CN102129064B - Universal satellite borne synthetic aperture radar (SAR) original data vector quantized codebook design algorithm - Google Patents

Abstract

The invention discloses a satellite borne synthetic aperture radar (SAR) original data vector quantized codebook design method. A distortion function in a multi-dimensional space is used as a cost function, and the codebook is solved according to the joint probability density function of input data. The method comprises the following steps of: 1, determining the joint probability density function of the input data according to the vector dimension; 2, performing cell division on a definitional domain of the data according to the nearest adjacent criteria, and 3, solving mass centers of corresponding cells according to a mass center solving formula, and performing cyclic iteration on the cell division and the mass center solution to solve the quantized codebook. The method has the advantages that: the vector quantized codebook with universality is designed aiming at the statistic characteristics of the satellite borne original data, meanwhile, offline design can be proved on the vector quantized codebook, and theoretical direction is provided for satellite borne practicability of vector quantization.

Description

Universality satellite-borne SAR raw data Codebook of Vector Quantization algorithm for design

Technical field

The present invention can be applicable to satellite-borne SAR compressing original data field, relates to particularly a kind of universality satellite-borne SAR raw data Codebook of Vector Quantization algorithm for design.

Background technology

The satellite-borne SAR compressing original data is to solve the effective way that data transfer bandwidth on mass data that satellite-borne SAR obtains and the star is difficult to matching problem.At present, although compression algorithm is of a great variety on the star, but compromise considering compression Algorithm Performance complicacy hard-wired with it, can practicality only have BAQ (Block Adaptive Quantization) and BFPQ (Block Floating PointQuantization).

Vector quantization is a kind of efficient data compress technique, is a kind of interrelated process of removing redundance of effectively utilizing between each component of vector.It can in the higher situation of data compression, obtain gratifying compression result.

The key issue of Vector Quantization algorithm is how to design high performance code book.There is a problem needing to overcome in the design of tradition SAR raw data Codebook of Vector Quantization: bad adaptability.Traditional algorithm is when realizing, all by specific training set data, carry out iterative computation, obtain best code book, for guaranteeing preferably compression performance, need to will regenerate code book every one piece of data, and namely need to generate code book according to the input online data, cause that the data compression system computation complexity increases greatly on the star.As not carrying out code book in line computation, only when input data statistics characteristic and training set statistical property correlativity are larger, quantization performance just can be relatively good, when code book and data mismatch to be compressed (correlativity is very little), can cause the decline of Vector Quantization algorithm compression performance, and then worsen image radiation resolution, and reduce picture quality, finally affect the use in actual applications of SAR raw data.

In sum, when the statistical property mismatch of Codebook of Vector Quantization and the packed data of wanting, the performance of Vector Quantization algorithm will obviously descend, and therefore, designing the Codebook of Vector Quantization with universality is the problem that must solve in the practicality.

Summary of the invention

The object of the present invention is to provide a kind of universality satellite-borne SAR raw data Codebook of Vector Quantization method for designing, to solve the poor problem of Codebook of Vector Quantization adaptivity.

For achieving the above object, satellite-borne SAR raw data Codebook of Vector Quantization method for designing provided by the invention, the distortion function on the hyperspace is found the solution code book as cost function according to the joint probability density function of input data; Its key step is as follows:

Step 1: the joint probability density function of determining the input data according to the vector dimension;

Step 2: in the field of definition of data, carry out cell according to the arest neighbors criterion and divide;

Step 3: according to the barycenter solution formula, find the solution the barycenter of corresponding cell, cell is divided to find the solution with barycenter carry out loop iteration and find the solution the quantification code book.

In the described Codebook of Vector Quantization method for designing, the cell in the step 2 is divided and is comprised:

Step 11: selected desired any one solution cell, find the solution all semispaces relevant with cell;

Step 12: the semispace of step 11 gained is got common factor obtain the cell division;

Step 13: repeating step 11 and step 12 obtain all cells and divide.

In the described Codebook of Vector Quantization method for designing, described semispace can be described as by vector parameters and the scalar parameter of correspondence:

H _ij＝{x：y _ij·x+b _ij≥0，j≠i}。

In the described Codebook of Vector Quantization method for designing, when finding the solution the cell barycenter in the step 3, according to cell barycenter analytical expression, find the solution every one dimension of barycenter:

$y_{\mathrm{ij}}=\frac{{\∫}_{R_i}{x}_{j}p\left(x\right)\mathrm{dx}}{{\∫}_{R_i}p\left(x\right)\mathrm{dx}}=\frac{1}{\mathrm{\Δ}{P}_i}{\∫}_{R_i}{x}_{j}p\left(x\right)\mathrm{dx},i=\mathrm{1,2},...N;j=\mathrm{1,2},...k.$

The invention has the beneficial effects as follows that for the statistical property of spaceborne raw data, design has obtained having the Codebook of Vector Quantization of universality, proved that simultaneously Codebook of Vector Quantization can carry out the off-line design, the spaceborne practical theoretical direction that provides of vector quantization is provided.

Description of drawings

Fig. 1-1 is conventional vector quantization encoding and decoding synoptic diagram;

Fig. 1-2 is vector quantization coding of the present invention and decoding synoptic diagram.

Fig. 2 is the theoretical Derivation process flow diagram of the pervasive code book of the present invention.

Fig. 3 is that the pervasive code book cell of the present invention is divided synoptic diagram.

Embodiment

The technical solution adopted in the present invention is: when code book generates, do not re-use the iterative algorithm based on training data, but from the joint probability density function of input vector, for the joint probability density function of input vector, obtain having the code book of universality by analytic method.

Concrete operations comprise: when generating code book, do not re-use training dataset, but use the joint probability density function of input data; When dividing cell, no longer adopt the clustering method for all training datas, but the nearest criterion of calculating according to the vector code book, the field of definition of data is divided into N cell (N is in the code book, the number of code vector); When finding the solution the cell barycenter, use the barycenter solution formula among the present invention; Then theoretical reasoning flow according to the present invention calculates, and can obtain having the code book of universality.

The present invention is further described below in conjunction with drawings and Examples.

Fig. 1-1 is conventional vector quantization encoding and decoding synoptic diagram, and Fig. 1-2 is vector quantization coding of the present invention and decoding synoptic diagram.Wherein, the dotted line frame is the part that the present invention is different from the conventional process mode, and the present invention carries out the design of universality code book according to the joint probability density function of input data.

Fig. 2 has provided the process flow diagram that pervasive code book is found the solution, and estimates to characterize input vector x and quantizes distortion between the output Q (x) with square error, that is:

$D=E\left[d(x,Q\left(x\right))\right]=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}E\left[d(x,y_i)\right]=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\∫}_{R_i}{|x-y_i|}^{2}p\left(x\right)\mathrm{dx}---\left(1\right)$

X=[x wherein ₁, x ₂... x _k] ^T, y _i=[y _I1, y _I2... y _Ik] ^T, R _iBe i division of correspondence, p (x) is the k dimension priori joint probability density function of input vector x, and N is code book length.Code book to be generated $Y={[y_1^T,y_2^T,...y_N^T]}^T.$

The design criteria of quantizer is exactly so that distortion in (1) is minimum, and quantizer Q (x) is fully only definite by given code book Y (one group of quantization vector) and the optimum division (quantization areas) relevant with Y.Therefore the design of quantizer is exactly to determine that { r (R), Y} is so that formula (1) obtains minimum value to a pair set, wherein

$r\left(R\right)=\{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="H2010100344078E00011.png,H2010100344078E00012.png"\; state="\{\{state\}\}">R</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="H2010100344078E00031.png"\; state="\{\{state\}\}">R</figure-callout>}}_2,...R_N;R=\underset{i=1}{\overset{N}{\&cup;}}{R}_i\}$

When r (R) determines, minimum for making quantizing distortion D, need to satisfy:

${\&dtri;}_{Y}D=0_{N\&times;k}---\left(2\right)$

In the formula

Be the gradient computing, Expression distortion function D is the matrix of N * k with respect to the gradient of real matrix Y, is called for short gradient matrix, and formula (2) can be rewritten as:

Formula (1) (3) formula of bringing into is got:

$\frac{\&PartialD;D}{\&PartialD;y_{\mathrm{ij}}}=-2{\&Integral;}_{R_i}(x_j-y_{\mathrm{ij}})p\left(x\right)\mathrm{dx}=0,i=\mathrm{1,2},...N;j=\mathrm{1,2},...k---\left(4\right)$

That is:

$y_{\mathrm{ij}}=\frac{{\&Integral;}_{R_i}{x}_{j}p\left(x\right)\mathrm{dx}}{{\&Integral;}_{R_i}p\left(x\right)\mathrm{dx}}=\frac{1}{\mathrm{\&Delta;}{P}_i}{\&Integral;}_{R_i}{x}_{j}p\left(x\right)\mathrm{dx},i=\mathrm{1,2},...N;j=\mathrm{1,2},...k---\left(5\right)$

Formula (5) is called the barycenter equation of Codebook of Vector Quantization design.

For given code book Y, minimum for making quantizing distortion D, cell is divided need satisfy the arest neighbors condition, that is:

R _i={ x:||x-y _i|| ²≤ || x-y _j|| ², j ≠ i} and

Formula (6) is equivalent to:

R _i＝{x：y _ij·x+b _ij≥0，j≠i}(7)

Y in the formula _Ij=y _i-y _j,

The operation of " " expression inner product.

Can be got by formula (7), for by vector parameters y _IjAnd scalar parameter b _Ij" partly " the space H that describes _Ij:

H _ij＝{x：y _ij·x+b _ij≥0，j≠i}(8)

Make L _Ij={ x:y _IjX+b _Ij=0} is constraint H _IjLineoid, can find out that any one cell all can be described by the common factor of limited semispace, and associated constraint lineoid has consisted of the surface (or border) of cell.Therefore, the cell R of vector quantizer _iCan be expressed as:

$R_i=\underset{i=1}{\overset{M}{\&cap;}}{H}_{\mathrm{ij}}---\left(9\right)$

M equals cell R in the formula _iConstraint lineoid quantity, surround R _iThe border be L _IjThus, can obtain the processing procedure that cell is divided, accompanying drawing 3 is in the situation of two dimension for vector, the example that cell is divided.

Fig. 3 divides flow process, given initial codebook with the cell that two-dimentional cell is divided into the whole code book of example explanation:

Y ₀=[0.3,0.5; 1.7,2; 0.1 ,-0.1;-1.5.1.7;-1.6 ,-2; 0.1 ,-2.4; 2.1 ,-0.9;-0.3,0.4] wherein: y ₁=[0.3,0.5], y ₂=[1.7,2], y ₃=[0.1 ,-0.1], y ₄=[1.5,1.7], y ₅=[1.6,1.2], y ₆=[0.1 ,-2.4], y ₇=[2.1 ,-0.9], y ₈=[0.3,0.4], 8 coordinates in the difference corresponding diagram 3, the joint probability density function of input data is:

$f(x_1,x_2)=\frac{1}{2\mathrm{\&pi;}}\exp \{-\frac{1}{2}(x_1^2+x_2^2)\}$

In computing, in order to reduce operand, when calculating, constant term 1/2 π in the joint probability density function is ignored, do not affect code book result of calculation.

At first carry out cell according to formula (7) and divide, with y ₁The cell R at place ₁Be example, according to formula (9) as can be known, with all " Half Space H _1j, j=2,3,4,5,6,7,8 " get it after determining and occur simultaneously and divide for final cell.

Step 1: determine H ₁₂y ₁₂=y ₁-y ₂=[1.4 ,-1.5],

H ₁₂={ x:y ₁₂X+b ₁₂〉=0};

Step 2: the disposal route of repeating step 1 is tried to achieve Half Space H ₁₃, H ₁₄, H ₁₅, H ₁₆, H ₁₇, H ₁₈, the gained semispace is got common factor obtains cell division R ₁, all cells divisions of vector quantization are protruding, and each summit of recording at last convex cell is used for representing R ₁, R in this example ₁Corresponding summit is { A1 (0.2067,1.6900); B 1 (0.0753,2.1130); C1 (1.7693,0.5320); D1 (1.2412 ,-0.14711); E1 (0.0324,0.2559) }.

Step 3: repeating step 1, step 2 are tried to achieve cell and are divided R ₂, R ₃..., R ₈

Cell R ₂Corresponding summit is respectively { A2 (0.0078,3.0000); B2 (3.0000,3.0000); C2 (3.0000,0.7017); D2 (1.7693,0.5320); E2 (0.0753,2.1130) }.

Cell R ₃Corresponding summit is respectively { A3 (1.1512 ,-0.6910); B3 (0.0324,0.2559); C3 (1.2412 ,-0.1471); D3 (0.8000 ,-1.2500); E3 (0.5265 ,-1.2500) }.

Cell R ₄Corresponding summit is respectively { A4 (3.0000 ,-0.1108); B4 (3.0000,3.0000); C4 (0.0078,3.0000); D4 (0.0753,2.1130); E4 (0.2067,1.6900); F4 (2.1815 ,-0.1329) }.

Cell R ₅Corresponding summit is respectively { A5 (3.0000 ,-3.0000); B5 (3.0000 ,-0.1108); C5 (2.1815 ,-0.1329); D5 (1.1512 ,-0.6910); E5 (0.5265 ,-1.2500); F5 (0.9382 ,-3.0000) }.

Cell R ₆Corresponding summit is respectively { A6 (0.9382 ,-3.0000); B6 (0.5265 ,-1.2500); C6 (0.8000 ,-1.2500); D6 (2.1125 ,-3.0000) }.

Cell R ₇Corresponding summit is respectively { A7 (0.8000 ,-1.2500); B7 (1.2412 ,-0.1471); C7 (1.7693,0.5320); D7 (3.0000,0.7017); E7 (3.0000 ,-3.0000); F7 (2.1125-3.0000) }.

Cell R ₈Corresponding summit is respectively { A8 (2.1815 ,-0.1329); B8 (0.2067,1.6900); C8 (0.0324,0.2559); D8 (1.1512 ,-0.6910) }.

Find the solution the barycenter operation: the barycenter of asking for each cell that obtains in the cell division according to formula (5); Trying to achieve barycenter is C ₁=[0.5938,0.7081], C ₂=[1.3077,1.5542], C ₃=[0.1077 ,-0.5086], C ₄=[1.2883,1.3121], C ₅=[1.3993 ,-1.1937], C ₆=[0.1908 ,-1.7577], C ₇=[1.6123 ,-0.6539], C ₈=[0.7351,0.3482].

Find the solution the distortion operation: use formula (1) calculated distortion: with initial codebook Y ₀Bring formula (1) into and try to achieve D ₀=4.3431, will find the solution barycenter and bring formula (1) into and try to achieve D ₁=2.8617.

Explain the finding the solution and the calculating of quantizing distortion of division, cell barycenter of cell by example, with above operation, found the solution process flow diagram according to pervasive code book shown in Figure 2 and carry out loop iteration, can try to achieve the code book with universality.

More than used embodiment, be not that the present invention is done any pro forma restriction, the related amendments that every foundation technical spirit of the present invention is carried out all still belongs in the present invention program's the scope.

Claims (3)

1. satellite-borne SAR raw data Codebook of Vector Quantization method for designing, the distortion function on the hyperspace is found the solution code book as cost function according to the joint probability density function of input data; Its key step is as follows:

Step 1: the joint probability density function of determining the input data according to the vector dimension;

Step 2: in the field of definition of data, carry out cell according to the arest neighbors criterion and divide;

Step 3: according to the barycenter solution formula

$y_{\mathrm{ij}}=\frac{{\&Integral;}_{R_i}{x}_{j}p\left(x\right)\mathrm{dx}}{{\&Integral;}_{R_i}p\left(x\right)\mathrm{dx}}i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;N;j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;k$

Find the solution the barycenter of corresponding cell, cell is divided to find the solution with barycenter carry out loop iteration and find the solution the quantification code book;

In the barycenter solution formula; x _jWherein one dimension for input vector x; R _iI division for correspondence; P (x) is the k dimension priori joint probability density function of input vector x.

2. Codebook of Vector Quantization method for designing according to claim 1, wherein, the cell in the step 2 is divided and is comprised:

Step 11: selected desired any one solution cell, find the solution all semispaces relevant with cell;

Step 12: the semispace of step 11 gained is got common factor obtain the cell division;

Step 13: repeating step 11 and step 12 obtain all cells and divide.

3. Codebook of Vector Quantization method for designing according to claim 2, wherein, described semispace can be described as by vector parameters and the scalar parameter of correspondence:

H _ij＝{x∶y _ij·x+b _ij≥0，j≠i}

In the formula: x is input k n dimensional vector n, y _IjBe vector parameters, b _IjBe scalar parameter.

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