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@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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@Article{Dahlen1993,
author={D{\AE}hlen, Morten
and Floater, Michael},
title={Iterative polynomial interpolation and data compression},
journal={Numerical Algorithms},
year={1993},
month={Mar},
day={01},
volume={5},
number={3},
pages={165-177},
abstract={In this paper we look at some iterative interpolation schemes and investigate how they may be used in data compression. In particular, we use the pointwise polynomial interpolation method to decompose discrete data into a sequence of difference vectors. By compressing these differences, one can store an approximation to the data within a specified tolerance using a fraction of the original storage space (the larger the tolerance, the smaller the fraction).},
issn={1572-9265},
doi={10.1007/BF02215679},
url={https://doi.org/10.1007/BF02215679}
}

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@techreport{ISO/IEC14495-1,
type = {Standard},
key = {LosslessJPG},
author = {JPEG},
month = dec,
year = {1999},
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181
title = {{Information technology - Lossless and near-lossless compression of continuous-tone still images}},
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volume = {1999},
address = {Geneva, CH},
institution = {International Organization for Standardization}
}
@INPROCEEDINGS{544819,
  author={Xiaolin Wu and Memon, N.},
  booktitle={1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings}, 
  title={CALIC-a context based adaptive lossless image codec}, 
  year={1996},
  volume={4},
  number={},
  pages={1890-1893 vol. 4},
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  doi={10.1109/ICASSP.1996.544819}
}
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