CN109874020A - The inseparable lifting wavelet transform method of quality and complexity hierarchical - Google Patents
The inseparable lifting wavelet transform method of quality and complexity hierarchical Download PDFInfo
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Abstract
The present invention discloses the inseparable lifting wavelet transform method of a kind of quality and complexity hierarchical, first, picture signal is handled as block, realizes real 2D transformation, than separable 2D wavelet transformation with better anisotropy, bigger freedom degree and more preferably filtering property；Secondly, carrying out wavelet transformation by the way of bit plane to input picture from highest bit plane to minimum bit plane, can directly being combined with the embedded encoded algorithm based on successive approximation to quantification, it is easy to accomplish the PSNR scalable coding of image and video；Finally, can stop at any bit plane according to the requirement of target bit rate in conversion process, so as to avoid the transformation compared with low pixel bit plane, achieve the purpose that computation complexity is gradable.The experiment show gradable characteristic of quality and computation complexity of the invention.
Description
Technical field
The present invention relates to the graduated encoding field of image and video, especially a kind of anisotropy, arithmetic speed are fast
The inseparable lifting wavelet transform method of quality and complexity hierarchical.
Background technique
Image and video graduated encoding algorithm, which have the variation of network bandwidth, well adapts to ability, but this adaptation
Ability is often to sacrifice encoder complexity or code efficiency as cost, such as fine granular encoded (Fine Granularity
Scalable, FGS) efficiency of method encodes lower than the MPEG-4 of Non-Gradable, and progressive fine granular encoded (Progressive
FGS) improve the code efficiency of FGS to a certain extent, computational complexity but correspondingly increase, this just gives decoding terminal
Processing capacity proposes higher requirement.In fact, the application environment of multimedia communication be it is extremely complex, especially isomery is whole
Video communication between end is more such.In this case, one description of the Part VII special definition of MPEG-21 standard
Tool set, i.e. digital item adaptation (Digital ItemAdaptation, DIA), to user personality, the network in multimedia application
Characteristic and terminal capability etc. are described, and take the lead in writing into the definition of terminal operational capability in multimedia application standard, this shows
Terminal operational capability, which becomes, has to one of an important factor for considering in image and video communication applications.In order to meet this application
Demand, the image and video coding of low complex degree start the extensive concern by researcher.
Although the encryption algorithm of low complex degree makes it possible the multimedia communication on particular platform, if every kind
The encoding scheme that application platform all customizes corresponding complexity is also unrealistic, so it is necessary to having the gradable energy of computation complexity
The encryption algorithm of power is studied.So-called " computation complexity is gradable " refers to, image or video encoder can be according to different
Application environment is adaptively adjusted between available computational resources and decoding and rebuilding quality.It can be advantageously applied to different
Under the conditions of network forming network, in the video communication of different computing capability terminal rooms.
Orthogonal transformation (such as discrete cosine transform and wavelet transformation) is a ring indispensable in image and video coding,
The pixel value of spatial domain is mapped to the coefficient value of frequency domain by it, to realize empty while removing adjacent pixel correlation
Between domain energy concentration.But, due to being related to a large amount of floating-point operations, the calculation amount of orthogonal transformation is shared in entire cataloged procedure
Ratio be highest in addition to inter-prediction.Therefore, a kind of transform method of complexity hierarchical is designed for computation complexity
Gradable image and video coding is of great significance.
Richardson et al. proposes discrete cosine transform (the Discrete Cosine with feedback mechanism
Transform, DCT) complexity administrative model, it is converted in an encoding process by adjusting the threshold value of coefficient truncation position to control
Complexity；Zhang Dongming et al. devises the butterfly computation of simplified block by establishing the coefficient distributed models of 3 class simplified blocks, into
And propose a kind of DCT method of complexity hierarchical；Zhang Shufang et al. then introduces high frequency coefficient truncation thought, by adjusting multiple
It is miscellaneous to spend control parameter to realize the complexity hierarchical of dct transform.Although above-mentioned dct transform method reaches to a certain extent
The purpose of complexity hierarchical, but the intrinsic characteristic of dct transform cause it be unfavorable for realizing and guarantee efficient image and
Video quality is gradable, spatial scalable coding.
With the development of the multiscale analysis such as small echo theory, it has been found that multi-scale transform can be picture breakdown at having
The subband signal of different spatial resolutions, different frequency and direction character not only has the None-linear approximation efficiency better than DCT,
And its multi-resolution characteristics makes it be more easily implemented flexible graduated encoding than DCT.So wavelet transformation is widely used
In image and video graduated encoding, such as towards EZW, SPIHT, SLCCA, EBCOT algorithm of still image graduated encoding
With VidWav, MC-EZBC algorithm towards video graduated encoding.However, current still rarely seen complexity hierarchical wavelet transformation
Correlative study and invention, the especially 2D non-separate wavelet of complexity hierarchical converts hardly seen report.
Summary of the invention
The present invention is to provide a kind of anisotropy, operation speed to solve above-mentioned technical problem present in the prior art
Spend the inseparable lifting wavelet transform method of fast quality and complexity hierarchical.
The technical solution of the invention is as follows: a kind of inseparable Lifting Wavelet direct transform of quality and complexity hierarchical
Method, it is characterised in that carry out in accordance with the following steps:
Step 1. inputs an image I to be processed, if its height is h pixel, width is w pixel；
The series L that step 2. input needs to convertmaxThe bit plane quantity N that need to be handled is converted with every gradebp, and enable conversion stage
Number L ← 1, " ← " indicate assignment operation；
The maximum value C of step 3. statistical picture Imax, highest bit plane N is calculated according to formula (1)max_bp:
Step 4. enables current bit plane Ncurrent←Nmax_bp；
Step 5. divide the stage: image I is divided into do not overlap and size be 2 × 2 pixels block, for each pixel
Block, the coordinate of top left corner pixel are (2i, 2j), and the coordinate of upper right corner pixel is (2i, 2j+1), and the coordinate of lower left corner pixel is
The coordinate of (2i+1,2j), lower right corner pixel are (2i+1,2j+1), and the i and j are integer, and
Step 6. is initialized as 0 for each block of pixels, by its wavelet conversion coefficient value, even W (2i, 2j) ← 0, W
(2i, 2j+1) ← 0, W (2i+1,2j) ← 0, W (2i+1,2j+1) ← 0, the W (2i, 2j), W (2i, 2j+1), W (2i+1,2j)
Top left corner pixel in block of pixels, upper right corner pixel, lower left corner pixel and lower right corner pixel are respectively indicated with W (2i+1,2j+1)
Wavelet conversion coefficient value；
Step 7. forecast period: according to step 7.1~step 7.5, block-by-block calculates the of non-separate wavelet transformation
NcurrentThe predictive coefficient value of bit plane, the block for arranging to be presently processing is referred to as " current block "；
Step 7.1 enables b ← (1 < < Ncurrent), " the < < " indicates arithmetic shift left operation；
Step 7.2 calculates the predictive coefficient value T of top left corner pixel in each 2 × 2 block of pixels according to formula (2), block-by-block
(2i, 2j):
T (2i, 2j)=sgn (I (2i, 2j)) × [abs (I (2i, 2j)) &b] (2)
The sgn () indicates that sign function, I (2i, 2j) indicate to be located at the pixel at coordinate (2i, 2j) in current block
Value, abs () indicate that the function that takes absolute value, " & " indicate step-by-step and operation；
Step 7.3 calculates the predictive coefficient value T (2i of lower left corner pixel in each 2 × 2 block of pixels according to formula (3), block-by-block
+ 1,2j):
The I (2i+1,2j) indicates that the pixel value in current block at coordinate (2i+1,2j), I (2i+2,2j) indicate
Top left corner pixel value below current block in adjacent block, " > > " indicate arithmetic shift right operation；
Step 7.4 calculates the predictive coefficient value T (2i of lower right corner pixel in each 2 × 2 block of pixels according to formula (4), block-by-block
+ 1,2j+1):
The I (2i+1,2j+1) indicates to be located at the pixel value at coordinate (2i+1,2j+1), I (2i, 2j+1) in current block
It indicates to be located at the pixel value at coordinate (2i, 2j+1) in current block, I (2i+2,2j+1) indicates the right side of adjacent block below current block
Upper angle pixel value, T (2i+1,2j) indicate the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j+2) indicates current
The predictive coefficient value of lower left corner pixel in the adjacent block of block right side；
Step 7.5 calculates the predictive coefficient value T of upper right corner pixel in each 2 × 2 block of pixels according to formula (5), block-by-block
(2i, 2j+1):
The I (2i, 2j+1) indicates that the pixel value in current block at coordinate (2i, 2j+1), I (2i, 2j+2) indicate
Top left corner pixel value on the right side of current block in adjacent block；
Step 8. improvement stage: according to step 8.1~step 8.4, block-by-block calculates the of non-separate wavelet transformation
NcurrentThe Lifting Coefficients value of bit plane；
Step 8.1 keeps the predictive coefficient value T (2i+1,2j+1) of lower right corner pixel in each 2 × 2 block of pixels constant, makees
For its Lifting Coefficients value U (2i+1,2j+1)；
Step 8.2 calculates the Lifting Coefficients value U of upper right corner pixel in each 2 × 2 block of pixels according to formula (6), block-by-block
(2i, 2j+1):
U (2i, 2j+1)=T (2i, 2j+1)+[T (2i+1,2j+1)+T (2i-1,2j+1)] > > 2 (6)
The T (2i, 2j+1) indicates the predictive coefficient value of upper right corner pixel in current block, and T (2i+1,2j+1) indicates current
The predictive coefficient value of lower right corner pixel in block, T (2i-1,2j+1) indicate the prediction of the lower right corner pixel of adjacent block above current block
Coefficient value；
Step 8.3 calculates the Lifting Coefficients of top left corner pixel in each 2 × 2 block of pixels according to the definition of formula (7), block-by-block
Value U (2i, 2j):
U (2i, 2j)=T (2i, 2j)+[T (2i, 2j-1)+T (2i, 2j+1)+T (2i-1,2j)+T (2i+1,2j)] > > 2 (7)
The T (2i, 2j) indicates the predictive coefficient value of top left corner pixel in current block, and T (2i, 2j+1) is indicated in current block
The predictive coefficient value of upper right corner pixel, T (2i+1,2j) indicate the predictive coefficient value of lower left corner pixel in current block, T (2i, 2j-
1) the predictive coefficient value of upper right corner pixel in adjacent block on the left of current block is indicated, T (2i-1,2j) indicates adjacent block above current block
The predictive coefficient value of middle lower left corner pixel；
Step 8.4 calculates the Lifting Coefficients value U (2i of lower left corner pixel in each 2 × 2 block of pixels according to formula (8), block-by-block
+ 1,2j):
U (2i+1,2j)=T (2i+1,2j)+[T (2i+1,2j-1)+T (2i+1,2j+1)] > > 2 (8)
The T (2i+1,2j) indicates the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j-1) indicates current
The predictive coefficient value of lower right corner pixel, T (2i+1,2j+1) indicate the prediction of lower right corner pixel in current block in the adjacent block of block left side
Coefficient value；
Step 9. is according to formula (9)~formula (12), and block-by-block is by NcurrentThe Lifting Coefficients value of bit plane is added to more
In the wavelet conversion coefficient value of high bit-planes:
W(2i,2j)←W(2i,2j)+U(2i,2j) (9)
W(2i,2j+1)←W(2i,2j+1)+U(2i,2j+1) (10)
W(2i+1,2j)←W(2i+1,2j)+U(2i+1,2j) (11)
W(2i+1,2j+1)←W(2i+1,2j+1)+U(2i+1,2j+1) (12)
Step 10. enables Ncurrent←Ncurrent- 1, if Ncurrent≥Nmax_bp-Nbp+ 1 and Ncurrent>=0, then it is transferred to step
7, otherwise it is transferred to step 11；
Step 11. reorganizes the wavelet conversion coefficient of each 2 × 2 block of pixels, group according to formula (13)~formula (16)
At LLL、LHL、HLLAnd HHLSubband；
LLL(i,j)←W(2i,2j) (13)
HLL(i,j)←W(2i,2j+1) (14)
LHL(i,j)←W(2i+1,2j) (15)
HHL(i,j)←W(2i+1,2j+1) (16)
The LLL、LHL、HLLAnd HHLRespectively indicate LL subband, LH subband, HL subband and the HH subband of L grades of transformation；
Step 12. enables L ← L+1, if L < Lmax, then I ← LL is enabledL, h ← h/2, w ← w/2 are transferred to step 3；Otherwise, it exportsAnd HLk、LHk、HHk, the 1≤k≤Lmax, non-separate wavelet conversion process terminates.
It is a kind of corresponding inseparable with the inseparable Lifting Wavelet direct transform method of above-mentioned quality and complexity hierarchical
From Lifting Wavelet inverse transformation method, it is characterised in that carry out in accordance with the following steps:
Step 1. inputs wavelet conversion coefficient matrix M, if its height is h row, width is w column；
The series L that step 2. input needs to convertmaxThe bit plane quantity N that need to be handled is converted with every gradebp, and enable conversion stage
Number L ← Lmax, " ← " indicates assignment operation；
Step 3. counts the coefficient C of maximum absolute value in the low frequency sub-band of Mmax, and then it is highest according to formula (17) calculating
Bit plane Nmax_bp:
Step 4. enables current bit plane Ncurrent←Nmax_bp；
Wavelet conversion coefficient tissue size is the block of 2 × 2 pixels, protected by step 5. according to formula (18)~formula (21)
Being stored to a size is (h/2L-1)×(w/2L-1) matrix W in:
W(2i,2j)←M(i,j) (18)
W(2i,2j+1)←M(i,j+w/2L) (19)
W(2i+1,2j)←M(i+h/2L,j) (20)
W(2i+1,2j+1)←M(i+h/2L,j+w/2L) (21)
The i and j is integer, and 0≤i < h/2L, 0≤j < w/2L；
Step 6. enables M (i, j), M (i, j+w/2L)、M(i+h/2L, j) and M (i+h/2L,j+w/2L) reset, the i and j
It is integer, and 0≤i < h/2L, 0≤j < w/2L；
Step 7. enables b ← (1 < < Ncurrent), " the < < " indicates arithmetic shift left operation；
Step 8. is against the improvement stage: according to step 8.1~step 8.4, block-by-block calculates the of non-separate wavelet inverse transformation
NcurrentThe predictive coefficient value of bit plane, the block for arranging to be presently processing is referred to as " current block "；
Step 8.1 calculates the predictive coefficient value T of lower left corner pixel in each 2 × 2 block of pixels according to formula (22), block-by-block
(2i+1,2j):
The sgn () indicates that sign function, abs () indicate that the function that takes absolute value, " & " indicate step-by-step and operation, " >
> " indicates arithmetic shift right operation, the wavelet conversion coefficient value of lower left corner pixel in W (2i+1,2j) expression current block, W (2i+1,
2j-1) indicate the wavelet conversion coefficient value of lower right corner pixel in adjacent block on the left of current block, W (2i+1,2j+1) indicates current block
The wavelet conversion coefficient value of middle lower right corner pixel；
Step 8.2 calculates the predictive coefficient value T of top left corner pixel in each 2 × 2 block of pixels according to formula (23), block-by-block
(2i, 2j):
The W (2i, 2j) indicates the wavelet conversion coefficient value of top left corner pixel in current block, and W (2i, 2j+1) indicates current
The wavelet conversion coefficient value of upper right corner pixel in block, W (2i, 2j-1) indicate on the left of current block the small of upper right corner pixel in adjacent block
Wave conversion coefficient value, T (2i+1,2j) indicate the predictive coefficient value of lower left corner pixel in current block, and T (2i-1,2j) indicates current
The predictive coefficient value of lower left corner pixel in the adjacent block of block top；
Step 8.3 calculates the predictive coefficient value T of upper right corner pixel in each 2 × 2 block of pixels according to formula (24), block-by-block
(2i, 2j+1):
The W (2i, 2j+1) indicates the wavelet conversion coefficient value of upper right corner pixel in current block, and W (2i+1,2j+1) is indicated
The wavelet conversion coefficient value of lower right corner pixel in current block, W (2i-1,2j+1) indicate lower right corner picture in the adjacent block of current block top
The wavelet conversion coefficient value of element；
Step 8.4 calculates the predictive coefficient value T of lower right corner pixel in each 2 × 2 block of pixels according to formula (25), block-by-block
(2i+1,2j+1):
T (2i+1,2j+1)=sgn (W (2i+1,2j+1)) × [abs (W (2i+1,2j+1)) &b] (25)
The W (2i+1,2j+1) indicates the wavelet conversion coefficient value of lower right corner pixel in current block；
The step 9. inverse prediction stage: according to step 9.1~step 9.4, block-by-block calculates the of non-separate wavelet inverse transformation
NcurrentThe pixel value of bit plane；
Step 9.1 according to formula (26), block-by-block calculate upper right corner pixel in each 2 × 2 block of pixels pixel value M ' (2i,
2j+1):
M ' (2i, 2j+1)=[T (2i, 2j)+T (2i, 2j+2)] > > 1 (26)
The T (2i, 2j) indicates the predictive coefficient value of top left corner pixel in current block, and T (2i, 2j+2) indicates that current block is right
The predictive coefficient value of top left corner pixel in the adjacent block of side；
Step 9.2 calculates the pixel value M ' (2i+ of lower right corner pixel in each 2 × 2 block of pixels according to formula (27), block-by-block
1,2j+1):
M ' (2i+1,2j+1)=[T (2i+1,2j)+T (2i+1,2j+2)+T (2i, 2j+1)+T (2i+2,2j+1)] > > 1 (27)
The T (2i+1,2j) indicates the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j+2) indicates current
The predictive coefficient value of lower left corner pixel, T (2i, 2j+1) indicate the prediction system of upper right corner pixel in current block in the adjacent block of block right side
Numerical value, T (2i+2,2j+1) indicate the predictive coefficient value of upper right corner pixel in adjacent block below current block；
Step 9.3 calculates the pixel value M ' (2i+ of lower left corner pixel in each 2 × 2 block of pixels according to formula (28), block-by-block
1,2j):
M ' (2i+1,2j)=[T (2i, 2j)+T (2i+2,2j)] > > 1 (28)
The T (2i+2,2j) indicates the predictive coefficient value of top left corner pixel in adjacent block below current block；
Step 9.4 keeps the predictive coefficient value T (2i, 2j) of top left corner pixel in each 2 × 2 block of pixels constant, as it
Pixel value M ' (2i, 2j)；
Step 10. is according to formula (29)~formula (32), and block-by-block is by NcurrentThe pixel value of bit plane is added to higher
In the pixel value of bit plane:
M(2i,2j)←M(2i,2j)+M′(2i,2j) (29)
M(2i,2j+1)←M(2i,2j+1)+M′(2i,2j+1) (30)
M(2i+1,2j)←M(2i+1,2j)+M′(2i+1,2j) (31)
M(2i+1,2j+1)←M(2i+1,2j+1)+M′(2i+1,2j+1) (32)
The i and j is integer, and 0≤i < h/2L, 0≤j < w/2L；
Step 11. enables Ncurrent←Ncurrent- 1, if Ncurrent≥Nmax_bp-Nbp+ 1 and Ncurrent>=0, then it is transferred to step
7, otherwise it is transferred to step 12；
Step 12. enables L ← L-1, if L > 0, is transferred to step 3；Otherwise, output matrix M, non-separate wavelet inverse transformation
Journey terminates.
The present invention compared with prior art, has four aspect characteristics: firstly, inseparable Lifting Wavelet of the invention becomes
Picture signal of changing commanders is handled as block, is handled not as individual row and column, is had compared with separable 2D wavelet transformation
There are better anisotropy, bigger freedom degree and more preferably filtering property (such as high-order vanishing moment), can provide and be more in line with people
The frequency decomposition ability of eye properties of human visual system；Input is schemed from highest bit plane to minimum bit plane secondly, the present invention is used
As carrying out wavelet transformation, it can directly be combined, be easy to based on the embedded encoded algorithm of successive approximation to quantification with EZW, SPIHT etc.
Realize the PSNR scalable coding of image and video；Then, conversion process of the invention can according to the requirement of target bit rate,
Stop at any time at any bit plane, to save transformation compared with calculation amount needed for low pixel bit plane, reaches computation complexity
Gradable purpose；Finally, the multiplying of arithmetic shift operation substitution traditional wavelet is introduced, completely without floating number
Operation ensure that the overall computation complexity of wavelet transformation is lower than traditional dct transform.Therefore, the present invention has anisotropy, fortune
The advantages of calculating fast speed, quality and complexity hierarchical.
Detailed description of the invention
Fig. 1 is original test image.
Fig. 2 is the result for carrying out 3 grades of inseparable Lifting Wavelet direct transforms to Lena image using the present invention.
Fig. 3 is the result for carrying out 2 grades of inseparable Lifting Wavelet direct transforms to Peppers image using the present invention.
Fig. 4 is the result for carrying out 2 grades of inseparable Lifting Wavelet direct transforms to Baboon image using the present invention.
Fig. 5 is the result for carrying out 3 grades of inseparable Lifting Wavelet inverse transformations to Lena image using the present invention.
Fig. 6 is the result for carrying out 2 grades of inseparable Lifting Wavelet inverse transformations to Peppers image using the present invention.
Fig. 7 is the result for carrying out 2 grades of inseparable Lifting Wavelet inverse transformations to Baboon image using the present invention.
Specific embodiment
The inseparable Lifting Wavelet direct transform method of quality and complexity hierarchical of the invention, it is characterised in that according to
Following steps carry out:
Step 1. inputs an image I to be processed, if its height is h pixel, width is w pixel；
The series L that step 2. input needs to convertmaxThe bit plane quantity N that need to be handled is converted with every gradebp, and enable conversion stage
Number L ← 1, " ← " indicate assignment operation；
The maximum value C of step 3. statistical picture Imax, highest bit plane N is calculated according to formula (1)max_bp:
Step 4. enables current bit plane Ncurrent←Nmax_bp；
Step 5. divide the stage: image I is divided into do not overlap and size be 2 × 2 pixels block, for each pixel
Block, the coordinate of top left corner pixel are (2i, 2j), and the coordinate of upper right corner pixel is (2i, 2j+1), and the coordinate of lower left corner pixel is
The coordinate of (2i+1,2j), lower right corner pixel are (2i+1,2j+1), and the i and j are integer, and
Step 6. is initialized as 0 for each block of pixels, by its wavelet conversion coefficient value, even W (2i, 2j) ← 0, W
(2i, 2j+1) ← 0, W (2i+1,2j) ← 0, W (2i+1,2j+1) ← 0, the W (2i, 2j), W (2i, 2j+1), W (2i+1,2j)
Top left corner pixel in block of pixels, upper right corner pixel, lower left corner pixel and lower right corner pixel are respectively indicated with W (2i+1,2j+1)
Wavelet conversion coefficient value；
Step 7. forecast period: according to step 7.1~step 7.5, block-by-block calculates the of non-separate wavelet transformation
NcurrentThe predictive coefficient value of bit plane, the block for arranging to be presently processing is referred to as " current block "；
Step 7.1 enables b ← (1 < < Ncurrent), " the < < " indicates arithmetic shift left operation；
Step 7.2 calculates the predictive coefficient value T of top left corner pixel in each 2 × 2 block of pixels according to formula (2), block-by-block
(2i, 2j):
T (2i, 2j)=sgn (I (2i, 2j)) × [abs (I (2i, 2j)) &b] (2)
The sgn () indicates that sign function, I (2i, 2j) indicate to be located at the pixel at coordinate (2i, 2j) in current block
Value, abs () indicate that the function that takes absolute value, " & " indicate step-by-step and operation；
Step 7.3 calculates the predictive coefficient value T (2i of lower left corner pixel in each 2 × 2 block of pixels according to formula (3), block-by-block
+ 1,2j):
The I (2i+1,2j) indicates that the pixel value in current block at coordinate (2i+1,2j), I (2i+2,2j) indicate
Top left corner pixel value below current block in adjacent block, " > > " indicate arithmetic shift right operation；
Step 7.4 calculates the predictive coefficient value T (2i of lower right corner pixel in each 2 × 2 block of pixels according to formula (4), block-by-block
+ 1,2j+1):
The I (2i+1,2j+1) indicates to be located at the pixel value at coordinate (2i+1,2j+1), I (2i, 2j+1) in current block
It indicates to be located at the pixel value at coordinate (2i, 2j+1) in current block, I (2i+2,2j+1) indicates the right side of adjacent block below current block
Upper angle pixel value, T (2i+1,2j) indicate the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j+2) indicates current
The predictive coefficient value of lower left corner pixel in the adjacent block of block right side；
Step 7.5 calculates the predictive coefficient value T of upper right corner pixel in each 2 × 2 block of pixels according to formula (5), block-by-block
(2i, 2j+1):
The I (2i, 2j+1) indicates that the pixel value in current block at coordinate (2i, 2j+1), I (2i, 2j+2) indicate
Top left corner pixel value on the right side of current block in adjacent block；
Step 8. improvement stage: according to step 8.1~step 8.4, block-by-block calculates the of non-separate wavelet transformation
NcurrentThe Lifting Coefficients value of bit plane；
Step 8.1 keeps the predictive coefficient value T (2i+1,2j+1) of lower right corner pixel in each 2 × 2 block of pixels constant, makees
For its Lifting Coefficients value U (2i+1,2j+1)；
Step 8.2 calculates the Lifting Coefficients value U of upper right corner pixel in each 2 × 2 block of pixels according to formula (6), block-by-block
(2i, 2j+1):
U (2i, 2j+1)=T (2i, 2j+1)+[T (2i+1,2j+1)+T (2i-1,2j+1)] > > 2 (6)
The T (2i, 2j+1) indicates the predictive coefficient value of upper right corner pixel in current block, and T (2i+1,2j+1) indicates current
The predictive coefficient value of lower right corner pixel in block, T (2i-1,2j+1) indicate the prediction of the lower right corner pixel of adjacent block above current block
Coefficient value；
Step 8.3 calculates the Lifting Coefficients of top left corner pixel in each 2 × 2 block of pixels according to the definition of formula (7), block-by-block
Value U (2i, 2j):
U (2i, 2j)=T (2i, 2j)+[T (2i, 2j-1)+T (2i, 2j+1)+T (2i-1,2j)+T (2i+1,2j)] > > 2 (7)
The T (2i, 2j) indicates the predictive coefficient value of top left corner pixel in current block, and T (2i, 2j+1) is indicated in current block
The predictive coefficient value of upper right corner pixel, T (2i+1,2j) indicate the predictive coefficient value of lower left corner pixel in current block, T (2i, 2j-
1) the predictive coefficient value of upper right corner pixel in adjacent block on the left of current block is indicated, T (2i-1,2j) indicates adjacent block above current block
The predictive coefficient value of middle lower left corner pixel；
Step 8.4 calculates the Lifting Coefficients value U (2i of lower left corner pixel in each 2 × 2 block of pixels according to formula (8), block-by-block
+ 1,2j):
U (2i+1,2j)=T (2i+1,2j)+[T (2i+1,2j-1)+T (2i+1,2j+1)] > > 2 (8)
The T (2i+1,2j) indicates the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j-1) indicates current
The predictive coefficient value of lower right corner pixel, T (2i+1,2j+1) indicate the prediction of lower right corner pixel in current block in the adjacent block of block left side
Coefficient value；
Step 9. is according to formula (9)~formula (12), and block-by-block is by NcurrentThe Lifting Coefficients value of bit plane is added to more
In the wavelet conversion coefficient value of high bit-planes:
W(2i,2j)←W(2i,2j)+U(2i,2j) (9)
W(2i,2j+1)←W(2i,2j+1)+U(2i,2j+1) (10)
W(2i+1,2j)←W(2i+1,2j)+U(2i+1,2j) (11)
W(2i+1,2j+1)←W(2i+1,2j+1)+U(2i+1,2j+1) (12)
Step 10. enables Ncurrent←Ncurrent- 1, if Ncurrent≥Nmax_bp-Nbp+ 1 and Ncurrent30, then it is transferred to step
7, otherwise it is transferred to step 11；
Step 11. reorganizes the wavelet conversion coefficient of each 2 × 2 block of pixels, group according to formula (13)~formula (16)
At LLL、LHL、HLLAnd HHLSubband；
LLL(i,j)←W(2i,2j) (13)
HLL(i,j)←W(2i,2j+1) (14)
LHL(i,j)←W(2i+1,2j) (15)
HHL(i,j)←W(2i+1,2j+1) (16)
The LLL、LHL、HLLAnd HHLRespectively indicate LL subband, LH subband, HL subband and the HH subband of L grades of transformation；
Step 12. enables L ← L+1, if L < Lmax, then I ← LL is enabledL, h ← h/2, w ← w/2 are transferred to step 3；Otherwise, it exportsAnd HLk、LHk、HHk, the 1≤k≤Lmax, non-separate wavelet conversion process terminates.
It is corresponding with the inseparable Lifting Wavelet direct transform method of above-mentioned quality and complexity hierarchical inseparable to mention
Rise wavelet inverse transformation method, it is characterised in that carry out in accordance with the following steps:
Step 1. inputs wavelet conversion coefficient matrix M, if its height is h row, width is w column；
The series L that step 2. input needs to convertmaxThe bit plane quantity N that need to be handled is converted with every gradebp, and enable conversion stage
Number L ← Lmax, " ← " indicates assignment operation；
Step 3. counts the coefficient C of maximum absolute value in the low frequency sub-band of Mmax, and then it is highest according to formula (17) calculating
Bit plane Nmax_bp:
Step 4. enables current bit plane Ncurrent←Nmax_bp；
Wavelet conversion coefficient tissue size is the block of 2 × 2 pixels, protected by step 5. according to formula (18)~formula (21)
Being stored to a size is (h/2L-1)×(w/2L-1) matrix W in:
W(2i,2j)←M(i,j) (18)
W(2i,2j+1)←M(i,j+w/2L) (19)
W(2i+1,2j)←M(i+h/2L,j) (20)
W(2i+1,2j+1)←M(i+h/2L,j+w/2L) (21)
The i and j is integer, and 0≤i < h/2L, 0≤j < w/2L；
Step 6. enables M (i, j), M (i, j+w/2L)、M(i+h/2L, j) and M (i+h/2L,j+w/2L) reset, the i and j
It is integer, and 0≤i < h/2L, 0≤j < w/2L；
Step 7. enables b ← (1 < < Ncurrent), " the < < " indicates arithmetic shift left operation；
Step 8. is against the improvement stage: according to step 8.1~step 8.4, block-by-block calculates the of non-separate wavelet inverse transformation
NcurrentThe predictive coefficient value of bit plane, the block for arranging to be presently processing is referred to as " current block "；
Step 8.1 calculates the predictive coefficient value T of lower left corner pixel in each 2 × 2 block of pixels according to formula (22), block-by-block
(2i+1,2j):
The sgn () indicates that sign function, abs () indicate that the function that takes absolute value, " & " indicate step-by-step and operation, " >
> " indicates arithmetic shift right operation, the wavelet conversion coefficient value of lower left corner pixel in W (2i+1,2j) expression current block, W (2i+1,
2j-1) indicate the wavelet conversion coefficient value of lower right corner pixel in adjacent block on the left of current block, W (2i+1,2j+1) indicates current block
The wavelet conversion coefficient value of middle lower right corner pixel；
Step 8.2 calculates the predictive coefficient value T of top left corner pixel in each 2 × 2 block of pixels according to formula (23), block-by-block
(2i, 2j):
The W (2i, 2j) indicates the wavelet conversion coefficient value of top left corner pixel in current block, and W (2i, 2j+1) indicates current
The wavelet conversion coefficient value of upper right corner pixel in block, W (2i, 2j-1) indicate on the left of current block the small of upper right corner pixel in adjacent block
Wave conversion coefficient value, T (2i+1,2j) indicate the predictive coefficient value of lower left corner pixel in current block, and T (2i-1,2j) indicates current
The predictive coefficient value of lower left corner pixel in the adjacent block of block top；
Step 8.3 calculates the predictive coefficient value T of upper right corner pixel in each 2 × 2 block of pixels according to formula (24), block-by-block
(2i, 2j+1):
The W (2i, 2j+1) indicates the wavelet conversion coefficient value of upper right corner pixel in current block, and W (2i+1,2j+1) is indicated
The wavelet conversion coefficient value of lower right corner pixel in current block, W (2i-1,2j+1) indicate lower right corner picture in the adjacent block of current block top
The wavelet conversion coefficient value of element；
Step 8.4 calculates the predictive coefficient value T of lower right corner pixel in each 2 × 2 block of pixels according to formula (25), block-by-block
(2i+1,2j+1):
T (2i+1,2j+1)=sgn (W (2i+1,2j+1)) × [abs (W (2i+1,2j+1)) &b] (25)
The W (2i+1,2j+1) indicates the wavelet conversion coefficient value of lower right corner pixel in current block；
The step 9. inverse prediction stage: according to step 9.1~step 9.4, block-by-block calculates the of non-separate wavelet inverse transformation
NcurrentThe pixel value of bit plane；
Step 9.1 according to formula (26), block-by-block calculate upper right corner pixel in each 2 × 2 block of pixels pixel value M ' (2i,
2j+1):
M ' (2i, 2j+1)=[T (2i, 2j)+T (2i, 2j+2)] > > 1 (26)
The T (2i, 2j) indicates the predictive coefficient value of top left corner pixel in current block, and T (2i, 2j+2) indicates that current block is right
The predictive coefficient value of top left corner pixel in the adjacent block of side；
Step 9.2 calculates the pixel value M ' (2i+ of lower right corner pixel in each 2 × 2 block of pixels according to formula (27), block-by-block
1,2j+1):
M ' (2i+1,2j+1)=[T (2i+1,2j)+T (2i+1,2j+2)+T (2i, 2j+1)+T (2i+2,2j+1)] > > 1 (27)
The T (2i+1,2j) indicates the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j+2) indicates current
The predictive coefficient value of lower left corner pixel, T (2i, 2j+1) indicate the prediction system of upper right corner pixel in current block in the adjacent block of block right side
Numerical value, T (2i+2,2j+1) indicate the predictive coefficient value of upper right corner pixel in adjacent block below current block；
Step 9.3 calculates the pixel value M ' (2i+ of lower left corner pixel in each 2 × 2 block of pixels according to formula (28), block-by-block
1,2j):
M ' (2i+1,2j)=[T (2i, 2j)+T (2i+2,2j)] > > 1 (28)
The T (2i+2,2j) indicates the predictive coefficient value of top left corner pixel in adjacent block below current block；
Step 9.4 keeps the predictive coefficient value T (2i, 2j) of top left corner pixel in each 2 × 2 block of pixels constant, as it
Pixel value M ' (2i, 2j)；
Step 10. is according to formula (29)~formula (32), and block-by-block is by NcurrentThe pixel value of bit plane is added to higher
In the pixel value of bit plane:
M(2i,2j)←M(2i,2j)+M′(2i,2j) (29)
M(2i,2j+1)←M(2i,2j+1)+M′(2i,2j+1) (30)
M(2i+1,2j)←M(2i+1,2j)+M′(2i+1,2j) (31)
M(2i+1,2j+1)←M(2i+1,2j+1)+M′(2i+1,2j+1) (32)
The i and j is integer, and 0≤i < h/2L, 0≤j < w/2L；
Step 11. enables Ncurrent←Ncurrent- 1, if Ncurrent≥Nmax_bp-Nbp+ 1 and Ncurrent>=0, then it is transferred to step
7, otherwise it is transferred to step 12；
Step 12. enables L ← L-1, if L > 0, is transferred to step 3；Otherwise, output matrix M, non-separate wavelet inverse transformation
Journey terminates.
(a)~(c) is 3 width original test images, respectively Lena, Peppers and Baboon in Fig. 1.
3 are carried out to 28 bit planes of highest of Lena image, 4 bit planes of highest, highest bit planes using the present invention
The result of grade wavelet transformation is respectively as shown in Fig. 2 (a)~(c).
Using the present invention to 28 bit planes of highest, 4 bit planes of highest, highest bit planes of Peppers image into
The result of 2 grades of wavelet transformations of row is respectively as shown in Fig. 3 (a)~(c).
28 bit planes of highest of Baboon image, 4 bit planes of highest, highest bit planes are carried out using the present invention
The result of 2 grades of wavelet transformations is respectively as shown in Fig. 4 (a)~(c).
After carrying out 3 grades of small echo direct transforms using 8 bit planes of highest of the present invention to Lena image, then to wavelet transformation system
8 several 2 bit planes of highest, 4 bit planes of highest, highest bit planes carry out the result of 3 grades of wavelet inverse transformations respectively such as Fig. 5
(a) shown in~(c).
After carrying out 2 grades of small echo direct transforms using 8 bit planes of highest of the present invention to Peppers image, then small echo is become
82 bit planes of highest, 4 bit planes of highest, highest bit planes for changing coefficient carry out the result difference of 2 grades of wavelet inverse transformations
As shown in Fig. 6 (a)~(c).
After carrying out 2 grades of small echo direct transforms using 8 bit planes of highest of the present invention to Baboon image, then to wavelet transformation
82 bit planes of highest of coefficient, 4 bit planes of highest, highest bit planes carry out the results of 2 grades of wavelet inverse transformations respectively such as
Shown in Fig. 7 (a)~(c).
With the increase of bit plane quantity, frequency domain decomposition quality of the invention and reconstruction matter it can be seen from Fig. 2~Fig. 7
Amount is gradually increased, and shows apparent quality scalability characteristic.Simultaneously as the bit plane quantity for participating in transformation is different, meter
It calculates complexity and also has gradable characteristic.
Claims (2)
1. a kind of inseparable Lifting Wavelet direct transform method of quality and complexity hierarchical, it is characterised in that according to following step
It is rapid to carry out:
Step 1. inputs an image I to be processed, if its height is h pixel, width is w pixel；
The series L that step 2. input needs to convertmaxThe bit plane quantity N that need to be handled is converted with every gradebp, and enable transformation series L ←
1, " ← " indicates assignment operation；
The maximum value C of step 3. statistical picture Imax, highest bit plane N is calculated according to formula (1)max_bp:
Step 4. enables current bit plane Ncurrent←Nmax_bp；
Step 5. divides the stage: image I is divided into and is not overlapped and size is the block of 2 × 2 pixels, for each block of pixels,
The coordinate of its top left corner pixel is (2i, 2j), and the coordinate of upper right corner pixel is (2i, 2j+1), and the coordinate of lower left corner pixel is (2i
+ 1,2j), the coordinate of lower right corner pixel is (2i+1,2j+1), and the i and j are integer, and
Step 6. is initialized as 0 for each block of pixels, by its wavelet conversion coefficient value, even W (2i, 2j) ← 0, W (2i, 2j+
1) ← 0, W (2i+1,2j) ← 0, W (2i+1,2j+1) ← 0, the W (2i, 2j), W (2i, 2j+1), W (2i+1,2j) and W (2i+
1,2j+1) respectively indicate the wavelet transformation of top left corner pixel in block of pixels, upper right corner pixel, lower left corner pixel and lower right corner pixel
Coefficient value；
Step 7. forecast period: according to step 7.1~step 7.5, block-by-block calculates the N of non-separate wavelet transformationcurrentPosition is flat
The predictive coefficient value in face, the block for arranging to be presently processing is referred to as " current block "；
Step 7.1 enables b ← (1 < < Ncurrent), " the < < " indicates arithmetic shift left operation；
Step 7.2 according to formula (2), block-by-block calculate top left corner pixel in each 2 × 2 block of pixels predictive coefficient value T (2i,
2j):
T (2i, 2j)=sgn (I (2i, 2j)) × [abs (I (2i, 2j)) &b] (2)
The sgn () indicates that sign function, I (2i, 2j) indicate to be located at the pixel value at coordinate (2i, 2j), abs in current block
() indicates that the function that takes absolute value, " & " indicate step-by-step and operation；
Step 7.3 according to formula (3), block-by-block calculate lower left corner pixel in each 2 × 2 block of pixels predictive coefficient value T (2i+1,
2j):
The I (2i+1,2j) indicates that the pixel value in current block at coordinate (2i+1,2j), I (2i+2,2j) indicate current
Top left corner pixel value below block in adjacent block, " > > " indicate arithmetic shift right operation；
Step 7.4 according to formula (4), block-by-block calculate lower right corner pixel in each 2 × 2 block of pixels predictive coefficient value T (2i+1,
2j+1):
The I (2i+1,2j+1) indicates that the pixel value in current block at coordinate (2i+1,2j+1), I (2i, 2j+1) indicate
The pixel value being located at coordinate (2i, 2j+1) in current block, I (2i+2,2j+1) indicate the upper right corner of adjacent block below current block
Pixel value, T (2i+1,2j) indicate the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j+2) indicates that current block is right
The predictive coefficient value of lower left corner pixel in the adjacent block of side；
Step 7.5 calculates predictive coefficient value T (2i, the 2j+ of upper right corner pixel in each 2 × 2 block of pixels according to formula (5), block-by-block
1):
The I (2i, 2j+1) indicates that the pixel value in current block at coordinate (2i, 2j+1), I (2i, 2j+2) indicate current
Top left corner pixel value on the right side of block in adjacent block；
Step 8. improvement stage: according to step 8.1~step 8.4, block-by-block calculates the N of non-separate wavelet transformationcurrentPosition is flat
The Lifting Coefficients value in face；
Step 8.1 keeps the predictive coefficient value T (2i+1,2j+1) of lower right corner pixel in each 2 × 2 block of pixels constant, as it
Lifting Coefficients value U (2i+1,2j+1)；
Step 8.2 calculates Lifting Coefficients value U (2i, the 2j+ of upper right corner pixel in each 2 × 2 block of pixels according to formula (6), block-by-block
1):
U (2i, 2j+1)=T (2i, 2j+1)+[T (2i+1,2j+1)+T (2i-1,2j+1)] > > 2 (6)
The T (2i, 2j+1) indicates the predictive coefficient value of upper right corner pixel in current block, and T (2i+1,2j+1) is indicated in current block
The predictive coefficient value of lower right corner pixel, T (2i-1,2j+1) indicate the predictive coefficient of the lower right corner pixel of adjacent block above current block
Value；
Step 8.3 calculates the Lifting Coefficients value U of top left corner pixel in each 2 × 2 block of pixels according to the definition of formula (7), block-by-block
(2i, 2j):
U (2i, 2j)=T (2i, 2j)+[T (2i, 2j-1)+T (2i, 2j+1)+T (2i-1,2j)+T (2i+1,2j)] > > 2 (7)
The T (2i, 2j) indicates the predictive coefficient value of top left corner pixel in current block, and T (2i, 2j+1) indicates upper right in current block
The predictive coefficient value of angle pixel, T (2i+1,2j) indicate the predictive coefficient value of lower left corner pixel in current block, T (2i, 2j-1) table
Show the predictive coefficient value of upper right corner pixel in adjacent block on the left of current block, T (2i-1,2j) indicates left in adjacent block above current block
The predictive coefficient value of inferior horn pixel；
Step 8.4 according to formula (8), block-by-block calculate lower left corner pixel in each 2 × 2 block of pixels Lifting Coefficients value U (2i+1,
2j):
U (2i+1,2j)=T (2i+1,2j)+[T (2i+1,2j-1)+T (2i+1,2j+1)] > > 2 (8)
The T (2i+1,2j) indicates the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j-1) indicates that current block is left
The predictive coefficient value of lower right corner pixel in the adjacent block of side, T (2i+1,2j+1) indicate the predictive coefficient of lower right corner pixel in current block
Value；
Step 9. is according to formula (9)~formula (12), and block-by-block is by NcurrentThe Lifting Coefficients value of bit plane is added to more high-order flat
In the wavelet conversion coefficient value in face:
W(2i,2j)←W(2i,2j)+U(2i,2j) (9)
W(2i,2j+1)←W(2i,2j+1)+U(2i,2j+1) (10)
W(2i+1,2j)←W(2i+1,2j)+U(2i+1,2j) (11)
W(2i+1,2j+1)←W(2i+1,2j+1)+U(2i+1,2j+1) (12)
Step 10. enables Ncurrent←Ncurrent- 1, if Ncurrent≥Nmax_bp-Nbp+ 1 and Ncurrent>=0, then it is transferred to step 7, it is no
Then it is transferred to step 11；
Step 11. reorganizes the wavelet conversion coefficient of each 2 × 2 block of pixels, composition according to formula (13)~formula (16)
LLL、LHL、HLLAnd HHLSubband；
LLL(i,j)←W(2i,2j) (13)
HLL(i,j)←W(2i,2j+1) (14)
LHL(i,j)←W(2i+1,2j) (15)
HHL(i,j)←W(2i+1,2j+1) (16)
The LLL、LHL、HLLAnd HHLRespectively indicate LL subband, LH subband, HL subband and the HH subband of L grades of transformation；
Step 12. enables L ← L+1, if L < Lmax, then I ← LL is enabledL, h ← h/2, w ← w/2 are transferred to step 3；Otherwise, it exports
And HLk、LHk、HHk, the 1≤k≤Lmax, non-separate wavelet conversion process terminates.
2. a kind of corresponding with the inseparable Lifting Wavelet direct transform method of quality described in claim 1 and complexity hierarchical
Inseparable Lifting Wavelet inverse transformation method, it is characterised in that carry out in accordance with the following steps:
Step 1. inputs wavelet conversion coefficient matrix M, if its height is h row, width is w column；
The series L that step 2. input needs to convertmaxThe bit plane quantity N that need to be handled is converted with every gradebp, and enable transformation series L ←
Lmax, " ← " indicates assignment operation；
Step 3. counts the coefficient C of maximum absolute value in the low frequency sub-band of Mmax, and then calculate highest position according to formula (17) and put down
Face Nmax_bp:
Step 4. enables current bit plane Ncurrent←Nmax_bp；
Wavelet conversion coefficient tissue size is the block of 2 × 2 pixels, is saved in by step 5. according to formula (18)~formula (21)
One size is (h/2L-1)×(w/2L-1) matrix W in:
W(2i,2j)←M(i,j) (18)
W(2i,2j+1)←M(i,j+w/2L) (19)
W(2i+1,2j)←M(i+h/2L,j) (20)
W(2i+1,2j+1)←M(i+h/2L,j+w/2L) (21)
The i and j is integer, and 0≤i < h/2L, 0≤j < w/2L；
Step 6. enables M (i, j), M (i, j+w/2L)、M(i+h/2L, j) and M (i+h/2L,j+w/2L) reset, the i and j are whole
Number, and 0≤i < h/2L, 0≤j < w/2L；
Step 7. enables b ← (1 < < Ncurrent), " the < < " indicates arithmetic shift left operation；
Step 8. is against the improvement stage: according to step 8.1~step 8.4, block-by-block calculates the N of non-separate wavelet inverse transformationcurrent
The predictive coefficient value of bit plane, the block for arranging to be presently processing is referred to as " current block "；
Step 8.1 according to formula (22), block-by-block calculate lower left corner pixel in each 2 × 2 block of pixels predictive coefficient value T (2i+1,
2j):
The sgn () indicates that sign function, abs () indicate that the function that takes absolute value, " & " indicate step-by-step and operation, " > > "
Indicate arithmetic shift right operation, W (2i+1,2j) indicates the wavelet conversion coefficient value of lower left corner pixel in current block, W (2i+1,2j-
1) the wavelet conversion coefficient value of lower right corner pixel in adjacent block on the left of current block is indicated, W (2i+1,2j+1) indicates right in current block
The wavelet conversion coefficient value of inferior horn pixel；
Step 8.2 according to formula (23), block-by-block calculate top left corner pixel in each 2 × 2 block of pixels predictive coefficient value T (2i,
2j):
The W (2i, 2j) indicates the wavelet conversion coefficient value of top left corner pixel in current block, and W (2i, 2j+1) is indicated in current block
The wavelet conversion coefficient value of upper right corner pixel, W (2i, 2j-1) indicate that the small echo of upper right corner pixel in adjacent block on the left of current block becomes
Coefficient value is changed, T (2i+1,2j) indicates the predictive coefficient value of lower left corner pixel in current block, and T (2i-1,2j) is indicated on current block
The predictive coefficient value of lower left corner pixel in square adjacent block；
Step 8.3 calculates predictive coefficient value T (2i, the 2j of upper right corner pixel in each 2 × 2 block of pixels according to formula (24), block-by-block
+ 1):
The W (2i, 2j+1) indicates the wavelet conversion coefficient value of upper right corner pixel in current block, and W (2i+1,2j+1) indicates current
The wavelet conversion coefficient value of lower right corner pixel in block, W (2i-1,2j+1) indicate lower right corner pixel in the adjacent block of current block top
Wavelet conversion coefficient value；
Step 8.4 according to formula (25), block-by-block calculate lower right corner pixel in each 2 × 2 block of pixels predictive coefficient value T (2i+1,
2j+1):
T (2i+1,2j+1)=sgn (W (2i+1,2j+1)) × [abs (W (2i+1,2j+1)) &b] (25)
The W (2i+1,2j+1) indicates the wavelet conversion coefficient value of lower right corner pixel in current block；
The step 9. inverse prediction stage: according to step 9.1~step 9.4, block-by-block calculates the N of non-separate wavelet inverse transformationcurrent
The pixel value of bit plane；
Step 9.1 calculates pixel value M ' (2i, the 2j+ of upper right corner pixel in each 2 × 2 block of pixels according to formula (26), block-by-block
1):
M ' (2i, 2j+1)=[T (2i, 2j)+T (2i, 2j+2)] > > 1 (26)
The T (2i, 2j) indicates the predictive coefficient value of top left corner pixel in current block, and T (2i, 2j+2) indicates phase on the right side of current block
The predictive coefficient value of top left corner pixel in adjacent block；
Step 9.2 calculates pixel value M ' (2i+1, the 2j+ of lower right corner pixel in each 2 × 2 block of pixels according to formula (27), block-by-block
1):
M ' (2i+1,2j+1)=[T (2i+1,2j)+T (2i+1,2j+2)+T (2i, 2j+1)+T (2i+2,2j+1)] > > 1 (27)
The T (2i+1,2j) indicates the predictive coefficient value of lower left corner pixel in current block, and T (2i+1,2j+2) indicates that current block is right
The predictive coefficient value of lower left corner pixel in the adjacent block of side, T (2i, 2j+1) indicate the predictive coefficient of upper right corner pixel in current block
Value, T (2i+2,2j+1) indicate the predictive coefficient value of upper right corner pixel in adjacent block below current block；
Step 9.3 according to formula (28), block-by-block calculate lower left corner pixel in each 2 × 2 block of pixels pixel value M ' (2i+1,
2j):
M ' (2i+1,2j)=[T (2i, 2j)+T (2i+2,2j)] > > 1 (28)
The T (2i+2,2j) indicates the predictive coefficient value of top left corner pixel in adjacent block below current block；
Step 9.4 keeps the predictive coefficient value T (2i, 2j) of top left corner pixel in each 2 × 2 block of pixels constant, as its pixel
Value M ' (2i, 2j)；
Step 10. is according to formula (29)~formula (32), and block-by-block is by NcurrentThe pixel value of bit plane is added to more high bit-planes
Pixel value in:
M(2i,2j)←M(2i,2j)+M′(2i,2j) (29)
M(2i,2j+1)←M(2i,2j+1)+M′(2i,2j+1) (30)
M(2i+1,2j)←M(2i+1,2j)+M′(2i+1,2j) (31)
M(2i+1,2j+1)←M(2i+1,2j+1)+M′(2i+1,2j+1) (32)
The i and j is integer, and 0≤i < h/2L, 0≤j < w/2L；
Step 11. enables Ncurrent←Ncurrent- 1, if Ncurrent≥Nmax_bp-Nbp+ 1 and Ncurrent>=0, then it is transferred to step 7, it is no
Then it is transferred to step 12；
Step 12. enables L ← L-1, if L > 0, is transferred to step 3；Otherwise, output matrix M, non-separate wavelet inverse transformation process knot
Beam.
Priority Applications (1)
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