ZERO-SEARCH, ZERO-MEMORY VECTOR QUANTIZATION

• US 20090208120A1
• Filed: 04/23/2009
• Published: 08/20/2009
• Est. Priority Date: 06/26/2003
• Status: Active Grant

• Current Assignee: Promptu Systems Corporation
• Original Assignee: Agiletv Corporation (Promptu Systems Corporation)
• Inventors: PRINTZ, Harry
• Granted Patent: US 8,185,390 B2
• Time in Patent Office: Days
• US Class Current: 382/232
• CPC Class Codes: G06Q 30/02 Marketing; Price estimation or determination; Fundraising
• CPC Class Codes: G10L 15/26 Speech to text systems G10L15/08 takes precedence
• CPC Class Codes: G10L 17/00 Speaker identification or verification techniques
• CPC Class Codes: G10L 19/00 Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis in musical instruments G10H
• CPC Class Codes: G10L 25/24 the extracted parameters being the cepstrum
• CPC Class Codes: H03M 7/3082 Vector coding for television signals, see H04N19/94
• CPC Class Codes: H04N 19/94 Vector quantisation

Abstract

The invention comprises a method for lossy data compression, akin to vector quantization, in which there is no explicit codebook and no search, i.e. the codebook memory and associated search computation are eliminated. Some memory and computation are still required, but these are dramatically reduced, compared to systems that do not exploit this method. For this reason, both the memory and computation requirements of the method are exponentially smaller than comparable methods that do not exploit the invention. Because there is no explicit codebook to be stored or searched, no such codebook need be generated either. This makes the method well suited to adaptive coding schemes, where the compression system adapts to the statistics of the data presented for processing: both the complexity of the algorithm executed for adaptation, and the amount of data transmitted to synchronize the sender and receiver, are exponentially smaller than comparable existing methods.

Claims

1. A computer-implemented method for data compression comprising the steps of:

establishing an implicit codebook comprising a set of code points for representing information elements, each information element constituting a vector, said set of code points implicitly represented by a hypercube radius vector;

inspecting the signs of each information element to determine in which orthant said each information element lies to determine the implicit code point to represent said each information element;

determining an index of the implicit code point associated with said each information element; and

transmitting or storing said each resulting index as the compressed representation of said each information element.

2. The method of claim 1, for decompressing an index obtained via compression with respect to the given hypercube radius vector, further comprising the steps of:

inspecting said index to determine in which orthant the corresponding implicit code point lies; and

returning the corresponding implicit code point to produce at least a partial facsimile of said information element.

3. The method of claim 1, further comprising the step of:

finding an optimal D-hypercube codebook, with respect to typical data.

4. The method of claim 1, wherein said data compression comprises

compressing digitized human speech;

and

further comprising the steps of;

transmitting or storing said compressed, digitized human speech;

receiving or retrieving said compressed, digitized human speech;

decompressing said compressed, digitized human speech; and

processing said digitized human speech with an automatic speech recognition system.

5. The method of claim 1, further comprising the step of:

applying an invertible transform to optionally translated information elements to be compressed, said transform determined so that an aggregate of typical data to be compressed will approximate a uniform distribution within a D-dimensional sphere, centered at the origin.

6. The method of claim 5, further comprising the step of:

finding an optimal D-hypercube codebook, with respect to typical transformed data.

7. The method of claim 5, said invertible transform comprising a symmetrizing transform.

8. The method of claim 7, said symmetrizing transform comprising a whitening transform.

9. The method of claim 8, further comprising the steps of:

projecting all data into a D−

1-dimensional space;

processing a resulting data set; and

wherein only D−

1 bits are transmitted for each vector processed.

10. The method of claim 8, further comprising the step of:

representing the whitening transform in a memory efficient manner as the product of a diagonal matrix, said matrix represented by only its D non-zero elements, and an orthogonal matrix;

the inverse of this transform therefore obtainable as the product, in the opposite order, of a diagonal matrix of D reciprocals of the original D non-zero elements, and the transpose of the original orthogonal matrix.

11. The method of claim 8, further comprising the steps of:

determining an optimal hypercube radius vector α

=α

₁, α

₂, . . . , α

_D that defines said hypercube codebook and yields minimal mean square coding distortion among all D-hypercube codebooks for typical data to be compressed.

12. The method of claim 11, further comprising the step of:

computing an optimal hypercube radius vector α

=α

₁, α

₂, . . . , α

_D from an example data collection E comprised of E=|E| typical data vectors v, by computing for each dimension i=1, . . . , D the quantity

13. The method of claim 6, further comprising the step of:

determining an optimal hypercube radius vector α

=α

₁, α

₂, . . . , α

_D, this vector defining said hypercube codebook, that yields minimal mean square coding distortion among all D-hypercube codebooks, with respect to typical transformed data.

14. The method of claim 13, further comprising the step of:

computing an optimal hypercube radius vector α

=α

₁, α

₂, . . . , α

_D from an example data collection E comprised of E=|E| typical data vectors v, to which has been applied the invertible transform of claim 5, to yield a collection U comprised of U=|U|=|E|=E typical data vectors u, by computing for each dimension i=1, . . . , D the quantity

15. The method of claim 1, for compressing a vector v=v₁, v₂, . . . , v_D, further comprising the steps of:

obtaining a vector v=v₁, v₂, . . . , v_D for compression;

forming a D-bit binary number i as a bitwise concatenation i=m(v_D)m(v_D-1) . . . m(v₂)m(v₁);

where the j th bit of i is 0 if v_j is zero or positive, and 1 if it is negative; and

transmitting or storing i.

16. The method of claim 7, for compressing a vector v, further comprising the steps of:

obtaining a vector v for compression;

computing u=Tv, where u is denoted u₁, u₂, . . . , u_D;

where T is the symmetrizing transform;

forming a D-bit binary number i as a bitwise concatenation i=m(u_D)m(u_D-1) . . . m(u₂)m(u₁);

where the j th bit of i is 0 if u_j is zero or positive, and 1 if it is negative; and

transmitting or storing i.

17. The method of claim 2, for decompressing an index i, obtained via compression with respect to a hypercube radius vector α

=α

₁, α

₂, . . . , α

_D, said method further comprises the steps of;

obtaining an index i for decompression;

setting

18. The method of claim 16, for decompressing an index i, obtained via compression with respect to a hypercube radius vector α

=α

₁, α

₂, . . . , α

_D, said method further comprises the steps of;

obtaining an index i for decompression;

setting

19. The compression method of claim 7, further comprising the step of:

incorporating a rotation in the symmetrizing transform to lower distortion.

20. The method of claim 19, further comprising the step of:

finding an optimal hypercube radius vector with respect to rotated symmetrized typical data.

21. The compression method of claim 1, further comprising the steps of:

increasing a number of implicit code points by increasing the number of hypercubes, wherein compression occurs with respect to a family of hypercube codebooks.

22. The compression method of claim 21, using a family of hypercubes A, each hypercube determined by its associated hypercube radius vector α

=α

₁, α

₂, . . . , α

_D, and using a symmetrizing transform T, said symmetrizing transformation comprising one of;

the identity transform;

a whitening transform;

or

some other symmetrizing transform;

further comprising the steps of;

given vector v to compress finding u=Tv;

finding the orthant of u, encoded as i=m(u_D)m(u_D-1) . . . m(u₂)m(u₁);

finding, via explicit search within the orthant, a hypercube index k of the closest hypercube α

^k ∈

A; and

transmitting or storing a result of said search, in the form of the said hypercube index k so determined, along with the identity i of the orthant.

23. The method of claim 22, using a multiplicity of hypercubes A;

varying with respect to one another in hypercube radius vector, in orientation, or. both;

said orientations being expressed by a rotation R^k associated to each hypercube radius vector α

^k, said rotation possibly being the identity; and

further comprising the steps of;

given vector v to compress

finding each u^k=R^kTv,

finding the orthant index i of u^k

finding, via explicit search among the multiplicity of hypercubes, the hypercube index k yielding the minimal distortion

transmitting or storing a result of said search, in the form of the said hypercube index k so determined, along with the identity i of the orthant.

24. The method of claim 22, further comprising the steps of:

decompressing the pair comprised of hypercube index k and orthant index i;

by using hypercube index k to select an appropriate hypercube radius vector α

^k; and

inspecting the coded orthant i to yield an appropriate vertex of the α

^k hypercube;

wherein said vertex is taken as ũ

, from which {tilde over (v)}=T<sup>−

1</sup>ũ

is computed, and the value {tilde over (v)} returned as the result.

25. The method of claim 23, further comprising the steps of:

decompressing the pair comprised of hypercube index k and orthant index i;

by using hypercube index k to select an appropriate hypercube radius vector α

^k; and

inspecting the coded orthant i to yield an appropriate vertex of the α

^k hypercube;

wherein said vertex is taken as ũ

, from which {tilde over (v)}=T<sup>−

1</sup>(R^k)<sup>−

1</sup>ũ

is computed, and the value {tilde over (v)} returned as the result.

26. A computer-implemented method for data compression and subsequent decompression comprising the steps of:

establishing an implicit codebook comprising a set of code points for representing information elements, each information element constituting a vector, said set of code points implicitly represented by a hypercube radius vector;

inspecting the signs of each information element to determine in which orthant said each information element lies to determine the implicit code point to represent said each information element;

determining an index of the implicit code point associated with said each information element;

transmitting or storing each resulting index as the compressed representation of each said information element; and

applying a decompression function to said compressed information elements to produce at least a partial facsimile of said information elements.

27. A computer-implemented method for finding a family A of K hypercube codebooks, comprising the steps of:

beginning with a fixed number K of desired hypercubes, and an example dataset U;

mapping each element u ∈

U, where u=u₁, . . . , u_D, to the positive orthant ^D, via the map p;

u₁, . . . , u_D→

u₁ |, |u₂ |, . . . , u_D|, yielding the set U⁺={p(u)|u ∈

U};

selecting an initial set of K radius vectors A⁽⁰⁾={ α

₀⁽⁰⁾, . . . , α

_K-1⁽⁰⁾};

setting an iteration count i to 0;

establishing a termination condition τ

, which depends upon one or more of;

the number of iterations executed;

the closeness of match between a current radius vector collection A⁽ⁱ⁾ and U⁺; and

the improvement of a statistic over a previous iteration, wherein said dependence is expressed as τ

(i,A⁽ⁱ⁾, U⁺);

testing τ

(i,A⁽ⁱ⁾, U⁺); and

if the termination condition is satisfied, returning A⁽ⁱ⁾ as the desired radius vector collection; and

stopping;

else, if the termination condition is not satisfied, computing a new radius vector collection A⁽ⁱ⁺¹⁾ as follows;

partitioning U⁺ into K sets S₀ . . . S_K-1, where

28. A computer-implemented method for data compression, comprising the steps of:

computing a compression function for information elements by;

first applying a symmetrizing transform;

inspecting the signs of said transformed information elements to determine in which quadrant of an implicit codebook a corresponding implicit code point lies;

determining an index of an associated implicit code point for each said information element; and

transmitting or storing each said resulting index as the compressed representation of each said information element.

29. The method of claim 28, further comprising the steps of:

rotating the data to be compressed, to lower distortion, and then compressing the rotated data.

30. The method of claim 28, further comprising the step of incorporating a rotation in the symmetrizing transform, to lower distortion, and then compressing.

31. The method of claim 28, further comprising the step of:

establishing an implicit codebook comprising an implicitly defined set of vectors, hereafter called code points, which are symmetrically placed with respect to the origin;

wherein said code points are used for representing information elements.

32. The method of claim 31, further comprising the step of:

increasing a number of code points by increasing the number of hypercubes, wherein compression occurs with respect to a family of hypercube codebooks, and the preferred hypercube is found by explicit search, once the orthant of the vector to be compressed has been determined

33. The method of claim 31, further comprising the step of:

increasing a number of code points by increasing the number of hypercubes, wherein compression occurs with respect to a family A of hypercube codebooks, the hypercubes varying with respect to one another in hypercube radius vector, in orientation, or both;

the selected hypercube and orthant index being found by explicit search among a set consisting of the preferred vertex of each hypercube, the preferred vertex of each hypercube being the one that lies in the same orthant of the vector to be compressed, for each hypercube.