Lossless Predictive coding - MATLAB CODE

A new pixel value is obtained by finding the difference between the current pixel and the predicted pixel value.

Encoding:

STEPS TO BE PERFORMED:

MATLAB CODE:

clear all

clc

%Read the input image

% A=imread('rice.png');

% figure,imshow(A);

% A=double(A);

A=[10 2 3 4;5 6 7 8];

display(A);

e=A;

%Perform prediction error

for i = 1:size(A,1)

    for j = 2:size(A,2)

        e(i,j)=e(i,j)-A(i,j-1);

    end

end

display(e);

%Huffman coding

C=reshape(e,[],1);

[D1,x]=hist(C,min(min(e)):max(max(e)));

sym=x(D1>0);

prob=D1(D1>0)/numel(e);

[dict,avglen] = huffmandict(sym,prob);

comp = huffmanenco(C,dict);

%Huffman Decoding

dsig = huffmandeco(comp,dict);

e=reshape(dsig,size(A,1),size(A,2));

d=e;

for i = 1:size(A,1)

    for j = 2:size(A,2)

        d(i,j)=d(i,j-1)+e(i,j);

    end

end

display(d);

%Decompressed Image

%figure,imshow(uint8(d));

2-D Prediction:

Consider an array [ a  b

                    c  d]

To perform prediction error using 2-D linear operator, e(2,2)=d-(c+b) i.e subtract the pixels left and top to the current pixel

To decompress, perform inverse operation f(2,2)=d+(c+b)

MATLAB CODE:

clear all

clc

%Input sequence

A=[10 11 12 13; 2 14 26 39];

display(A);

e=A;

A1=padarray(A,[1,0],0);

%Prediction error

for i = 2:size(A1,1)-1

    for j = 2:size(A1,2)

        fx=round(A1(i,j-1)+A1(i-1,j));

         e(i-1,j)=e(i-1,j)-fx;

    end

end

display(e);

%Huffman encoding

C=reshape(e,[],1);

[D1,x]=hist(C,min(min(e)):max(max(e)));

sym=x(D1>0);

prob=D1(D1>0)/numel(e);

[dict,avglen] = huffmandict(sym,prob);

comp = huffmanenco(C,dict);

%Huffman decoding

dsig = huffmandeco(comp,dict);

e=reshape(dsig,size(A,1),size(A,2));

%Inverse operation

d=e;

e1=padarray(e,[1,0],0);

for i = 2:size(e1,1)-1

    for j = 2:size(e1,2)

        fx=round(e1(i,j-1)+e1(i-1,j));

        d(i-1,j)=d(i-1,j)+fx;

        e1=padarray(d,[1,0],0);

    end

end

display(d);

  

A is the input value, e is the encoded value, d is the decoded value