimir; Egiazarian, Karen (16 July 2007). "Image denoising by sparse 3D transform-domain collaborative filtering". IEEE Transactions on Image Processing. 16 (8): 2080–2095. Bibcode:2007ITIP...16.2080D. CiteSeerX 10.1.1.219.5398. doi:10.1109/TIP.2007.901238. PMID 17688213. S2CID 1475121. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Manjón, José V.; Carbonell-Caballero, José; Lull, Juan J.; García-Martí, Gracián; Martí-Bonmatí, Luís; Robles, Montserrat (2008-08-01). "MRI denoising using Non-Local Means". Medical Image Analysis. 12 (4): 514–523. doi:10.1016/j.media.2008.02.004. ISSN 1361-8415. PMID 18381247. <a href="https://www.sciencedirect.com/science/article/pii/S1361841508000248" target="_blank">https://www.sciencedirect.com/science/article/pii/S1361841508000248</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Maggioni, M.; Katkovnik, V.; Egiazarian, K.; Foi, A. (January 2013). "Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction". IEEE Transactions on Image Processing. 22 (1): 119–133. doi:10.1109/TIP.2012.2210725. ISSN 1057-7149. PMID 22868570. S2CID 1295558. <a href="https://ieeexplore.ieee.org/document/6253256" target="_blank">https://ieeexplore.ieee.org/document/6253256</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Danielyan, Aram; Katkovnik, Vladimir; Egiazarian, Karen (30 June 2011). "BM3D Frames and Variational Image Deblurring". IEEE Transactions on Image Processing. 21 (4): 1715–28. arXiv:1106.6180. Bibcode:2012ITIP...21.1715D. doi:10.1109/TIP.2011.2176954. PMID 22128008. S2CID 11204616. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Ahn, Byeongyong; Ik Cho, Nam (3 April 2017). "Block-Matching Convolutional Neural Network for Image Denoising". arXiv:1704.00524 [Vision and Pattern Recognition Computer Vision and Pattern Recognition]. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>"BMCNN-ISPL". Seoul National University. Retrieved 3 January 2018. <a href="http://ispl.snu.ac.kr/clannad/BMCNN/" target="_blank">http://ispl.snu.ac.kr/clannad/BMCNN/</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>"LASIP - Legal Notice". Tampere University of Technology (TUT). Retrieved 2 January 2018. <a href="http://www.cs.tut.fi/~foi/GCF-BM3D/legal_notice.html" target="_blank">http://www.cs.tut.fi/~foi/GCF-BM3D/legal_notice.html</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>Lebrun, Marc (8 August 2012). "An Analysis and Implementation of the BM3D Image Denoising Method". Image Processing on Line. 2: 175–213. doi:10.5201/ipol.2012.l-bm3d. <a href="https://doi.org/10.5201%2Fipol.2012.l-bm3d" target="_blank">https://doi.org/10.5201%2Fipol.2012.l-bm3d</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
</ol>

Block-matching and 3D filtering open-in-new

Block-matching and 3D filtering