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+\bibcite{LeastSquaredProblem}{AWxx}
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+\bibcite{LZW}{Wel84}

main.bbl

+\newcommand{\etalchar}[1]{$^{#1}$}
+\begin{thebibliography}{HMvdW{\etalchar{+}}20}
+
+\bibitem[AAB97]{ABRARDO1997321}
+Andrea Abrardo, Luciano Alparone, and Franco Bartolini.
+\newblock Encoding-interleaved hierarchical interpolation for lossless image
+  compression.
+\newblock {\em Signal Processing}, 56(3):321--328, 1997.
+
+\bibitem[AAB02]{AIAZZI20021619}
+Bruno Aiazzi, Luciano Alparone, and Stefano Baronti.
+\newblock Near-lossless image compression by relaxation-labelled prediction.
+\newblock {\em Signal Processing}, 82(11):1619--1631, 2002.
+
+\bibitem[AW20]{DBLP:journals/corr/abs-2010-05846}
+Josh Alman and Virginia~Vassilevska Williams.
+\newblock A refined laser method and faster matrix multiplication.
+\newblock {\em CoRR}, abs/2010.05846, 2020.
+
+\bibitem[AWxx]{LeastSquaredProblem}
+Josh Alman and Virginia~Vassilevska Williams.
+\newblock Algorithm 853: an efficient algorithm for solving rank-deficient
+  least squares problems.
+\newblock {\em ACM Transactions on Mathematical Software}, Vol. x, No. x,,
+  20xx.
+
+\bibitem[Bla99]{LAPACKAlgorithms}
+Susan Blackford.
+\newblock {LAPACK Benchmark}.
+\newblock \url{http://www.netlib.org/lapack/lug/node71.html}, October 1999.
+\newblock Accessed: 2022-6-23.
+
+\bibitem[Deu96]{PNGdetails}
+L.~Peter Deutsch.
+\newblock {DEFLATE Compressed Data Format Specification version 1.3}.
+\newblock \url{https://www.w3.org/Graphics/PNG/RFC-1951}, 1996.
+\newblock Accessed: 6/14/2022.
+
+\bibitem[HMvdW{\etalchar{+}}20]{Numpy}
+Charles~R. Harris, K.~Jarrod Millman, St{\'{e}}fan~J. van~der Walt, Ralf
+  Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor,
+  Sebastian Berg, Nathaniel~J. Smith, Robert Kern, Matti Picus, Stephan Hoyer,
+  Marten~H. van Kerkwijk, Matthew Brett, Allan Haldane, Jaime~Fern{\'{a}}ndez
+  del R{\'{i}}o, Mark Wiebe, Pearu Peterson, Pierre G{\'{e}}rard-Marchant,
+  Kevin Sheppard, Tyler Reddy, Warren Weckesser, Hameer Abbasi, Christoph
+  Gohlke, and Travis~E. Oliphant.
+\newblock Array programming with {NumPy}.
+\newblock {\em Nature}, 585(7825):357--362, September 2020.
+
+\bibitem[Huf52]{Huffman}
+D.~A. Huffman.
+\newblock A method for the construction of minimum redundancy codes.
+\newblock {\em Proceedings of the Institute of Radio Engineers},
+  40(9):1098--1101, September 1952.
+
+\bibitem[{Mar}03]{PNGoverview}
+{Mark Adler, Thomas Boutell, John Bowler, Christian Brunschen, Adam M.
+  Costello, Lee Daniel Crocker, Andreas Dilger, Oliver Fromme, Jean-loup
+  Gailly, Chris Herborth, Alex Jakulin, Neal Kettler, Tom Lane, Alexander
+  Lehmann, Chris Lilley, Dave Martindale, Owen Mortensen, Keith S. Pickens,
+  Robert P. Poole, Glenn Randers-Pehrson, Greg Roelofs, Willem van Schaik, Guy
+  Schalnat, Paul Schmidt, Michael Stokes, Tim Wegner, Jeremy Wohl}.
+\newblock {Portable Network Graphics (PNG) Specification (Second Edition)}.
+\newblock \url{https://www.w3.org/TR/PNG/}, November 2003.
+\newblock Accessed: 6/23/2022.
+
+\bibitem[Wel84]{LZW}
+Welch.
+\newblock A technique for high-performance data compression.
+\newblock {\em Computer}, 17(6):8--19, 1984.
+
+\end{thebibliography}

main.bib

+
+@Article{         Numpy,
+ title         = {Array programming with {NumPy}},
+ author        = {Charles R. Harris and K. Jarrod Millman and St{\'{e}}fan J.
+                 van der Walt and Ralf Gommers and Pauli Virtanen and David
+                 Cournapeau and Eric Wieser and Julian Taylor and Sebastian
+                 Berg and Nathaniel J. Smith and Robert Kern and Matti Picus
+                 and Stephan Hoyer and Marten H. van Kerkwijk and Matthew
+                 Brett and Allan Haldane and Jaime Fern{\'{a}}ndez del
+                 R{\'{i}}o and Mark Wiebe and Pearu Peterson and Pierre
+                 G{\'{e}}rard-Marchant and Kevin Sheppard and Tyler Reddy and
+                 Warren Weckesser and Hameer Abbasi and Christoph Gohlke and
+                 Travis E. Oliphant},
+ year          = {2020},
+ month         = sep,
+ journal       = {Nature},
+ volume        = {585},
+ number        = {7825},
+ pages         = {357--362},
+ doi           = {10.1038/s41586-020-2649-2},
+ publisher     = {Springer Science and Business Media {LLC}},
+ url           = {https://doi.org/10.1038/s41586-020-2649-2}
+}
+
+
+@misc{PNGoverview,
+  title = "{Portable Network Graphics (PNG) Specification (Second Edition)}",
+  howpublished = {\url{https://www.w3.org/TR/PNG/}},
+  year = 2003,
+  author = "{Mark Adler,
+Thomas Boutell,
+John Bowler,
+Christian Brunschen,
+Adam M. Costello,
+Lee Daniel Crocker,
+Andreas Dilger,
+Oliver Fromme,
+Jean-loup Gailly,
+Chris Herborth,
+Alex Jakulin,
+Neal Kettler,
+Tom Lane,
+Alexander Lehmann,
+Chris Lilley,
+Dave Martindale,
+Owen Mortensen,
+Keith S. Pickens,
+Robert P. Poole,
+Glenn Randers-Pehrson,
+Greg Roelofs,
+Willem van Schaik,
+Guy Schalnat,
+Paul Schmidt,
+Michael Stokes,
+Tim Wegner,
+Jeremy Wohl}",
+  month = nov,
+  note = {Accessed: 6/23/2022}
+}
+
+
+@misc{PNGdetails,
+	title = "{DEFLATE Compressed Data Format Specification version 1.3}",
+  howpublished = {\url{https://www.w3.org/Graphics/PNG/RFC-1951}},
+  year = 1996,
+  author = "L. Peter Deutsch",
+  note = {Accessed: 6/14/2022}
+}
+
+
+@Article{         Huffman,
+ title         = {A Method for the Construction of Minimum Redundancy Codes},
+ author        = {D. A. Huffman},
+ year          = {1952},
+ month         = sep,
+ journal       = {Proceedings of the Institute of Radio Engineers},
+ volume        = {40},
+ number        = {9},
+ pages         = {1098-1101},
+}
+
+@misc{LAPACKAlgorithms,
+  title        = "{LAPACK Benchmark}",
+  author       = "Susan Blackford",
+  howpublished = "\url{http://www.netlib.org/lapack/lug/node71.html}",
+  year         = 1999,
+  month        = oct,
+  note         = "Accessed: 2022-6-23"
+}
+
+@article{DBLP:journals/corr/abs-2010-05846,
+  author    = {Josh Alman and
+               Virginia Vassilevska Williams},
+  title     = {A Refined Laser Method and Faster Matrix Multiplication},
+  journal   = {CoRR},
+  volume    = {abs/2010.05846},
+  year      = {2020},
+  url       = {https://arxiv.org/abs/2010.05846},
+  eprinttype = {arXiv},
+  eprint    = {2010.05846},
+  timestamp = {Tue, 20 Oct 2020 15:08:10 +0200},
+  biburl    = {https://dblp.org/rec/journals/corr/abs-2010-05846.bib},
+  bibsource = {dblp computer science bibliography, https://dblp.org}
+}
+
+@article{LeastSquaredProblem,
+  author    = {Josh Alman and
+               Virginia Vassilevska Williams},
+  title     = {Algorithm 853: an Efficient Algorithm for Solving Rank-Deficient Least Squares Problems},
+  journal   = {ACM Transactions on Mathematical Software},
+  volume    = {Vol. x, No. x,},
+  year      = {20xx},
+  url       = {http://www.math.sjsu.edu/~foster/foster_kommu.pdf},
+
+}
+
+@ARTICLE{LZW,
+  author={Welch},
+  journal={Computer}, 
+  title={A Technique for High-Performance Data Compression}, 
+  year={1984},
+  volume={17},
+  number={6},
+  pages={8-19},
+  doi={10.1109/MC.1984.1659158}}
+  
+@article{ABRARDO1997321,
+title = {Encoding-interleaved hierarchical interpolation for lossless image compression},
+journal = {Signal Processing},
+volume = {56},
+number = {3},
+pages = {321-328},
+year = {1997},
+issn = {0165-1684},
+doi = {https://doi.org/10.1016/S0165-1684(97)00034-0},
+url = {https://www.sciencedirect.com/science/article/pii/S0165168497000340},
+author = {Andrea Abrardo and Luciano Alparone and Franco Bartolini},
+keywords = {Image compression, Lossless compression, Progressive transmission, Hierarchical interpolation, Cyclic differences encoding},
+abstract = {In this correspondence an improved version of the Hierarchical INTerpolation (HINT) algorithm is proposed for multi-resolution reversible compression of still images. The efficiency of the basic scheme is increased by splitting the non-separable interpolation process into two cascaded directional steps interleaved with encoding. Interpolation errors from the former are encoded to yield error-free pixel values, from which the left-over pixels are interpolated in the latter step. The outcome benefit is twofold: interpolation is executed starting from all error-free pixel values, and different directional correlations may be exploited. In addition, the differences between true and interpolated pixel values are encoded cyclically with respect to the range of pixel values within square blocks, thus saving extra bits compared to plain entropy coding. Results and comparisons witness the improved coding performance.}
+}
+
+@article{AIAZZI20021619,
+title = {Near-lossless image compression by relaxation-labelled prediction},
+journal = {Signal Processing},
+volume = {82},
+number = {11},
+pages = {1619-1631},
+year = {2002},
+issn = {0165-1684},
+doi = {https://doi.org/10.1016/S0165-1684(02)00305-5},
+url = {https://www.sciencedirect.com/science/article/pii/S0165168402003055},
+author = {Bruno Aiazzi and Luciano Alparone and Stefano Baronti},
+keywords = {Differential pulse code modulation (DPCM), Data compression, Near-lossless image compression, Relaxation labelling, Statistical context modelling},
+abstract = {This paper describes a differential pulse code modulation scheme suitable for lossless and near-lossless compression of monochrome still images. The proposed method is based on a classified linear-regression prediction followed by context-based arithmetic coding of the outcome residuals. Images are partitioned into blocks, typically 8×8, and a minimum mean square error linear predictor is calculated for each block. Given a preset number of classes, a clustering algorithm produces an initial guess of as many predictors to be fed to an iterative labelling procedure that classifies pixel blocks simultaneously refining the associated predictors. The final set of predictors is encoded, together with the labels identifying the class, and hence the predictor, to which each block belongs. A thorough performance comparison, both lossless and near-lossless, with advanced methods from the literature and both current and upcoming standards highlights the advantages of the proposed approach. The method provides impressive performances, especially on medical images. Coding time are affordable thanks to fast convergence of training and easy balance between compression and computation by varying the system's parameters. Decoding is always real-time thanks to the absence of training.}
+}
+
+
+
+
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+\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
+\BOOKMARK [1][-]{section.2}{Related Work}{}% 2
+\BOOKMARK [2][-]{subsection.2.1}{PNG}{section.2}% 3
+\BOOKMARK [2][-]{subsection.2.2}{LZW}{section.2}% 4
+\BOOKMARK [2][-]{subsection.2.3}{A Method to Save Some of the Interpolated Errors}{section.2}% 5
+\BOOKMARK [2][-]{subsection.2.4}{A Method of Interpolation by Clustering}{section.2}% 6
+\BOOKMARK [1][-]{section.3}{Background}{}% 7
+\BOOKMARK [1][-]{section.4}{The Approach}{}% 8
+\BOOKMARK [1][-]{section.5}{Results}{}% 9
+\BOOKMARK [1][-]{section.6}{Discussion}{}% 10