Method for compressing digital images
View Patent ↗The invention concerns a method for compressing data, in particular images, by transform, in which method this data is projected onto a base of localized orthogonal or biorthogonal functions, such as wavelets. To quantize each of the localized functions with a quantization step that enables an overall set rate R c to be satisfied, the method includes the following steps: a probability density model of coefficients in the form of a generalized Gaussian is associated with each subband, the parameters α and β of this density model are estimated, while minimizing the relative entropy, or Kullback-Leibler distance, between this model and the empirical distribution of coefficients of each subband, and from this model, for each subband, an optimum quantization step is determined such that the rate allocated is distributed in the various subbands and such that the total distortion is minimal. As a preference, for each subband, the graphs of rate R and distortion D are deduced, from the parameters α and β, as a function of the quantization step and these graphs are tabulated to determine said optimum quantization step.
1. A computer implemented method for compressing data by transform, in which method the data is projected onto a base of localized orthogonal or biorthogonal functions, and each of the localized functions is quantize to enable an overall set rate R c to be satisfied, the method comprising:
associating a respective probability density model of coefficients in the form of a generalized Gaussian with each of a plurality of subbands,
estimating parameter β of the density model, while minimizing a relative entropy, or Kullback-Leibler distance, between the model and an empirical distribution of coefficients of each of the plurality of subbands,
estimating parameter α based on the estimating parameter β, and
determining and allocating a respective rate to each of the plurality of subbands such that a total distortion is minimal.
2. The computer implemented method claimed in claim 1 , wherein said localized orthogonal or biorthogonal functions are wavelets.
3. The computer implemented method claimed in claim 2 , wherein, to determine said respective parameter β of the generalized Gaussian corresponding to a subband of index j,k, the following expression is minimized:
H
(
p
1
||
G
α
(
β
)
,
β
)
=
1
β
+
1
β
log
(
β
W
jk
β
)
+
log
(
2
Γ
(
1
/
β
)
β
)
in which formula the first term represents said relative entropy,
W
jk
β
has the value:
W
jk
β
=
1
n
jk
∑
n
,
m
W
jk
[
n
,
m
]
β
W jk [n,m] being a coefficient of the subband of index j,k, and n jk being the number of coefficients in the subband of index j,k.
4. The computer implemented method claimed in claim 3 , wherein said parameter α of the generalized Gaussian corresponding to the subband of index j,k is determined by the following formula:
α
=
β
W
jk
β
β
.
5. The computer implemented method claimed in claim 1 , wherein, for each of the plurality of subbands, graphs of rate R and distortion D are deduced, from the respective parameters α and β, as a function of the quantization and said graphs are tabulated to determine the respective rate.
6. The computer implemented method claimed in claim 5 , wherein the tabulation of the distortion D is carried out for a sequence of values of the parameter β.
7. The computer implemented method claimed in claim 5 , wherein the tabulation of the rate R is carried out for a sequence of values of the parameter β.
8. The computer implemented method claimed in claim 6 , wherein the sequence of values of the parameters β is
{
1
2
,
1
2
,
1
,
2
,
2
}
.
9. The computer implemented method claimed in claim 1 , wherein a total bit budget is distributed to each of the plurality of subbands according to respective ability of each of the plurality of subbands to reduce the distortion of the compressed image.
10. The computer implemented method claimed in claim 9 , wherein a bit budget corresponding to the highest tabulated quantization is assigned to each of the plurality of subbands and wherein remain of the bit budget is then cut into individual parts that are gradually allocated to the localized functions having the greatest ability to make the total distortion decrease, this operation being repeated until the bit budget is exhausted.
11. The computer implemented method claimed in claim 1 , wherein the localized functions and the quantization for each of the plurality of subbands and the parameters α and β of the density model are coded using a lossless entropy coder.