predictive coding

By-Er Payal SutharME(MSU)

It is a approach that achieves good compression without significant overload.

It is Based on eliminating the inter pixel redundancies of closely spaced pixels by extracting and coding only the new information in each pixel.

The new information of a pixel is defined as the difference between the actual and predicted value of that pixel.

Two types are there, 1) loss less

2)lossy

+Symbol encoder

PredictorNearest integer

e(n)f(n)Input sequence

fˆ (n)

Compressed sequence

•Figure : lossless predictive coding model ,encoder

•The prediction error is coded using f(n) and fˆ (n)

e(n)=f(n)-fˆ (n)•Which is encoded using variable-length code(by symbol encoder) to generate next element

+Symbol decoder

Predictor

e(n) f(n)

fˆ (n)

Compressed sequence

Decompressed sequence

+

•Figure : lossless predictive coding model ,decoder

•Reconstructs e(n) from received variable code words and performs inverse operation to recreate original input sequence.

f(n)=e(n) + fˆ (n)

Prediction is usually formed by a linear combination of m previous pixels.

1

m

i n in

i

f round f

•m-is the order of linear predictor,•round is function used to denote the rounding to nearest integer operation.•αi for i = 1,2… m are prediction coefficients.

1-D linear predictive coding : the m samples use to predict value of each pixel come from current scan line.

2-D linear predictive coding : the m samples use to predict value of each pixel come from current and previous scan line.

3-D linear predictive coding : the m samples use to predict value of each pixel come from current and previous image from sequence of images.

For 1-D,

1

( , ) ( , )m

in

i

f x y round f x y i

Compression achieved is directly related to the entropy reduction that mapped in to a prediction error sequence called a prediction residual.

+Symbol

encoder

Predictor

Quantizer

e˙(n)

f˙(n)

Input

sequence

fˆ (n)

Compressed

sequence

+

+

•Figure : lossy predictive coding model ,encoder

f(n)

e(n)

•Quantizer, which replaces the nearest-integer function of the error-free encoder, is inserted between the symbol encoder and the point at which the prediction error is formed.

+Symbol

encoder

Predictor

e˙(n)

Decompressed

sequence

f˙(n)

fˆ (n)

Compressed

sequence

+

•Figure : lossy predictive coding model ,decoder

It maps prediction error into a limited range of outputs, e˙(n) which establishes the amount of compression and distortion associated with lossy predictive coding.

Here,f˙(n)=e˙(n) + fˆ (n)

Example: Delta Modulation

in which, fˆ (n)= α f˙(n-1)

and e˙(n)={ +ζ for e(n)>0

- ζ o.wα= prediction coefficient ζ= positive constant