# 3.4 Jpeg entropy coding

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This module gives a clever method of coding, JPEG entropy coding.

The entropy plots of the Quantisation of the DCT coefficients show the theoretical entropies of each DCT sub-band. In practise this would be a poor way to code thedata because:

• 64 separate entropy codes would be required (each requiring many extra states to represent run-length coding of zeros).
• The statistics for each code are likely to vary significantly from image to image.
• To transmit the code table for each sub-band as header information would involve a large coding overhead (many extra bits).
• Coding the sub-bands separately does not take account of the correlations which exist between the positions of the non-zero coefsin one sub-band with those of nearby sub-bands (see subfigures (c) and (d) from a previous module).
JPEG uses a clever alternative method of coding, based on combining run-length and amplitude information into a single Huffman code forthe whole of the image (except the DC sub-band which is coded separately because its statistics are so different).

The code is applied to each block of $8\times 8$ quantised DCT coefs from a single $8\times 8$ pel region. The blocks are the coefs before reordering as shown in subfigure (b) of a previous module and comprise one coef from each of the 64 sub-bands.

Each block of $8\times 8$ quantised coefs is formed into a 1-D vector by zig-zag scanning in the sequence: $\begin{pmatrix}0 & 1 & 5 & 6 & 14 & 15 & 27 & 28\\ 2 & 4 & 7 & 13 & 16 & 26 & 29 & 42\\ 3 & 8 & 12 & 17 & 25 & 30 & 41 & 43\\ 9 & 11 & 18 & 24 & 31 & 40 & 44 & 53\\ 10 & 19 & 23 & 32 & 39 & 45 & 52 & 54\\ 20 & 22 & 33 & 38 & 46 & 51 & 55 & 60\\ 21 & 34 & 37 & 47 & 50 & 56 & 59 & 61\\ 35 & 36 & 48 & 49 & 57 & 58 & 62 & 63\\ \end{pmatrix}$

## The jpeg code for dc coefs

The first coefficient (0) of each block (vector) is the DC coef, which represents the mean value of the pels in the block (see the top leftbasis function in subfigure (a) from previous discussion).

The DC coefs still exhibit significant local correlations (top left of subfigure (b) ), so differential coding is used in which the value to be codedis the difference between the current DC coef and that of the previous block - the blocks are scanned from left toright, row by row. The first block in each row is coded with respect to zero.

The histogram of entropies of the DC coef differences is compared in with that of the raw DC coefs from this previous figure . We note the histogram peak around zero and see that the entropy is reduced from 6.42 bits to 6.07 bits.

The size of the differences can in theory be up to $±(255\times 8)=±(2040)$ if the input pels occupy the range $-128$ to $+(127)$ (the DCT has a gain of 8 at very low frequencies). Hence the Huffman code table would have to bequite large. JPEG adopts a much smaller code by using a form of floating-point representation, where Size is the base-2 exponent and Additional Bits are used to code the polarity and precise amplitude as follows:

DC Coef Difference Size Typical Huffman codes for Size Additional Bits (in binary)
0 0 00 -
-1,1 1 010 0,1
-3,-2,2,3 2 011 00,01,10,11
-7,…,-4,4,…,7 3 100 000,…,011,100,…111
-15,…-8,8,…,15 4 101 0000,…,0111,1000,…,1111
-1023,…-512,512,…,1023 10 1111 1110 00 0000 0000,…,11 1111 1111
-2047,…-1024,1024,…2047 11 1 1111 1110 000 0000 0000,…,111 1111 1111

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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