JPEG Lifting Algorithm Based on Adaptive Block Compressed Sensing

Algorithm 1

JPEG-ABCS algorithm based on OMP (orthogonal matching pursuit).

(1)	Input:
	Original image I; rate control bpp;
	Subimage dimension n = 64;
(2)	Initialization:
	; N = R × C;
	;//
	;//
	//step1: adaptive blocking and vectorization
(3)	for j = 1, …, T2 do
(4)	;
(5)
(6)	;
(7)	;
(8)	end for
(9)	;
(10)	;
(11)	;
(12)
(13)	if ;
(14)	if //Condition = 1
(15)	;
	//: horizontal scanning and vertical linking
(16)	else if //Condition = 2
(17)	;
	//: vertical scanning and horizontal linking
(18)	end if
(19)	else if
(20)	if //Condition = 3
(21)	;
	//: zigzag along the main diagonal direction
(22)	else if //Condition = 4
(23)	;
	//: zigzag along the counter-diagonal direction
(24)	end if
(25)	end if
	//step2: adaptive observing and bit rate control
(26)	for i = 1, …, T1 do
(27)	; ;
(28)	;
	//synthetic feature (J)
(29)	end for
(30)	;
(31)	;
(32)	;
	//-- sampling ratio of subimages
(33)	;
(34)
	//prevent undersampling and oversampling
(35)	;
(36)	;
(37)	;
	//: noiseless; : noise
(38)	;
(39)
	//step3: codec and antiquantization
(40)
(41)
(42)
	//step4: reconstruction and denoising
(43)	if Condition = = 1
(44)
(45)	else if Condition = = 2
(46)
(47)	else
(48)	end if
(49)
(50)	for i = 1, …, T1 do
(51)	;
	//-- column vector of
(52)	;
	//calculate optimal iterative of subimages
(53)	for do
(54)	;
(55)	;
(56)	;
(57)	end for
(58)	;
	//: reconstruction sparse representation
(59)	;
	//: reconstruction original signal of subimages
(60)	end for
(61)	;
	//step5: antivectorization and jointing
(62)	;
	//: recovered image with JPEG-ABCS