Algorithm 112 Refining DC Coefficients

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GLOBAL SUCCESSIVEAPPROXIMATION Procedure RefineDCDataUnit (COEFFICIENTS [063]) Begin BIT = ReadLiteralBits (1) DCCOEFFICIENTS [0] = DCCOEFFICIENTS [0] Or (BIT LeftShift SUCCESSIVEAPPROXIMATION) End

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Data Unit Decoding First AC Scans

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The simplicity of decoding DC coefficients is more than compensated for by the complexity of decoding AC coefficients For the first scan of an AC band the encoding is similar to sequential with some additions Progressive JPEG adds the concept of an end-of-band (EOB) run This is a run of data units where the AC coefficients within the band are all zero In sequential JPEG each data unit is encoded independently from every other Because of EOB runs, data units are not independent in AC scans In sequential JPEG the Huffman-encoded value 0016 is used to set the remaining coefficients in a data unit to zero This is equivalent to an EOB run of 1 Progressive scans can contain much longer EOB runs Table 112 lists the EOB codes and the possible EOB run lengths associated with them Raw bits following the Huffman-encoded byte are used to specify EOB runs just as they are with literal values The 4 high-order bits specify the number of additional bits when used as part of an EOB code Since EOB runs are always positive, the Extend() function is not used Instead, the conversion from raw bits to the EOB run length is EOBRUN = (1 LeftShift HIGHBITS) + ReadRawBits (HIGHBITS) If an EOB code occurs in the compressed stream when a band has been partially processed, the current band becomes the first data unit in the EOB run and the remaining coefficients are set to zero Be sure to count the current band when processing an EOB run

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Table 112 AC Codes and Corresponding EOB Run Length

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Code Value 0016 1016 2016 3016 4016 5016 6016 7016 8016 9016 A016 B016 C016 D016 E016

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EOB Run Length

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1 2-3 4-7 8-15 16-31 32-63 64-127 128-127 256-511 512-1023 1,024-2047 2,048-4095 4,096-8191 8,192-16,383 16,384-32,767

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Progressive JPEG Algorithm 113 shows how the first scan for an AC band is decoded The main differences between sequential and progressive processing are: Only coefficients within the spectral selection band are updated Coefficient values are left-shifted by the successive approximation value EOB run processing

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Refining AC Scans Refining AC scans is the nightmare of progressive JPEG decoding The implementation problem is that these scans contain data to refine all previously nonzero coefficients that are skipped as a result of a zero run or EOB run In a refining AC scan, the 4 low-order bits of the Huffman-encoded values can be only 1 or zero This should make sense since a refining scan only adds 1 bit per coefficient If a coefficient needed more than 1 bit it would have been encoded in earlier scans The processing of refining AC scans is nearly identical to that of initial scans Whenever the value of the 4 low-order bits of the Huffman-encoded value is 1, a coefficient is being made nonzero for the first time This value is immediately followed in the input stream by 1 raw sign bit The new coefficient value is If SignBit = 1 Then CoefficientValue = 1 LeftShift ScanSuccessiveApproximation Else If SignBit = 0 Then CoefficientValue = -1 LeftShift ScanSuccessiveApproximation This is essentially the same as using the Extend function The major difference in refining scans is the processing of zero and EOB runs Zero runs in a refining scan only count zero-valued coefficients This sequence of coefficients would be skipped by a zero run of 4 (not 6):

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0 0 4 0 2 0

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Whenever a nonzero coefficient is skipped, as a result of a zero or EOB run, the input stream contains 1 raw bit to refine that coefficient In our previous example, suppose that the Huffman-encoded value were 4116 Three raw bits would follow this code: The first bit would be the sign bit for the coefficient being made nonzero; the next bit would refine the coefficient with the value 4, and the last would refine the coefficient with the value 2 Algorithm 114 shows the process for refining a previously nonzero coefficient Once the correct number of zero-valued coefficients has been skipped, the next coefficient is assigned the value found at the start of the procedure Notice that the data for coefficients is not stored strictly in order The data for the last coefficient comes first in the input stream

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