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Communications of the ACM, April 1991 (vol. 34 no. 4), pp. 30-44.
(Adjacent articles in that issue discuss MPEG motion picture compression,
applications of JPEG, and related topics.)  If you don't have the CACM issue
handy, a PostScript file containing a revised version of Wallace's article is
available at http://www.ijg.org/files/wallace.ps.gz.  The file (actually
a preprint for an article that appeared in IEEE Trans. Consumer Electronics)
omits the sample images that appeared in CACM, but it includes corrections
and some added material.  Note: the Wallace article is copyright ACM and IEEE,
and it may not be used for commercial purposes.
 
A somewhat less technical, more leisurely introduction to JPEG can be found in
"The Data Compression Book" by Mark Nelson and Jean-loup Gailly, published by
M&T Books (New York), 2nd ed. 1996, ISBN 1-55851-434-1.  This book provides
good explanations and example C code for a multitude of compression methods
including JPEG.  It is an excellent source if you are comfortable reading C
code but don't know much about data compression in general.  The book's JPEG
sample code is far from industrial-strength, but when you are ready to look
at a full implementation, you've got one here...
 
The best currently available description of JPEG is the textbook "JPEG Still
Image Data Compression Standard" by William B. Pennebaker and Joan L.
Mitchell, published by Van Nostrand Reinhold, 1993, ISBN 0-442-01272-1.
Price US$59.95, 638 pp.  The book includes the complete text of the ISO JPEG
standards (DIS 10918-1 and draft DIS 10918-2).
 
The original JPEG standard is divided into two parts, Part 1 being the actual
specification, while Part 2 covers compliance testing methods.  Part 1 is
titled "Digital Compression and Coding of Continuous-tone Still Images,
Part 1: Requirements and guidelines" and has document numbers ISO/IEC IS
10918-1, ITU-T T.81.  Part 2 is titled "Digital Compression and Coding of
Continuous-tone Still Images, Part 2: Compliance testing" and has document
numbers ISO/IEC IS 10918-2, ITU-T T.83.
 
The JPEG standard does not specify all details of an interchangeable file
format.  For the omitted details we follow the "JFIF" conventions, revision
1.02.  JFIF 1.02 has been adopted as an Ecma International Technical Report
and thus received a formal publication status.  It is available as a free
download in PDF format from
http://www.ecma-international.org/publications/techreports/E-TR-098.htm.
A PostScript version of the JFIF document is available at
http://www.ijg.org/files/jfif.ps.gz.  There is also a plain text version at
http://www.ijg.org/files/jfif.txt.gz, but it is missing the figures.
 
The TIFF 6.0 file format specification can be obtained by FTP from
ftp://ftp.sgi.com/graphics/tiff/TIFF6.ps.gz.  The JPEG incorporation scheme
found in the TIFF 6.0 spec of 3-June-92 has a number of serious problems.
IJG does not recommend use of the TIFF 6.0 design (TIFF Compression tag 6).
Instead, we recommend the JPEG design proposed by TIFF Technical Note #2