JPH01240032A - Adaptive kl transformation encoding system and its decoding system - Google Patents

Abstract

PURPOSE:To reduce the number of information to transmit and to improve an encoding characteristic by providing a KL transformation matrix code book, a proper value table, self correlation coefficient table and an optimum bit distribution table in an encoding part and providing the optimum bit distribution table, transformation coefficient code book and a KL inverse transformation matrix code book in a decoding part. CONSTITUTION:An optimum representative transformation matrix searching device 10 finds out a representative transformation matrix to give 8 minimum distortion among inputted distortions out of a transformation matrix code book 6 and outputs its number. The number of said optimum representative transformation matrix is encoded by an encoder 12 and sent out to the decoding part through a multiplexer 13 together with the output of a quantizer 4. The optimum representative transformation matrix is obtained out of a KL inverse transformation matrix code book 28 at a table reference part 24 based on the number of the optimum representative matrixes decoded by the decoder. A KL inverse transformation is executed to a KL transformation coefficient decoded at a vector multiplier 25 with the use of the optimum representative transformation matrix and a reproduction signal is obtained. Thus, an information quantity to be transmitted is reduced, the encoding characteristic is improved and an operation quantity can be reduced.

Description

DETAILED DESCRIPTION OF THE INVENTION [Object of the Invention] (Industrial Application Field) The present invention relates to an adaptive KL transform encoding method and its decoding method for efficiently encoding audio signals and image signals.

(Prior Art) KL transform is known as an effective method that minimizes the mean square error associated with encoding among various orthogonal transforms such as DFT and DCT. However, when applying KL transform to orthogonal transform encoding, an autocorrelation matrix is obtained every time a vectorized input signal is input, its eigenvector is calculated, and the transformation matrix created from the eigenvector is calculated. There was a problem in that the amount of information that had to be encoded and the amount of calculation to be transmitted increased significantly.

If the order of the input vector is N, the number of multiplications required to calculate the eigenvector is H, which is known as an efficient method.
householder -Q R- Even when using the reverse iterative solution method, -KoN3+ is required for Householder transformation.
Yu N2° QR repetition to 9N2. ION” for inverse iteration, N 3 N 2 for eigenvector transformation. Total 1-2-N゛+1
It becomes 9.5N'.

However, since the number of repetitions of QR repetition and inverse repetition depends on the input signal, the number of multiplications is not exact but is based on experience (see Publication 1: J.

B athe, E. L., Wi13ON, translated by Fumio Kikuchi, Numerical Calculation of the Finite Element Method, Science and Technology Publishing).

In orthogonal transform coding, the order N is often set to 100 or more, and even if N=128, the number of multiplications required to calculate the eigenvectors would be as large as 3,814,741 times. Furthermore, the transformation matrix becomes NXN, increasing the amount of information to be transmitted.

Therefore, in order to reduce the amount of transmitted information, a method has been proposed in which the parameters of a prediction model are encoded instead of the transformation matrix, and the decoding section estimates an autocorrelation matrix from the parameters to obtain the transformation matrix (known literature 2; JP-A-62-53
026. Adaptive orthogonal transform coding method and its device i! f
).

FIG. 3 shows a diagram of the principle of the method described in this document. Specifically, in FIG. 3, the autocorrelation coefficient estimator 31 calculates the parameters of the all-pole prediction model by
The autocorrelation coefficient r(k) is estimated using the following recursive formula from the parameters obtained using the in method.

Here, aitkL is the α parameter and the parameter of the prediction model, respectively, and p is the order.

Note that in FIG. 3, the encoding unit 30 includes an autocorrelation coefficient estimator 31. Eigenvalue expansion calculator 32, coefficient sequence calculator 33.
It is composed of encoders 34 and 35 and a multiplexer 36. The decoding unit 40 is composed of a demultiplexer 41, decoders 42, 43, an autocorrelation coefficient calculator 44, an eigenvalue expansion calculator 45, and a reproduction signal generator 46. Note that 37.47 indicates an input terminal, and 38.48 indicates an output terminal.

(Problem to be solved by the invention) In the conventional method shown in FIG. 3, the autocorrelation coefficient r
(k) can be accurately calculated from only up to p parameters of the prediction model, and N−p parameters include estimation errors.

When calculating the KL transformation matrix from the estimated autocorrelation coefficients, no consideration is given to estimation errors.

For this reason, conventional methods do not necessarily perform optimal conversion on input signals.

Therefore, in order to reduce the estimation error of the autocorrelation coefficient, it has to approach the first order pttN, and in that case, there is a problem that the amount of information to be transmitted increases and the encoding efficiency deteriorates.

Furthermore, as can be seen from FIG. 3, the conventional method requires eigenvalue expansion, that is, calculation of eigenvectors, in both the encoding section 30 and the decoding section 40, resulting in a problem that the amount of calculation becomes enormous.

As mentioned above, the number of multiplications required to obtain the eigenvector is , and the number of multiplications required to obtain the parameters of p prediction models using the Durbin method is p''+
3 p + 1 The number of multiplications required to obtain all the autocorrelation coefficients from the parameters of the prediction model can be expressed as -(P+1)+p(N+p).

In the end, the number of multiplications required to obtain the transformation matrix in the conventional method is 1-N+19.5N2+-2-P2+(N
+ ding) P+1, which is huge.

This invention was made to solve the above problems, and is an encoding method that reduces the amount of information to be transmitted, improves encoding characteristics, and reduces the amount of calculations to reduce the hardware scale. The purpose is to provide a method.

[Structure of the invention]

(Means for Solving the Problems) In order to achieve the above object, in the present invention, the encoding unit includes a KL transformation matrix codebook created in advance by an LBG algorithm, etc., and eigenvalues determined corresponding to this KL transformation matrix codebook. a table, an autocorrelation coefficient table, an optimal bit allocation table, and means for determining an autocorrelation coefficient of an input signal, the autocorrelation coefficient of the input signal, one representative transformation in the KL transformation matrix codebook; A queue and
The distortion when the input signal is transformed by the representative transformation matrix is calculated from the eigenvalues in the eigenvalue table corresponding to this representative transformation matrix and the autocorrelation coefficient in the autocorrelation coefficient table, and this distortion is minimized. Search for the optimal representative transformation matrix.

The input signal is subjected to KL transformation using the found optimal representative transformation matrix, the obtained transformation coefficients are encoded under optimal bit allocation, and the number of this optimal representative transformation matrix is encoded and decoded. transmitted to the department.

On the other hand, the decoding unit has a KL transformation matrix codebook and an optimal bit allocation table common to the encoding unit, and selects an optimal representative transformation matrix from the KL transformation matrix codebook based on the number of the transmitted optimal transformation matrix. is obtained, and the KL inverse transform is performed on the decoded KL transform coefficients using this optimal representative transform matrix to obtain a reproduced signal.

(Effect) Let the input signal vector be λ, its autocorrelation coefficient be r(k),
k"O+1+"'tN It autocorrelation matrix 1Rxx
Then, RxX is. However, N is the order of the input signal vector X.

Assuming that the eigenvalue of the autocorrelation matrix IRxx is λj, and the eigenvector is ' t + j=Og 1 e, N-1,
The KL transformation matrix A is obtained as a matrix with γ1 as a row vector.

A= (yo+ txt ”'vN-t)tQD This means that the eigenvalue expansion of IRxx Rxx: Iu1DLIt lu = ('uo+ 11x+ ””UN-1)
(5) iD==diag (λ., λ1.
...λ. -0].

Using the transformation matrix of formula (■), perform KL transformation on the input vector, and use the KL transformation coefficient obtained by the transformation as θky k=o
, i, ..., N-1, then 6=A, x = [θ. , θ1. ...θN-1) (
6). When Ok is quantized under the optimal bit allocation determined by λ1, the average 2 due to encoding and decoding
The multiplicative error σ2 is expressed as follows. (Publicly known document 3:
N, S, Jayant, Peter No11. D
IG I TALC:0 DING OF WAVEFO
RMS, 'PRENTiCE-HALL) where E* is a parameter representing the performance of the quantizer, and R is the average number of bits of the quantizer.

Also σ. ′, j are the variances of the transformation coefficients θj, and the bow j=
:Ro, (jtj) (s)=λ
j where IRa a is the autocorrelation matrix of the KL transform coefficients. 1Roo is expressed as fRθo=AIRxxAt(9).

Next, add another input vector to 1. The corresponding autocorrelation matrix and KL transformation matrix are IRxxyA and..., N
-1, if the input vector It is expressed as follows.

However, cr5j= IRB B (jr j )
(12) Here, Δ1Rxx = 1Rxx −1'Rxx
(13), the first term on the right side of this equation is that A is an orthogonal matrix whose row vectors are the eigenvectors of (Rxx).

This becomes a diagonal matrix with the eigenvalues λl as diagonal elements. In other words, if the second term on the right side is ΔR, its diagonal element ΔRL
l is expressed as follows.

Therefore, equation (10) giving the mean square error σ2 is:
Equations (12), (14), (15), (16)
It is expressed as follows using .

σ”=i”, 2−δR[π(λj+ΔRJJ))
(17) Ja.

This formula is transformed as follows.

σ2=ε:2−δR[πλJ(1+ΔRjj/λJ))
-a ......(18) However, c = Qn (i '', 2-'') and λj) Δ
Since RJj... (19) In the above equation, C is a constant that does not exist in the transformation matrix A, so the following distortion measure is used when the input vector X is orthogonally transformed by A instead of the transformation matrix A. Define d(8, A).

j: mouth j+a.

Since d (A, A)>O, if d (8, A) is small, the mean square error σ2 will also be small.

Therefore, using the LBG algorithm or the like under the distortion scale of equation (20), KL is calculated in advance from a large number of training signals.
By creating a transformation matrix codebook and its corresponding eigenvalue table and autocorrelation coefficient table, the autocorrelation coefficient r(j) of the input signal, one representative transformation matrix in the KL transformation matrix codebook, A and the corresponding eigenvalue λj in the eigenvalue table.

The distortion when the input signal is orthogonally transformed using the representative transformation matrix can be calculated from the autocorrelation coefficient r (j) using equation (20). The optimal representative transformation matrix that minimizes this distortion is found from the transformation matrix codebook, and the KL transformation matrix determined by the input signal is expressed by that number.

The method of this invention provides a concrete means for encoding a KL transformation matrix by vector quantization. Vector quantization is Rate −DistortionTh
The method of this invention is known as a method that approaches the information theory limit based on Eory, and the method of this invention uses distortion that directly corresponds to the mean squared error accompanying encoding and decoding as a distortion measure during vector quantization of the KL transformation matrix. I am using it. As a result, the method of the present invention can be calculated in advance to improve the distortion-bit rate characteristics compared to the conventional method.
At the time of encoding, only ΔRjJ in equation (16) needs to be calculated.

As described above, in the method of the present invention, there is no need to calculate eigenvectors during encoding and decoding, so the amount of calculation can be significantly reduced.

(Example) Hereinafter, one embodiment of the present invention will be described with reference to the drawings.

FIG. 1 shows the configuration of the encoding section of this embodiment. In FIG. 1, 2 is a buffer for vectorizing an input signal. In addition, 6 is a transformation matrix codebook created in advance by applying clustering and LBG algorithms to a large number of training input signals, and 7 and 8 are eigenvalue tables and self-phases created in advance corresponding to transformation matrix codebook 6, respectively. This is a relationship number table.

When an input signal is input to terminal 1 in FIG. 1 and vectorized in buffer 2, the autocorrelation coefficient of the input signal is first calculated by autocorrelation coefficient calculator 5, and the obtained autocorrelation coefficient and From one representative transformation matrix in the transformation matrix codebook 6, the corresponding eigenvalues in the eigenvalue table 7, and the autocorrelation coefficient in the autocorrelation coefficient table 8, the distortion of equation (20) described above is calculated by the distortion calculator 9. calculated by
It is output to the optimal representative transformation matrix searcher 10.

The optimal representative transformation matrix searcher 10 finds a representative transformation matrix that gives the smallest distortion among the input distortions from the transformation matrix codebook 7, and outputs its number.

Next, the input vector is processed by the vector multiplier 3, which performs the operation represented by
is orthogonally transformed.

The transform coefficients thus obtained are each scalar quantized by the quantizer 4 under the bit allocation given by the optimum bit allocation table.

Now, the transformation matrix is A, and the corresponding eigenvalue is λj.

i = Ot 1 r..., N-1, the exchange coefficient obtained by orthogonal transformation using the transformation matrix A is θ(g l =O
If p 1 +..., N-1, the optimal bit allocation b
The number of bits when quantizing i, that is, θl, is given by the following equation.

Here, R is the average number of bits for the entire quantization, bits/sample. Since the value of the above equation is uniquely determined for the transformation matrix A, it can be calculated in advance.

The optimal bit allocation table 11 is the transformation matrix codebook 6
A table contains a bit allocation pattern calculated in advance using equation (21) for each representative transformation matrix in the table.

Finally, the number of the optimal representative transformation matrix found by the optimal representative transformation matrix searcher 10 is encoded by the encoder 12, and together with the output of the quantizer 4 is sent to the multiplexer 1.
3 and then sent to the decoding unit.

FIG. 2 shows the h configuration of the decoding section of this embodiment.
20 is a demultiplexer, 21.22 is a decoder, 23
, 24 is a table reference unit, 25 is a vector multiplier for KL inverse transformation, and the decoding unit is also provided with an optimal bit allocation table 26, a transformation coefficient codebook 27, and a KL inverse transformation matrix codebook 28. .

With this configuration, the signal transmitted from the encoder is divided into KL transform coefficients and the optimal representative transform matrix number via the demultiplexer 20 of the decoder.

The former is input to the inverse quantizer 2I, and the latter is input to the decoder 22.

The signal restored by the dequantizer 21 is input to the table reference section 23, where bit allocation is performed using the signal from the table 26 of the decoding section, which is the same as the optimum bit allocation table 1'1 of the encoding section. Then, the KL transform coefficients are selected by referring to the transform coefficient codebook 27. On the other hand, the table reference unit 24 calculates the optimal representative transformation matrix from the KL inverse transformation matrix codebook 28 based on the number of the optimal representative matrix decoded by the decoder.

Using this optimal representative transformation matrix, the vector multiplier 25 performs KL inverse transformation on the decoded KL transformation coefficients to obtain a reproduced signal.

In this way, the encoding section is provided with the KL transformation matrix codebook 6, the eigenvalue table 7, the autocorrelation coefficient table 8, and the optimal bit allocation table, and the decoding section is provided with the optimal bit allocation table 26, the transformation coefficient codebook 27. By providing the KL inverse transform matrix codebook 28, the number of information to be transmitted can be reduced and an encoding system with excellent encoding characteristics can be achieved.

It should be noted that the present invention is not limited to the above-mentioned embodiments, and may have different configurations without changing the gist.

〔Effect of the invention〕

According to the present invention, it is possible to provide an encoding method that can reduce the amount of information to be transmitted, improve encoding characteristics, and reduce the amount of calculations to reduce the hardware scale.

[Brief explanation of the drawing]

FIG. 1 is a block diagram of an encoding section according to an embodiment of the present invention, and FIG.
This figure is a block diagram of the decoding section of the same embodiment, and FIG. 3 is a block diagram showing the principle of the conventional encoding system. 1...Terminal 2...Buffer 3...Vector multiplier 4...Quantizer 5...Autocorrelation coefficient calculator 6...Transformation matrix codebook 7...Eigenvalue table 8. ...Autocorrelation coefficient table 9...Distortion calculator 1
0... Optimal representative transformation matrix searcher 11... Optimal bit allocation table 12... Encoder 13... Multiplexer 20... Demultiplexer 21... Inverse quantizer 22... Decoding Vessel 2
3, 24...Table reference unit 25...Vector multiplier 26...Optimum bit allocation table 27...Transformation coefficient codebook 28...KL inverse transformation matrix codebook FIG.

Claims (2)

[Claims] (1) In an adaptive KL transform encoding method in which a vectorized input signal is KL-transformed and the KL transform coefficients obtained by the transform are encoded, the encoding section calculates the autocorrelation coefficient of the input signal. means, a KL transformation matrix codebook created from eigenvectors of autocorrelation matrices obtained in advance for various training input signals, an eigenvalue table determined corresponding to this codebook, and an autocorrelation coefficient table. Calculating the distortion of the representative vector from the optimal bit allocation table, the autocorrelation coefficient obtained by the first means, the representative vector of the KL transformation matrix codebook, the eigenvalue table, and the autocorrelation coefficient table; means for searching for an optimal representative vector that minimizes distortion; means for subjecting the input signal to KL transformation determined by the optimal representative vector; and encoding the transform coefficients obtained by this transformation under optimal bit allocation. and means for encoding the number of the optimal representative vector. (2) A signal encoded by the encoding unit according to claim 1,
In the decoding unit, a KL transformation matrix codebook and an optimal bit allocation table that are the same as the KL transformation matrix codebook that the encoding unit has, means for decoding the transformation coefficients and the representative vector numbers, and decoded transformation coefficients. An adaptive KL transform decoding method, characterized in that a KL inverse transform is performed on a KL transform matrix in the KL transform matrix codebook determined by the decoded number to obtain a reproduced signal.