Losslessy Compression of Multimedia Data Hao Jiang
Computer Science Department
Sept. 25, 2007
Losslessy Compression of Multimedia Data Hao Jiang
Computer Science Department
Sept. 25, 2007
Lossy Compression
Apart from lossless compression, we can further reduce the bits to represent media data by discarding “unnecessary” information.
Media such as image, audio and video can be “modified” without seriously affecting the perceived quality.
Lossy multimedia data compression standards include JPEG, MPEG, etc.
Methods of Discarding Information
Original image 1/2 resolution and zoom in Reducing resolution
½ color levels Original image Reduce pixel color levels
2.3bits/pixel (JPEG) For audios and videos we can similarly reduce the sampling rate, the sample levels, etc.
These methods usually introduce large distortion. Smarter schemes are necessary!
Distortion
Distortion: the amount of difference between the encoded media data and the original one.
Distortion measurement
Mean Square Error (MSE)
mean( ||xorg – xdecoded||2)
Signal to Noise Ratio (SNR)
SNR = 10log10 (Signal_Power)/(MSE) (dB)
Peak Signal to Noise Ratio
PSNR = 10log10(255^2/MSE) (dB)
The Relation of Rate and Distortion
D Bit Rate 0 D_max H The lowest possible rate (average codeword length per symbol) is correlated with the distortion.
Quantization
Maps a continuous or discrete set of values into a smaller set of values.
The basic method to “throw away” information.
Quantization can be used for both scalars (single numbers) or vectors (several numbers together).
After quantization, we can generate a fixed length code directly.
Uniform Scalar Quantization
xmin xmax Quantization step D =(xmax-xmin)/N Decision boundaries Quantization value Assume x is in [xmin, xmax]. We partition the interval
uniformly into N nonoverlapping regions. A quantizer Q(x) maps x to the quantization value in the region
where x falls in.
xn xn+1 Quantization error x Quantization
value To minimize the possible maximum error, the quantization value should be at the center of each decision interval.
If x randomly occurs, Q(x) is uniformly distributed in [-D/2, D/2]
Quantization and Codewords
xmin xmax Each quantization value can be associated with a binary
codeword.
In the above example, the codeword corresponds to the
index of each quantization value. 000 001 010 011 100 101
Another Coding Scheme
xmin xmax 000 001 011 010 110 111 The above codeword is different in only 1bit
for each neighbors.
Gray code is more resistant to bit errors than the
natural binary code. Gray code
Bit Assignment
bits dB 1 more bit About 6db gain If the # of quantization interval is N, we can use log2(N) bits to represent each quantized value.
For uniform distributed x, The SNR of Q(x) is proportional to 20log(N) = 6.02n, where N=2n
Non-uniform Quantizer
0 Perceived distortion ~ D / s For audio and visual, the tolerance of a distortion is proportional to the signal size.
So, we can make quantization step D proportional to the signal level.
If signal is not uniformly distributed, we also prefer non-uniform quantization.
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