Progressive JPEG

A progressive JPEG (frame marker FF C2, SOF2) sends the same quantised coefficients as a sequential one, but in several scans, so a viewer can show a rough picture and sharpen it as more data arrives. Each scan carries a part of the coefficients, set by its Ss, Se, Ah and Al bytes.

Spectral selection and successive approximation

Spectral selection splits the 64 coefficients into bands. The band of a scan runs from Ss to Se, in zig-zag order. Successive approximation sends the high bits of the coefficients first and refines them in later scans: Al is the lowest bit a scan sends, and Ah is the bit position the band had reached before.

Scan type	Ss	Se	Ah	Components	What it does
DC, first	0	0	0	one or several	Each DC coefficient, shifted down by Al bits
DC, refinement	0	0	not 0	one or several	One more low bit of each DC coefficient
AC, first	1 or more	Ss to 63	0	one	The coefficients of the band, each divided by 2^Al and rounded towards zero
AC, refinement	1 or more	Ss to 63	not 0	one	One more low bit of the coefficients of the band

In a refinement scan, Al is Ah − 1, so one bit is added. An AC scan has a single component, so its blocks are not gathered into MCUs. DC scans may be interleaved, in MCUs, as a sequential scan is.

An example set of scans

The default that libjpeg uses for a colour image is:

Scan	Components	Coefficients	Bits
1	Y, Cb, Cr	0–0	all but the lowest (Al = 1)
2	Y	1–5	high bits (Al = 2)
3	Cr	1–63	high bits (Al = 1)
4	Cb	1–63	high bits (Al = 1)
5	Y	6–63	high bits (Al = 2)
6	Y	1–63	refines to Al = 1
7	Y, Cb, Cr	0–0	refines to Al = 0
8	Cr	1–63	refines to Al = 0
9	Cb	1–63	refines to Al = 0
10	Y	1–63	refines to Al = 0

DC scans

A first DC scan codes each block's DC coefficient, arithmetically shifted right by Al, as a difference from the previous block, just as a sequential scan does. A later DC scan sends one bit per block, with no Huffman code: the bit at position Al of the coefficient. It is added to the value so far.

AC scans

A first AC scan codes each block's band with the same run and size symbols as a sequential scan, starting at coefficient Ss, except that a block can end early with an end-of-band run.

End-of-band runs

A symbol n0, with n from 0 to 14 (00 to E0), means that this block and some blocks after it have no more non-zero coefficients in this band. n further bits follow the code. The number of blocks is

EOBRUN = 2^n + (the n bits, read as a number)

In a first AC scan, the blocks counted in the run after the first have no bits at all, so a long run takes only a few bits.

Refinement

In a refinement scan each coefficient of the band is either already non-zero, from earlier scans, or still zero. The scan's symbols describe only the still-zero coefficients:

A symbol with size 1 means: skip R still-zero coefficients, then make the next one a new non-zero value of ±2^Al. Its one bit, straight after the code, gives the sign: 1 for positive, 0 for negative.
ZRL (F0) means: skip 16 still-zero coefficients.
An EOB run symbol works as before. The blocks in the run have no further codes.

Every coefficient of the band that is already non-zero gets one correction bit in the data, read in order, after the codes before it and the sign bit of any new coefficient. A 1 adds 2^Al to the coefficient's magnitude. Blocks in an end-of-band run get these correction bits too, so a run is not always free of bits.