Introductions

What Is Data Compression ? Data compression is the process of reduction in the amount of signal space that must be allocated to a given message set or data sample set Data compression is the process of reduction in the amount of signal space that must be allocated to a given message set or data sample set The signal space maybe in a physical volume, such as a data storage medium like magnetic tape; an interval of time; or in a portion of the electromagnetic spectrum such as the bandwidth to transmit the given message set The signal space maybe in a physical volume, such as a data storage medium like magnetic tape; an interval of time; or in a portion of the electromagnetic spectrum such as the bandwidth to transmit the given message set

What Is Data Compression ? All of these forms of the signal space-volume, time, and bandwidth are interrelated as follow All of these forms of the signal space-volume, time, and bandwidth are interrelated as follow Volume = ƒ ( time  bandwidth )

Why Data Compression ? bytes bytes, Cr=34.0

Why Data Compression ? bytes bytes, Cr=23.78

Why Data Compression ? bytes bytes, Cr=15.80

Why Data Compression ? bytes bytes, Cr=29.55

Why Data Compression ? bytes bytes, Cr=30.86

Why Data Compression ? bytes bytes, Cr=67.0

Why Data Compression ? bytes bytes, Cr=67.0

Why Data Compression ? bytes bytes, Cr=50.0

Why Data Compression ? bytes 7865 bytes, Cr=100

Why Data Compression ? bytes bytes, Cr=67

Why Data Compression ? To meet an operation requirement under an existing system performance constraint, such as limited bandwidth To meet an operation requirement under an existing system performance constraint, such as limited bandwidth To realize a cost saving in the design of a new system To realize a cost saving in the design of a new system Multimedia Communication = Data Compression + Networking + System Integration Multimedia Communication = Data Compression + Networking + System Integration

Test Images Used in This Class : BootsLena

Compression Model Source coding and channel coding Source coding and channel coding

Compression Model The encoder is made up of a source encoder, which removes input redundancies, and a channel encoder, which increases the noise immunity of the source encoder ’ s output The encoder is made up of a source encoder, which removes input redundancies, and a channel encoder, which increases the noise immunity of the source encoder ’ s output If the channel between the encoder and decoder is noise free ( not prone to error), the channel encoder and decoder are omitted If the channel between the encoder and decoder is noise free ( not prone to error), the channel encoder and decoder are omitted

Compression Model The source encoder is responsible for reducing or eliminating any coding, interpixel, or psychovisual redundancies in the input image The source encoder is responsible for reducing or eliminating any coding, interpixel, or psychovisual redundancies in the input image As the output of the source encoder contains little redundancy, it would be highly sensitive to transmission noise without the addition of the controlled redundancy. As the output of the source encoder contains little redundancy, it would be highly sensitive to transmission noise without the addition of the controlled redundancy.

What to Be Compressed ? PACS ( Image database, etc ) PACS ( Image database, etc ) HDTV ( Video Conference, VCD, DVD, etc ) HDTV ( Video Conference, VCD, DVD, etc ) ECG ( Audio, Speech, etc ) ECG ( Audio, Speech, etc ) Text Text

HDTV and TV Image Size Image Size NTSC: 512  480 NTSC: 512  480 PAL: 512  512 PAL: 512  512 CCIR 601: 720  480/576 CCIR 601: 720  480/576 HDTV: 1440  960 HDTV: 1440  960 Super HDTV: 4000  2000 Super HDTV: 4000  2000 CIF ( low bit-rate ): 360  240/288 CIF ( low bit-rate ): 360  240/288 QCIF: 180  120/144 QCIF: 180  120/144 A 512  512  8  3 = 6 M bits TV image should be transmitted in about 1/30 sec by any transmission line A 512  512  8  3 = 6 M bits TV image should be transmitted in about 1/30 sec by any transmission line

Why Data Can Be Compressed ? Data and Information Data and Information Data are the means by which information is conveyed Data are the means by which information is conveyed Various amounts of data may be used to represent the same amount of information Various amounts of data may be used to represent the same amount of information Consider the expression of an image. Consider the expression of an image.

Coding Redundancy Let r K be a discrete random variable representing the gray level (sample value) and that each r K occurs with probability Pr(r K ) Let r K be a discrete random variable representing the gray level (sample value) and that each r K occurs with probability Pr(r K ) Then Pr(r K ) = n K /n, k = 0, 1, 2, 3,..., h-1, where h is the number of gray levels, n K is the number of time that the k-th gray level appears in the image and n is the total number of pixels in the image Then Pr(r K ) = n K /n, k = 0, 1, 2, 3,..., h-1, where h is the number of gray levels, n K is the number of time that the k-th gray level appears in the image and n is the total number of pixels in the image

Coding Redundancy Let l(r K ) be the number of bits used to represent the value of r k. Then the average number of bits required to represent each pixel is Let l(r K ) be the number of bits used to represent the value of r k. Then the average number of bits required to represent each pixel is A natural binary coding of the gray levels assigns the same number of bits to both the most and least probable values, thus failing to minimize Lavg and resulting in coding redundancy A natural binary coding of the gray levels assigns the same number of bits to both the most and least probable values, thus failing to minimize Lavg and resulting in coding redundancy

Coding Redundancy r K p r (r K ) Code1 l1(r K ) Code2 l2(r K ) r 0 = r 1 = r 2 = r 3 = r 4 = r 5 = r 6 = r 7 =

Coding Redundancy L avg (Code2) =  l 2 (r K ) Pr(r K ) = 2(0.19)+2(0.25)+2(0.21)+3(0.16)+4(0.08) +5(0.06)+6(0.03)+6(0.02) = 2.7 bits If the gray levels of an image are coded in a way that use more code symbols than absolutely necessary to represent each gray level, i.e., the code fails to minimize Lavg, the resulting image is said to contain coding redundancy If the gray levels of an image are coded in a way that use more code symbols than absolutely necessary to represent each gray level, i.e., the code fails to minimize Lavg, the resulting image is said to contain coding redundancy

Psycho-visual Redundancy Certain information has less relative importance than other information in normal visual processing Certain information has less relative importance than other information in normal visual processing This information is said to be psycho-visual redundant This information is said to be psycho-visual redundant Psycho-acoustic redundancy in MPEG audio coding Psycho-acoustic redundancy in MPEG audio coding

Psycho-visual Redundancy

Temporal Redundancy

Fidelity Criteria Objective fidelity criteria Objective fidelity criteria signal-to-noise ratio ( SNR ) signal-to-noise ratio ( SNR ) Peak signal-to-noise ratio PSNR Peak signal-to-noise ratio PSNR

Standards JPEG (still image) JPEG (still image) DCT based baseline system (ch.10) DCT based baseline system (ch.10) extended system features (progressive build-up) extended system features (progressive build-up) lossless compressor lossless compressor Huffman coding and Arithmetic coding Huffman coding and Arithmetic coding JPEG2000 JPEG2000 wavelet-based wavelet-based Standard appeared in 2001 Standard appeared in 2001

Standards MPEG, H.261 ( full motion video, video conference ) MPEG, H.261 ( full motion video, video conference ) MPEG1, MPEG2 ( 1.5 M bits/sec, 3~10Mbits/sec ) MPEG1, MPEG2 ( 1.5 M bits/sec, 3~10Mbits/sec ) 30 frames of 352*240 pel/sec, or 25 frames of 352*288 pel/sec, 1/6 for audio, 5/6 for video 30 frames of 352*240 pel/sec, or 25 frames of 352*288 pel/sec, 1/6 for audio, 5/6 for video MPEG4 MPEG4 Telephone line ( 64 k bits/s ) Telephone line ( 64 k bits/s ) Low bit rate coding Low bit rate coding