Lossy compression of images deals with compression processes where decompression yields an imperfect reconstruction of the original image data.

Regardless of the compression method that being used:

Given the level of image loss (or distortion), there is always a bound on the minimum bit rate of the compressed bit stream.

Rate-Distortion or Distortion-Rate theory.

Figure:
Rate-distortion  relationship. For a discrete signal zero distortion coding is achieved when  the source entropy. For a continuous source the rate rises without limit (---).

BASIC SCHEMES FOR LOSSY COMPRESSION

Sample-Based Coding
Scalar predictive coder
Example:	DPCM

	For each input sample , a residual signal  is formed using the prediction signal .

	 is quantised 

	Decoder’s estimate for 

DPCM coders do not yield performance close to the 

Block-Based Coding

Spatial-domain block coding

The pixels are grouped into blocks and the blocks are then compressed in the spatial domain.
Example:	Vector quantization

Transform-domain block coding

The pixels are grouped into blocks and the blocks are then transformed to another domain, such as the frequency domain.
Example:	DCT
		DFT
		DHT
		KL

DCT-BASED CODING

A Generic DCT-Based Image Coding System

Spatial to DCT Domain
Transformation
8x8 DCT

Discard Unimportant
DCT Domain Samples
Quantisation

Lossless Coding
of DCT Domain Samples
Entropy Coding

Lossy Compressed Data

DCT Based Coding Examples

Example 1
The input  block (labeled original) is taken from a low activity region; that is there are very small differences among pixel values in that area.

In order to provide for uniform processing, most standard DCT coders require that image pixels are preprocessed so that their expected mean value is zero.

DCT

After subtracting 128 from each element of , the  DCT output block is given by

QUANTISATION

It is the process of quantisation which leads to compression in DCT domain coding. Quantisation of  is expressed as

Design of  depends on
	Psychovisual characteristics.
	Compression-ratio considerations.

QUANTIZED DCT

Only 11 values are needed to represent .

Compression ratio of 5.8.

 is entropy coded

DECOMPRESSION

Entropy decoding of the coded bit stream to get 

Inverse quantization on 
.

	IDCT

Observe that 

Example 2