Practical low bit rate predictive image coder using multirate processing and adaptive entropy coding
ABSTRACT The modified differential pulse coded modulation (DPCM) codec with multirate processing has been shown to able to efficiently code the source with monotonically decreasing spectrum at low bit rates [A.N. Kim and T.A. Ramstad]. A practical image coder is designed based on this approach. Two dimensional DPCM is used along with decimation and interpolation to reduce the number of transmitted samples. The decimation rate depends on the signal spectrum and the bit rate. Further bit rate reduction is achieved through adaptive entropy coding. Wiener filter is appended in the decoder for minimizing distortion caused by quantization noise. The decimation filter can be implemented using simple IIR filters. The necessary side information is low. Simulation results show that the coder is able to give good compression performance at low bit rates which is superior to conventional DPCM codec and JPEG. Subjective quality can be as good as JPEG2000. While at very low bit rates the proposed codec is able to retain certain image characteristics better than JPEG2000.

Conference Paper: Combined error protection and compression using turbo codes for error resilient image transmission
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ABSTRACT: A joint source channel coding scheme for error resilient image transmission is proposed. A practical image coder was introduced in AN Kim et al, (2004) using modified differential pulse coded modulation (DPCM) codec with multirate processing and adaptive entropy coding. In this paper the residual redundancy of the prediction error image is exploited by using turbo codes for both data compression and error protection. In the paper we deal with robust transmission of the source over a BSC channel, but the results can be easily extended for non binary channels. Note also that simple modification of the quantizer allows for progressive transmission and successive refinement of information. With properly chosen rate and puncturing, the system is able to approach the limit theoretically attainable and to outperform the separated approach that consists on the concatenation of the system in AN Kim et al, (2004) and the best turbo codes for the same spectral efficiency.Image Processing, 2005. ICIP 2005. IEEE International Conference on; 10/2005  SourceAvailable from: pastel.archivesouvertes.fr
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PRACTICAL LOW BIT RATE PREDICTIVE IMAGE CODER USING MULTIRATE
PROCESSING AND ADAPTIVE ENTROPY CODING
Anna N. Kim and Tor A. Ramstad
Department of Telecommunications, NTNU
O.S. Bragstads plass 2B, N7491 Trondheim, Norway
ABSTRACT
ThemodifiedDifferentialPulseCodedModulation(DPCM)codec
with multirate processing has been shown to able to code source
with monotonically decreasing spectrum efficiently at low bit rates
[1]. A practical image coder is designed based on this approach.
Two dimensional DPCM is used along with decimation and inter
polation to reduce the number of transmitted samples. The deci
mation rate depends on the signal spectrum and the bit rate. Fur
ther bit rate reduction is achieved through adaptive entropy cod
ing. Wiener filter is appended in the decoder for minimizing dis
tortion caused by quantization noise. The decimation filter can be
implemented using simple IIR filters. The necessary side infor
mation is low. Simulation results show that the coder is able to
give good compression performance at low bit rates which is su
perior to conventional DPCM codec and JPEG. Subjective quality
can be as good as JPEG2000. While at very low bit rates the pro
posed codec is able to retain certain image characteristics better
than JPEG2000.
1. INTRODUCTION
The main advantage of DPCM is its ability to perform efficient
codingwithlowcomplexity. DPCMcodersgenerallyperformwell
at high rates (34 bits/pixel), when quantization steps are small and
the optimal predictor is able to minimize the prediction error vari
ance. However at low bit rate regions, the additive noise model
is no longer applicable. An exact analysis of the system becomes
very involved or even impossible. It is then interesting to modify
the DPCM structure to comply with ratedistortion theory while
at the same time using a rather applicable system model. The as
sumptions would have to be examined from experimental results.
In [1], we proposed a modified DPCM codec with multirate
processing. It is designed for encoding of sources with monotoni
cally decreasing spectra at low bit rates. Similar to the coder in [2],
our codec was motivated by ratedistortion theory. It incorporates
multirate processing and a Wiener receiver filter. Simulation with
Gaussian AR(1) processes show that the decimation and interpola
tion process are able to provide further rate reduction so the over
all ratedistortion performance is much closer to the ratedistortion
bound at low bitrate regions compared to [2].
In this paper we want to verify the potential of the proposed
method in practice by designing an image coder based on this ap
proach. The goal is to have a practical image coder with good
lowbit rate performance, yet lowcomplexity implementation.
2. DPCM WITH MULTIRATE PROCESSING
The ratedistortion theory states that the optimal lossy coding of
a discrete time, continuous Gaussian amplitude source is done by
coding only portions of the source spectrum that is above the noise
floor. This is commonly described as the reverse “Water Filling”
principle. Consider for example a 1st order GaussMarkov pro
cess (AR(1)) which has monotonically decreasing spectrum. At
low target bit rates (high distortion), the high frequency portion
of the source spectrum that is below the additive noise should not
contribute to the rate. This is achieved by applying a lowpass filter
to shape the source spectrum prior to encoding with the standard
DPCM.
However, the lowpass filtered source leads to a lowpass in
put to the quantizer, which is correlated and oversampled. To over
comethisproblem, weapplydownsamplingtothesourcetolower
the sampling rate before coding and corresponding upsampling
and interpolation is performed in the decoder. This modification
leads to further overall rate reduction due to the fact that the num
berofsamplesforcodingafterdownsamplingisreduced. Therate
at the coder output is measured in bits per coded sample. However,
for the overall ratedistortion performance, the rate is measured in
bits per source sample. The actual bit rate is then the obtained rate
divided by the downsampling rate. A simple uniform quantizer
is used for quantization of the prediction error followed by an en
tropy coder. We also append a Wiener filter to the decoder. Its role
is to further suppress distortion due to quantization and it does not
affect the rate.
Simulation results showed that the proposed codec was able
to perform very close to the ratedistortion bound for highly cor
related AR(1) process (correlation coefficient α = 0.9) at low bit
rates. When the codec is not operating at the optimal point, that
is, when there is a mismatch between the lowpass filter cutoff
frequency and the quantization noise level, the Wiener filter was
able to provide significant compensation. More detailed descrip
tion and discussion of the system can be found in [1].
3. LOW BITRATE PREDICTIVE IMAGE CODER WITH
ADAPTIVE ENTROPY CODING
We now introduce the practical image coder based on the codec
described in the previous section.
The image coder has essentially the same structure (Figure 1).
The source image is first lowpass filtered and downsampled two
dimensionally. It is then fed through the DPCM encoder, where
the difference between the downsampled image and its prediction
is quantized using a uniform quantizer and the quantization indices
are entropy coded. On the decoder side, the received quantization
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Fig. 1. Block Diagram of Image Coder: (a) Encoder (b) De
coder. EC: Entropy Coder, ED: Entropy Decoder, L Low
pass Filter, P: Prediction Filter, W: Wiener Filter, r: Decima
tion/Interpolation Rate
indices first go through entropy decoder and DPCM decoder, fol
lowed by the Wiener filter. The resulting image is then upsampled
and interpolated using the same lowpass filter.
A two dimensional DPCM (2DDPCM) is used in the pro
posed image coder. We model the downsampled images as a sep
arable 1st order GaussMarkov model which has autocorrelation
function:
R(i,j) = σ2ρi
1ρj
2,
ρ1 < 1,ρ2 < 1
(1)
where ρ1 and ρ2 are the one step correlation coefficients in the
row and column direction after decimation and σ2is the variance.
The current pixel value can be calculated by its three surrounding
pixels [3]:
ˆ x(i,j) = ρ1˜ x(i−1,j)+ρ2˜ x(i,j−1)−ρ1ρ2˜ x(i−1,j−1) (2)
The Wiener filter gives an optimal tradeoff in the mean squared
sense between suppression of additive quantization noise and lin
ear distortion due to filtering. Its frequency response is given by:
W(ωi,ωj) =
Sxx(ωi,ωj)
Sxx(ωi,ωj) + σ2
q,
(3)
whereSxx(ωi,ωj)isthepowerspectraldensityofthedownsampled
image and σ2
filter is generally not separable even if the point spread function
and the variance covariance functions are [3]. The required auto
correlationfunctioncanbederivedfromthepredictioncoefficients,
whereas the quantization noise variance that can be approximated
by σ2
We would like to stress that although the overall image coder
is designed for lowbit rate operation, due to downsampling, the
DPCM part of the system is in fact operating at fairly high rates
(above 2 bits/pixel)1.The additive noise model is then applicable
and the assumption that the noise and the signal are uncorrelated
is quite accurate when a uniform quantizer is applied. It is safe to
consider that the quantization noise is uncorrelated with the quan
tizer input. The approximation of σ2
Further rate reduction of the system is obtained through adap
tive entropy coding. For our codec in Section 2, the prediction
qis the quantization noise variance. The 2D Wiener
q= ∆2/12, where ∆ is the quantization step.
qis then also valid.
1[4] defines high rate above 2 bits/pixel
error is quantized by the uniform quantizer then coded by one en
tropy coder. However, images have varying local statistics. When
a fixed predictor is used in the DPCM encoder, the prediction error
image will also have this property. It can be split into small blocks
with size that makes their internal statistics constant. One should
note that the block size must not be too small, in which case a large
amount of side information is required. These blocks can then be
classified into a small number of classes depending on their vari
ances. After uniform quantization with the same quantizer for the
entire image, an entropy coder can be designed for each class.
A method for optimal selection of class boundaries and en
tropy coders for each class for a given number of classes was de
signed in [5],[6]. It was shown that there is an optimal number
of classes for which the gain in increasing the number of classes
is counteracted by the increase of side information needed for in
forming the receiver about the block classification. The number
of classes, of course, depends on the block size as well. [5] also
showed it is adequate to keep the source splitting class number
M between 4 and 6. For our proposed coder, M = 4 is cho
sen along with block size of 4x4 pixels. We then use the iteration
algorithm in [5] to find the optimal variance decision levels to de
termine where to apply the four different entropy coders.
4. SIMULATION RESULTS AND DISCUSSION
Fig. 2. Coding performance at decimation rate of 3/2x3/2, 2x2 and
3x3 comparing with JPEG. Image “Lena”.
In the first experiment we used the 512x512, monochrome
“Lena”imagetoassessthesourcecodingperformanceofourcoder.
Figure 2 shows the results for downsampling rates3
3x3 compared with JPEG and JPEG2000
DPCM performance at such low bit rate region is unsurprisingly
substantially worse, hence not included in the plot. The collection
of curves of the proposed coder have the same shape as the ones
show in [1]. The convex hull of the curves are the best operation
point of the codec. For each downsampling rate, there is an op
timal quantization step ∆. When the quantization noise level is
too low, the lowpass filtering before downsampling removes too
much of the source spectrum so the ratedistortion performance
2x3
2, 2x2 and
2. The conventional
2JPEG2000 standard used here was implemented in Java through The
JJ2000 project. Source code v5.1 http://jj2000.epfl.ch
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Fig. 3. Coding performance at decimation rate of 2x2. Image
“Lena”.
is further away from the “elbow” of the curve. As the quantiza
tionnoiseincreases, theperformanceimproves. The“elbow”point
is reached when the quantization noise level intercepts the source
spectrum at the same frequency of the stopband of lowpass filter.
The performance is again worsened when the quantization noise
becomes too high for the source shaping lowpass filter. In prac
tice, for a chosen downsampling rate, the quantization step ∆ for
the ideal operating point can be determined through simple itera
tion since the quantization noise level is approximated by ∆2/12.
Figure3showstheeffectofadaptiveentropycodingandWiener
filter. As our results in [1] indicated, improvement by Wiener filter
is more pronounced beyond the convex hulls when the quantiza
tion noise level is higher. The adaptive entropy coding shows re
duction rate around 0.15 bits/pixel. Figure 4 compares the original
and coded version of “Lena”. The downsampling rate is limited
to3
due to much removal of the high frequency components. It can
be observed in Figure 2 however, that the three decimation factors
are adequate to cover a large range of bit rates at almost optimal
quality. The common blocking artifact seen in Transform Coding
is not present. The ringing noise is very limited when decimation
rate is low.
Necessary side information includes prediction coefficient (2
bytes), quantization step size (2 bits), decimation rate (2 bits) and
entropy coder location table. The number of bits required for the
first three quantities is negligible when the image size is large.
Information needed for adaptive entropy coding can be coded as
such: in the case of 4 entropy coders and 4x4 block size, the sim
plest way is to use 2 extra bits per block. which gives 0.125 bpp
extra. With decimation rate r the number of bits spent per source
pixel is then 0.125/r2. The alternative, which is more efficient,
is to entropy code the entropy coder location table since the dis
tribution of the coders is not uniform. The probability distribution
needed for entropy coding can be modelled as generalized Gaus
sian distribution and requires 2 additional bytes for the necessary
parameters. The resulting overall side information is low.
FIR filters are generally used in image processing since they
can be designed with linear phase. For lower complexity, IIR filers
are good alternatives. Phase distortion can be avoided by filtering
the image in the reverse direction during interpolation. As an ex
2x3
2, 2x2 and 3x3 since higher rates result more blurred images
ample, the lowpass filter for decimation and interpolation rate of
2x2 can be implemented in simple form using an allpass filter and
a delay [7]:
H(z) =1
2
with α < 1 for stability. The transfer function can be realized with
only one multiplication and three additions.
?
z−1+α + z−2
1 + αz−2
?
(4)
Fig. 4. Comparison of original and coded versions of “Lena”.
Top Left: Original. Top Right: Decimation Rate 3/2x3/2 Bit
Rate 0.97 bits/pixel. Bottom Left: Decimation Rate 2x2 Bit Rate
0.55 bits/pixel. Bottom Right: Decimation Rate 3x3 Bit Rate 0.25
bits/pixel.
ItisknownthatthelatestimagecompressionstandardJPEG2000
is able to offer high quality performance at low bit rates. In terms
ofpeaktopeaksignaltonoiseratio(PSNR),JPEG2000hasclearly
an advantage (Figure 2). However in terms of subjective quality,
thedifferenceisbarelynoticeable(Figure5). Herewecomparethe
subjective quality by processing the 512x512, monochrome im
age “Peppers”. In Figure 6 one can see that at very low bit rates,
JPEG2000 coder although has better edge sharpness, it “smears
out” the object surface. For our proposed codec, the sharpness
is compromised due to decimation but the retained texture of the
objects in the image is clearly closer to the original.
Finally, we would like to comment on the complexity of the
proposed codec. JPEG2000 requires at least 5 multiplications per
pixel to achieve sufficient wavelet transform decomposition plus
additional complexity from the context based arithmetic coder [8].
For our coder, 3 multiplications per pixel are needed for prediction
and variance calculation for adaptive entropy coding. The Wiener
filter can be implemented using FIR filters to lower computational
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complexity [3]. Again since this is operated on decimated image,
theactualmultiplicationperpixelisreduceddependingonthedec
imation rate. As stated earlier decimation filters can be realized in
very simple IIR filter forms so the overall complexity remains low.
5. CONCLUSIONS
In this paper, we proposed a practical image coder based on our
modified DPCM codec with multirate processing. Simulation re
sults show that the proposed coder provides great improvement
over conventional DPCM coders and is able to outperform JPEG
coders at low bit rates. In addition to the rate reduction by re
ducing the number of coded sample through downsampling, we
adopted the adaptive entropy coding scheme which provides fur
ther improvements of the source coding performance. The key
feature of the image coder is its relatively low complexity. The
lowpass decimation and interpolation filters can be implemented
using very simple IIR filters. Very few downsampling rates are
needed to maintain the coder gain close to the ones provided by
the optimal operating points. The inclusion of the Wiener filter
further ensures less degradation when the coder is operating away
from the ideal operation points. The adaptive entropy coding is a
small and simple addition to the original codec but gives substan
tial rate gain. The necessary side information to be transmit to the
receiver is little and can be efficiently coded. Our image coder is
shown to be a good alternative for coding images with monotoni
cally decreasing spectra at low bit rates.
6. REFERENCES
[1] A.N. Kim and T.A. Ramstad, “Improving the rate distortion
performance of dpcm,” in Proceedings of Int. Symposium on
Signal Proc. and its Applications (ISSPA), 2003.
[2] O. Guleryuz and M. T. Orchard, “On the dpcm compression
of gaussian autoregressive sequences,” IEEE Transactions on
Information Theory, vol. 47, no. 3, pp. 945–956, 2001.
[3] A. K. Jain, Fundamentals of Digital Image Processing, Infor
mation and System Science. PrenticeHall, Englewood Cliffs,
New Jersy, U.S.A., 1st edition, 1989.
[4] N.S. Jayant and P. Noll, Digital Coding of Waveforms  Prin
ciples and Applications to Speech and Video, Signal Process
ing. PrenticeHall, Englewood Cliffs, New Jersy, U.S.A., 1st
edition, 1984.
[5] J.M. Lervik and T.A. Ramstad, “Optimality of multiple en
tropy coder systems for nonstationary sources modelled by a
mixture distribution,” in Proceedings of Int. Conf. on Acous
tics, Speech and Signal Proc. (ICASSP), 1996.
[6] J.M. Lervik, Subband Image Communication Over Digital
Transparent And Analog Waveform Channels, PhD Disserta
tion, Department of Telecommunications, NTNU, Trondheim,
Norway, 1996.
[7] N. Viswanadham R.N. Madan and R.L. Kashyap, Systems and
Signal Processing, Oxford and IBH, New Delhi, India, 1991.
[8] D.S. Taubman and M.W. Marcellin, JPEG2000: Image Com
pression Fundamentals, Standards and Practice, Kluwar Aca
demic Publishers, 2002.
Fig. 5. Subjective quality comparison of JPEG2000 and the pro
posed codec. Top: Original. Bottom left: Proposed codec. Dec
imation rate 2x2, Bit rate 0.42bpp; Bottom Right: JPEG2000 Bit
rate 0.42bpp
Fig. 6. Comparison of JPEG2000 and the proposed codec. Left:
Proposed codec. Decimation rate 2x2, Bit rate 0.27bpp; Right:
JPEG2000 Bit rate 0.27bpp