JP2003258645A - Method and device for hadamard transformation processing - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method and device for Hadamard transformation processing for carrying out integer-type reversible Hadamard transformation, having simple construction and small operation delays. <P>SOLUTION: A transformation process, wherein input signals [X0, X1, X2, X3] are subjected to transformation processing according to a 4-point Hadamard transformation matrix, is carried out (S301), and the least significant data of a first transformed data among the transformed data obtained in the transformation process are rounded up (S302), and respective least significant data of remaining odd number of data are rounded off (S303) to obtain an integer. When these transformed data are restored, inverse Hadamard transformation is carried out, and then the rounding up and rounding off the processing in S302, S303 are carried out, to restore the original data [X0, X1, X2, X3]. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a Hadamard transform processing method and apparatus capable of performing reversible transform.

[0002]

2. Description of the Related Art An image, especially a multi-valued image contains a great deal of information, and when storing or transmitting the image, a huge amount of data becomes a problem. Therefore, when storing or transmitting an image, the redundancy of the multi-valued image is removed, or the deterioration of the image quality is difficult to visually recognize, and the content of the image is changed to encode it. High efficiency coding is used to reduce the amount of data. For example, ISO and IT are used as international standard encoding methods for still images.
According to JPEG recommended by UT, image data is discrete cosine transformed (D) for each block (8 pixels × 8 pixels).
After CT) to convert to DCT coefficients, each DCT coefficient is quantized, and the quantized value is entropy coded to compress the image data.
In addition to JPEG, compression technology using this DCT
H261, MPEG1 / 2/4, etc.

Hadamard transform is a process related to this DCT transform or a process for transforming image data. In this Hadamard transformation, each element of the transformation matrix is "1".
Or, it is an orthogonal transform consisting only of "-1", which is the simplest orthogonal transform that can be realized only by addition and subtraction.

Among the Hadamard transforms, the transformation matrix H2 of the two-point Hadamard transform is defined as follows.

[0005]

[Equation 1]

(1) A general N (= 2n) -point Hadamard transform matrix HN is (N
/ 2) It can be recursively defined by the Kronecker product between the Hadamard transform matrix HN / 2 and the Hadamard transform matrix H2.

[0007]

[Equation 2]

(2) Obtaining the 4-point Hadamard transformation matrix from the above definition,

[0009]

[Equation 3] (3) This 4-point Hadamard transform matrix is called a natural type, and the basis vectors are not arranged in the order of sequence. Therefore, if the replacement of the basis vector is repeated and the basis vector of the second row is moved to the fourth row, the order of the basis vector becomes the conversion matrix WH4 in the sequence order.

[0010]

[Equation 4]

(4) This transformation matrix WH4 is called a Walsh type or Walsh Hadamard transformation matrix. It is known that the Hadamard transform is a reversible orthogonal transform. Both the natural type and the Walsh type are capable of reversible transformation, and the transformation matrix is a symmetric matrix.

Another symmetric matrix obtained by replacing the basis vectors of the natural Hadamard transform matrix H4 exists in addition to the Walsh type. The following matrix HH4 is so.

[0013]

[Equation 5]

(5) This conversion matrix HH4 has an important meaning later in the detailed description of the present invention.

As mentioned above, it is generally said that the Hadamard transform is a reversible transform.
This is to hold the fractional part of the integer data generated when the Hadamard transform is performed without rounding.

If the decimal part is simply rounded, the reversibility is lost. For example, if four data of 123, 78, 84, 56 are Hadamard transformed, the following is obtained.

170.5 (= (123 + 78 + 84 + 56) / 2), 36.5 (= (123-78 + 84-56) / 2), 30. 5, (= (123 + 78-84-56) / 2) 8.5 (= (123-78-84 + 56) / 2) If each of these is simply rounded to an integer, 171, 37, 31 and 9 and the inverse transformation (the matrix used in the inverse transformation is the transposed matrix of the transformation matrix, which is the same as the transformation matrix), the results are 124, 78, 84, and 56. Here, “123” of the head data has become “124” due to the Hadamard transform and its inverse transform. In this way, reversibility cannot be guaranteed by Hadamard transform that outputs integerized data. Hereinafter, the Hadamard transform that outputs integerized data will be referred to as an integer Hadamard transform, and the integer Hadamard transform capable of reversible transform will be referred to as an integer reversible Hadamard transform.

The present invention relates to a calculation and rounding method for realizing an integer type reversible Hadamard transform.

Conventionally, the integer type reversible Hadamard transform has been realized as follows. The 4-point Hadamard transform matrix H4 is decomposed into a product of triangular matrices whose diagonal elements are "1". A row exchange operation Q is added to the original transformation matrix. From the above, QH4 is decomposed into the following matrix product form.

[0020]

[Equation 6]

(6) This conversion is expressed by a signal flow (as shown in FIG. 1). The data after the decimal point generated by the multiplication process in this signal flow is rounded to an integer.

It is realized by the above items. Some supplementary explanation is added below.

The signal flow shown in FIG. 1 is a ladder network (Ladd) which is often used to realize a reversible conversion process.
er Network) configuration.

In this Ladder Network, integer type data is converted by introducing rounding processing (200 and 201 in FIG. 2) for integerization on the output side of the multipliers 100 and 101 which generate data below the decimal point. Reversible output conversion processing is used as a general method (in the field of reversible conversion processing).

If the rounding process of the corresponding multiplication output is the same between the conversion process and the inverse conversion process, the rounding process 2
The contents of 00 and 201 may be anything.

FIG. 2 shows a signal flow reversible by introducing a rounding process into the signal flow of FIG. 1 (allowing reversible conversion). This is the conventional arithmetic method for realizing the integer type reversible Hadamard transform.

The Hadamard transform defined by the above equations (3), (4) and (5) can be realized by regular addition and subtraction processing, and SIMD (Single Instructi) provided in recent CPUs is provided.
Although an on stream multiple data stream) type instruction can be efficiently processed in parallel, the conventional reversible conversion calculation method described above is complicated to be processed by a SIMD type instruction and few calculations can be performed in parallel. In other words, it can be said that the conventional integer-type reversible Hadamard transform is not suitable for high-speed processing on a widely used personal computer.

[0028]

As described above, the conventional integer type reversible Hadamard transform is not suitable for processing by SIMD type instructions and cannot be processed at high speed on a widely used personal computer. In addition, when it is realized by hardware, there is a problem that since the number of stages of calculation increases, the data path becomes long and the delay time due to the calculation increases.

The present invention has been made in view of the above-mentioned conventional example. Of the converted data obtained by the Hadamard conversion process, the least significant bit of the odd number of data is rounded up, and the least significant bit of the remaining odd number of data is rounded up. An object of the present invention is to provide a Hadamard transform processing method and apparatus that realize an integer-type reversible Hadamard transform process by truncating data.

Another object of the present invention is to round up the least significant bit data of an odd number of conversion outputs and round down the remaining least significant bit data of an odd number of conversion outputs to perform rounding and Hadamard conversion. It is an object of the present invention to provide a Hadamard transform processing method and apparatus that realize an integer-type reversible Hadamard transform process by performing them simultaneously.

Another object of the present invention is to provide a Hadamard transform processing method and apparatus capable of performing an integer type reversible Hadamard transform with a small configuration and a small calculation delay.

[0032]

In order to achieve the above object, the Hadamard transform processing apparatus of the present invention has the following configuration. That is, the Hadamard transforming means and a rounding means for rounding up the odd number least significant bit data of the transformed outputs of the Hadamard transforming means and rounding down the remaining least significant bit data of the odd number of transformed outputs. And are included.

In order to achieve the above object, the Hadamard transform processing apparatus of the present invention has the following configuration. That is,
A conversion processing unit that performs a Hadamard conversion process using a 4-point Hadamard conversion matrix, rounds down the least significant bit data of an odd number of conversion outputs among the outputs of the conversion results by the conversion processing unit, and outputs the remaining odd number of conversion outputs. Rounding processing means for rounding down the least significant bit data, inverse conversion processing means for performing an inverse Hadamard conversion processing on the converted output rounded by the rounding processing means, and the same rounding processing as the rounding processing in the rounding processing means. Restoration means for restoring the original data by performing the conversion result of the conversion processing means,
It is characterized by having.

In order to achieve the above object, the Hadamard transform processing method of the present invention comprises the following steps. That is,
A conversion step of performing a conversion process by an Hadamard conversion matrix on the input signal, and among the conversion data converted in the conversion step, each least significant bit data of the odd number of data is rounded up, and the remaining odd number of data Rounding processing step of rounding down each least significant bit data of (1) to make it an integer.

In order to achieve the above object, the Hadamard transform processing method of the present invention comprises the following steps. That is,
A conversion processing step of performing a Hadamard conversion processing by a 4-point Hadamard conversion matrix, and rounding down the least significant bit data of an odd number of conversion outputs among the outputs of the conversion results by the conversion processing step, and the remaining odd number of conversion outputs Rounding process for rounding down the least significant bit data of R, inverse transform processing process for performing an inverse Hadamard transform process on the transformed output rounded in the rounding process, and the same rounding process as the rounding process in the rounding process. A restoration step of restoring the original data by performing the conversion result of the conversion processing step,
It is characterized by having.

[0036]

Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

<Embodiment 1> FIG. 3 is a flowchart showing the flow of processing according to Embodiment 1 of the present invention.

In the figure, in step S301, a four-point Hadamard transformation matrix H4 is used in fixed-point arithmetic.
The conversion process is performed using (Equation (3)). here,
Input data is Xi = [X0, X1, X2, X3], and Di =
The calculation indicated by H4 · Xi is executed. In step S302, of the conversion results obtained in step S301, only the first data (D0) is rounded up. Then step S
In 303, the remaining three conversion results (D1, D2, D3)
Are truncated.

In step S301, the integer type input data is added / subtracted and assigned to a fixed point variable to obtain 4
Performs fixed-point arithmetic for point Hadamard transform. Here, the fractional part is only the least significant 1 bit (hereinafter referred to as LSB), and the weight of this LSB is "0.5". Step S
In the rounding-up process of 302, "1" is added to the first data (D0) and then the data is shifted to the right by 1 bit. This added "1" is interpreted as "0.5" which is the same as the weight of this LSB. Then, the 1-bit right shift cuts off the decimal part of the addition result and leaves only the integer part and converts it to integer type data.

In the truncation process of step S303, nothing is added and the bit is shifted right by 1 bit. As a result, the fractional part of the conversion result of step S301 is truncated, leaving only the integer part, and converted into integer type data.

The round-down processing and round-up processing according to this embodiment are performed by mathematical floor function operation and ceilin.
Means g-function operation. The former is a conversion process to the maximum integer value that does not exceed the input data, and the latter is a conversion process to the input data or a minimum integer value larger than the input data.

From another aspect, the round-down process may decrease the value but not increase it, and the round-up process may increase the value but not decrease the value. For example, the result of rounding down "-7.5" is "-8", which is small.
The result of rounding up is "-7", which is larger than the original value.

In the present embodiment, the inverse transformation has the same processing flow as that shown in FIG. When the integer type reversible Hadamard transform process of the present embodiment is applied to the above four data 123, 78, 84, 56, the transformed data after the rounding process is 171 (= (123 + 7
8 + 84 + 56) / 2 rounded up to one decimal place), 36 (=
(123-78 + 84-56) / 2 rounded down to the first decimal place),
30 (= (123 + 78-84-56) / 2 rounded down to the first decimal place), 8 (= (123-78-84 + 56) / 2 rounded down to the first decimal place). Inverse conversion is performed on these converted data in the same process flow as in FIG.

If only the Hadamard inverse transformation is applied to 171, 36, 30, and 8, 122.5 (=
(171 + 36 + 30 + 8) / 2), 78.5 (= (171-36 + 30-8) / 2),
84.5 (= (171 + 36-30-8) / 2), 56.5 (= (171-36-30
+8) / 2) is obtained. Here, by rounding up the bottom of the first data and discarding the bottom of the remaining data, 123, 78, 84, 56 are obtained, and it can be seen that the original data is restored. The reason why such a reversible conversion can be realized will be described below.

It is well known that the LSB value of the four data subjected to the Hadamard transform processing by the fixed point arithmetic operation in step S301 of FIG. 3 is the same for all four values.
The value of this LSB is uniquely determined by the number of odd data in the four data before conversion. That is, when there is an even number of odd data, the value of this LSB becomes "0", and when there is an odd number of odd data, the value of this LSB becomes "1".

When the value of this LSB is "0", the fractional part becomes zero, so that the output of the conversion processing in step S301 has already become integer data. Therefore, no error occurs in the rounding processing in steps S302 and S303 thereafter. In this case, even in the inverse conversion process, only the conversion process of step S301 results in integer data, and the original data is restored regardless of the rounding process.

On the other hand, in the conversion process of step S301, when the value of LSB is "1" (in the case of 0.5), it is rounded to integer data to obtain "+0.5" or "-".
An error of 0.5 "is superimposed on each data. When the above four data are processed by the flow of FIG. 3, an error of “+0.5” is superimposed on the first conversion data Y0, and “−0.5” is added to the other three data Y1 to Y3. Error is superimposed.

When the conversion data on which such an error is superimposed is subjected to the inverse conversion processing in the flow of FIG. 3, the conversion data D0 before the rounding processing is "-0.5", and D1 to D3 are "+0.5".
Error will be propagated. In order to cancel this propagation error, only D0 is rounded up and the other three data D1 to D
It can be seen that 3 may be rounded down. Step S
By performing such processing in 302 and step S303, the original data is restored.

Therefore, not only the integer type reversible Hadamard transform process is possible in the process flow of FIG. 3, but also the inverse transform process is possible.

The conversion process and the inverse conversion process can be realized by the same process only when the rounding process of the first conversion data Y0 is different from the other three rounding processes. There is another type of processing in which the rounding processing of the converted data Y0 is different from the other three. That is, only Y0 is rounded down and the other three are rounded up. Also in this case, the conversion process and the inverse conversion process can be realized by the same process.

The process of FIG. 3 can be modified as shown in FIG. 4, and the conversion and the rounding process can be performed at the same time.

<Second Embodiment> In a second embodiment of the present invention, a case where the contents of the rounding process are different between the conversion process and the inverse conversion process will be described. In the second embodiment, only the second converted data (D1) is rounded up, and the other three converted data (D0, D2, D3) are rounded down. The conversion processing flow of the second embodiment is shown in FIG. 5, and its inverse conversion processing flow is shown in FIG.

Also in the second embodiment, reversibility becomes a problem when the LSB of four operation results is "1" in the fixed-point operation in step S301, as in the first embodiment. When the LSB is "0", no error occurs due to the rounding process, so reversible conversion is possible.

Therefore, only the case where the LSB is "1" will be described below.

When processed by the flow shown in FIG. 5, an error of "+0.5" is superimposed only on the second conversion data Y1 and "-0. Y. Y2, Y3" is added to the other conversion data (Y0, Y2, Y3).
The error of "5" is superimposed.

When this is subjected to the inverse conversion processing according to the flow shown in FIG. 6, first, in the conversion processing of the fixed point arithmetic in step S601, only the third conversion data E2 is "+0.5".
Error propagates, and the other three conversion data (E0, E1,
An error of "-0.5" propagates to E3).

Therefore, in step S602, the lowest order of the converted data E0, E1, E3 is rounded up, and in step S603, the lowest order of the third converted data E2 is rounded down. As a result, the original data R0 to R3 before conversion can be obtained by canceling this propagation error.

<Third Embodiment> In the third embodiment of the present invention, another conversion matrix (7), which is neither the natural type nor the Walsh type, is used.

[0059]

[Equation 7]

(7) This is a replacement of the natural type basis vector in the fourth row twice and moving to the second row. The conversion data obtained by performing the integer type Hadamard conversion using such a conversion matrix is (S
0, S1, S2, S3) to enable reversible conversion 8
The types of rounding processing (type 0 to type 7) are defined as follows.

The types of rounding up three converted data and rounding down only one are classified into 0 type to 3 type, and
The types in which one conversion data is rounded down and only one is rounded up are classified into types 4 to 7. More specifically, in the case where only one piece of the converted data is Si, when the one converted data is Si, it is treated as the i-type, and when the one converted data is rounded up, the one converted data is Sj. Classify as j + 4 type.

With the above definition, when the i-type rounding process is performed at the time of conversion, the rounding process in the inverse conversion process for restoring the original data is the (8's complement of i) type. For example, when rounding processing is performed with the 2 type at the time of conversion, the original data can be restored by performing inverse conversion using the rounding processing of the 6 type which is the complement of 8 of 2.

For each of the rounding processes of 0 type to 7 type, 4
FIG. 7A shows an error that is superimposed on one converted output data, FIG. 7B shows a propagation error at the time of reverse conversion, and FIG. 7C shows a rounding process at the time of reverse conversion for canceling the propagation error. Show.

7 (a) and 7 (c), if the rounding process at the time of conversion is numbered in the order of the third embodiment, the rounding process at the time of conversion and the rounding process at the inverse conversion thereof are in the complement of 8's. You can see that it has a relationship. Even when a conversion matrix other than the conversion matrix (7) is used, there are eight types of rounding processing at the time of conversion, and the rounding processing at the time of inverse conversion is a processing that is uniquely determined. (However, the relation is not a simple rule as described above.) <Fourth Embodiment> The fourth embodiment of the present invention is the rounding process at the time of conversion shown in the third embodiment and the reverse conversion. The correspondence of the rounding process at time is shown by the hardware configuration.

FIG. 8 is a block diagram showing the configuration of Hadamard transform processing unit 801 according to Embodiment 4 of the present invention. This processing unit 801 is used in both the conversion processing and the inverse conversion processing.

FIG. 9 shows the rounding process after Hadamard transformation.
It is a figure which shows together the structure of the integer type reversible Hadamard conversion process part corresponding to 0 type-7 type, and the structure of the inverse conversion process part corresponding to this conversion process part. In the figure, the left side of the broken line 901 shows the processing by the conversion processing unit, and the right side shows the processing by the inverse conversion processing unit.

Hadamard conversion unit (HT unit)
The unit group 903 in the first stage of the output of 801 is “1”.
Is an addition unit for adding. "1" to add here
The actual weight (converted to the output result) of is 0.5. The unit group 905 in the second stage is a 1-bit shift unit for removing the LSB which is the decimal point data and leaving only the integer part. Physically, the decimal part is not connected and only the integer part is connected. The description of these units applies to both the transformation processor and the inverse transformation processor.

<Embodiment 5> Embodiment 5 of the present invention
Is not limited to two types of rounding-up processing and rounding-down processing, but is more generalized. That is,
Nothing is added (or it can be said that "0" is added) at the time of rounding processing, or it is not limited to adding "1",
It allows addition of other values. FIG. 10 shows a conversion process in which the integer type reversible Hadamard transform is performed even when the added value is other than “0” and “1”. This is,
It is a conversion process according to the fifth embodiment. Although the Walsh-Hadamard transform matrix is used here as the transform matrix, any of the three types of transform matrices may be used.

Calculation process S of addition value for rounding process of FIG.
In 1001, Mi (i = 0,1,2,3) is an integer, Si = 0 or 1 (i = 0,1,2,3), and S
0 + S1 + S2 + S3 = 1 or 3. Under this condition, the conversion process S1003 in FIG. 8 is an integer-type reversible Hadamard conversion process. The embodiment in which Mi is limited to “0” is the embodiment described so far.

When continuous reversible Hadamard transform is performed on data collected by the same rounding process, S1001 of the calculation process of the added value of the rounding process only needs to be performed once at the beginning, and then the Hadamard transform of S1003 is performed. The rounding process is repeated as many times as necessary.

<Sixth Preferred Embodiment> The fifth preferred embodiment is effective when performing integer-type reversible Hadamard transform processing in cascade. This is useful for alleviating the locally concentrated rounding error when transposing the data converted in units of 4 with respect to 16 data and further converting in units of 4. FIG. 11 shows an example of the configuration.

In the figure, reference numerals 1101 to 1108 denote Hadamard transform units (HT units), and the transform matrix of this transform unit may be any of the above three types, but the same transform matrix is used for all eight. 1111 is an addition unit for adding "1", 1113 is an addition unit for adding "-1", 1115 is an addition unit for adding "2", 1
121 is a bit shift unit.

In the case of the configuration shown in FIG. 11, focusing on the four HT units in the latter stage (right side), the rounded-up data is concentrated in the HT unit 1105,
The truncated data is concentrated in the units 1106-1108. The data rounded up is "+0.
A rounding error of "5" is superimposed, and a rounding error of "-0.5" is superimposed on the truncated data.

When these data are further subjected to Hadamard transform, their errors are concentrated on the transform coefficient Y0. That is,
In the conversion coefficient Y0 of the HT unit 1105, the errors superposed on the input data are collected, and the maximum is "+1". On the other hand, in the other conversion coefficients Y1, Y2 and Y3, the error is canceled and the average value becomes "0". HT unit 11
Similarly, in 06 to 1108, the error is collected in the conversion coefficient Y0 and becomes the minimum "-1", and the other conversion coefficients Y1, Y2, Y
In 3, the error is canceled and becomes "0" on average.

Conversion coefficient Y in HT unit 1105
Make the error superimposed on the output of 0 the same as other conversion coefficients 1
One of the methods is to convert M1 = −1,
S0 = 1, and all others correspond to setting to “0”. With this setting, the conversion coefficients Y0, Y1, Y
For both 2 and Y3, the error superimposed on the output conversion coefficient is-
It is distributed from 1 to +0.5.

Similarly, HT units 1106-1108
One method of making the error superposed on the output of the conversion coefficient Y0 in the same manner as the other conversion coefficients is to set M1 = 1, S1 = S2 = S3 = 1 in the conversion processing of FIG. It is equivalent to doing. With this setting, all four conversion coefficients Y0, Y1, Y2, and Y3 have errors distributed over the output conversion coefficient of −0.5 to +1.

The integer type reversible Hadamard transform processing method and its processing apparatus according to the present embodiment can also be used as a part of the DCT transformation, as described in the prior art. That is, when realizing a reversible transformable DCT that outputs integer type data, by replacing the Hadamard transform processing unit with the reversible Hadamard transform processing method or the reversible Hadamard transform processing unit according to the present embodiment, high speed is achieved. It is possible to realize a DCT transform capable of reversible transform suitable for processing.

The Hadamard transform processing method and apparatus described above are processing for four one-dimensional data. However, this processing is performed for 4 × 4 two-dimensional array data in the horizontal and vertical directions, respectively. By applying it, it becomes possible to perform two-dimensional conversion. A reversible Hadamard transform processing method and processing apparatus for such two-dimensional data are naturally included in the scope of the present invention.

Even when the present invention is applied to a system including a plurality of devices (for example, a host computer, an interface device, a reader, a printer, etc.), a device including one device (for example, a copying machine, a facsimile device, etc.) ) May be applied.

Further, an object of the present invention is to supply a storage medium (or recording medium) recording a program code of software for realizing the functions of the above-described embodiments to a system or an apparatus, and to supply the storage medium (or recording apparatus) to the system or the apparatus. It is also achieved by the computer (or CPU or MPU) reading and executing the program code stored in the storage medium. In this case, the program code itself read from the storage medium realizes the functions of the above-described embodiments, and the storage medium storing the program code constitutes the present invention. Further, by executing the program code read by the computer, not only the functions of the above-described embodiment are realized, but also an operating system (OS) running on the computer is executed based on the instruction of the program code. This also includes a case where a part or all of the actual processing is performed and the processing realizes the functions of the above-described embodiments.

Further, after the program code read from the storage medium is written in the memory provided in the function expansion card inserted into the computer or the function expansion unit connected to the computer, based on the instruction of the program code. , The CPU provided in the function expansion card or the function expansion unit performs some or all of the actual processing,
The case where the functions of the above-described embodiments are realized by the processing is also included.

As described above, according to the present embodiment, the Hadamard transform process of four points is performed by one matrix operation, and the lowest of the odd number of data among the four data obtained by the transform process. By rounding up and rounding down the bottom of the remaining odd number of data
The integer type reversible Hadamard transform process and the inverse transform process for restoring the original data corresponding to the transform process can be realized at high speed by simple calculation.

Further, by rounding up the results of the odd number of converted outputs and rounding down the remaining odd number of converted outputs, the rounding process and the conversion process by the 4-point Hadamard transform matrix are performed at the same time. The integer type reversible Hadamard transform process and the inverse transform process for restoring the original data corresponding to the transform process can be realized at high speed by simple calculation.

Further, (constituted only by butterfly operation)
A four-point Hadamard transform unit and an odd number of outputs of this Hadamard transform unit are rounded up, and a rounding process of rounding down the remaining odd number of transformed outputs is performed, resulting in a simple configuration and a delay in operation. It has become possible to realize a small integer type reversible Hadamard transform processing device and an inverse transform processing device that restores original data corresponding to a transform process.

[0085]

As described above, according to the present invention, among the converted data obtained by the Hadamard transform processing, the lowest of the odd number of data is rounded up, and the lowest of the remaining odd number of data is rounded down. Thus, there is an effect that integer-type reversible Hadamard transform processing can be realized.

Further, according to the present invention, the lowest number of the odd number of converted outputs is rounded up, and the lowest number of the remaining odd number of converted outputs is rounded down to perform the rounding process.
An integer type reversible Hadamard transform process can be realized.

Further, according to the present invention, there is an effect that an integer type reversible Hadamard transform with a small operation delay can be performed with a simple structure.

[Brief description of drawings]

FIG. 1 is a diagram illustrating a signal flow that is a basis for realizing a conventional integer type reversible Hadamard transform process.

FIG. 2 is a diagram illustrating a signal flow of a conventional integer-type reversible Hadamard transform process with rounding added.

FIG. 3 is a flowchart illustrating a flow of a reversible Hadamard transform process according to the first embodiment of the present invention.

FIG. 4 is a flowchart showing a modified example of Hadamard transform processing and rounding processing according to the first embodiment of the present invention.

FIG. 5 is a flowchart showing a process flow of lossless Hadamard transform according to the second embodiment of the present invention.

FIG. 6 is a flowchart showing a flow of inverse conversion processing of lossless conversion processing according to the second embodiment of the present invention.

FIG. 7 is a diagram illustrating an error generated in a rounding process of eight sets of reversible Hadamard transform processes according to the third embodiment of the present invention, an error propagated in an inverse transform process corresponding to each transform process, and a rounding of the inverse transform process. It is a figure explaining the error which occurs in processing.

FIG. 8 is a block diagram showing a configuration of a 4-point Hadamard transform processing unit according to Embodiment 4 of the present invention.

FIG. 9 is a block diagram showing a configuration of eight sets of reversible Hadamard transform processing units and an inverse transform processing unit corresponding to each of them according to a fourth embodiment of the present invention.

FIG. 10 is a flowchart showing a flow of rounding processing addition value calculation processing, Hadamard transform, and rounding processing according to the fifth embodiment of the present invention.

FIG. 11 is a block diagram showing a configuration of a reversible Hadamard transform processing unit for 16 pieces of data according to a sixth embodiment of the present invention.

Claims (24)

[Claims] 1. A conversion step of performing conversion processing by an Hadamard conversion matrix on an input signal, and rounding down each least significant data of an odd number of data among the conversion data converted in the conversion step and And a rounding step of rounding down each lowest-order data of an odd number of data and converting it to an integer, a Hadamard transform processing method. 2. The method according to claim 1, further comprising a restoration process for restoring the original data by performing a rounding process corresponding to the inverse transforming process and the rounding process corresponding to the transforming process. Hadamard transform processing method. 3. The Hadamard transform processing method according to claim 1, wherein the Hadamard transform matrix is a four-point Hadamard transform matrix. 4. The Hadamard transform according to claim 2, wherein the rounding processing in the restoration step is uniquely determined for the rounding processing step and is the same as the rounding processing in the rounding processing step. Processing method. 5. The rounding process in the rounding process is 8
The Hadamard transform processing method according to claim 3, wherein there are types. 6. The Hadamard transform according to claim 2, wherein the type of the rounding process in the rounding process and the type of the rounding process in the inverse transform in the restoring process are made to correspond to each other in a complementary relationship. Processing method. 7. A conversion processing step of performing a Hadamard conversion processing by a four-point Hadamard conversion matrix, and rounding up the lowest of odd-numbered conversion outputs among the output of the conversion result by the conversion processing step, and the remaining odd number. Rounding processing step of rounding down the lowest level of the conversion output, an inverse conversion processing step of performing an inverse Hadamard conversion processing on the converted output rounded in the rounding processing step, and the same rounding processing as the rounding processing in the rounding processing step. And a restoration step of restoring the original data by performing the conversion result of the inverse transformation processing step. 8. The method according to claim 7, wherein there are eight types of rounding processing in the rounding processing step, and the rounding processing in the restoration step is uniquely determined with respect to the rounding processing in the previous rounding processing step. Hadamard transform processing method described. 9. The rounding process in the restoration process is made to correspond to the rounding process at the time of eight types of conversion process in the rounding process step in a relationship of 8's complement. Hadamard transform processing method described. 10. A Hadamard transforming means, and rounding means for rounding up the odd least significant bits of the transformed outputs of the Hadamard transforming means and rounding down the least significant odd number of the transformed outputs. A Hadamard transform processing device comprising: 11. The Hadamard according to claim 10, further comprising a restoring unit that restores the original data by performing an inverse transform process corresponding to the Hadamard transform unit and a rounding process corresponding to the rounding process unit. Conversion processing device. 12. The Hadamard transform matrix is a four-point Hadamard transform matrix, according to claim 10 or 1.
The Hadamard transform processing device according to 1. 13. The Hadamard transform according to claim 11, wherein the rounding processing in the restoring means is uniquely determined for the rounding processing means and is the same processing as the rounding processing in the rounding processing means. Processing equipment. 14. The Hadamard transform processing device according to claim 12, wherein there are eight types of rounding processing in said rounding processing means. 15. The Hadamard transform according to claim 11, wherein the type of the rounding process in the rounding process unit and the type of the rounding process in the inverse transform in the restoring unit are made to correspond to each other in a complementary relationship. Processing equipment. 16. A conversion processing means for performing a Hadamard conversion processing by a four-point Hadamard conversion matrix; and a conversion result output by the conversion processing means; Rounding processing means for rounding down the bottom of the conversion output, inverse conversion processing means for performing inverse Hadamard conversion processing on the converted output rounded by the rounding processing means, and the same rounding processing as the rounding processing in the rounding processing means A Hadamard transform processing device, comprising: a restoration unit that restores the original data by performing the conversion result of the inverse transformation processing unit. 17. The rounding process in the rounding unit has eight types, and the rounding process in the restoring unit is uniquely determined with respect to the rounding process in the previous rounding unit. Hadamard transform processing device described. 18. The rounding process in the restoring unit corresponds to the rounding process at the time of the conversion process in the rounding unit, which has eight types, in a relationship of 8's complement. Hadamard transform processing device described. 19. A program for executing the Hadamard transform processing method according to claim 1. Description: 20. A computer-readable storage medium storing a program for executing the Hadamard transform processing method according to claim 1. Description: 21. Addition / subtraction means for performing addition / subtraction processing based on Hadamard transform matrix for four integer input data, and rounding means for rounding off the least significant bit after adding a predetermined value to the calculation result by the addition / subtraction means. And the predetermined value is 2Mi + Si (i = 0, 1, 2, 3), where Mi is an integer, Si = 0 or 1, S0 + S1 + S
2 + S3 = 1 or 3 is a Hadamard transformation device. 22. An addition / subtraction step of performing addition / subtraction processing based on a Hadamard transform matrix on four integer input data; and after adding a predetermined value to a calculation result in the addition / subtraction step,
Rounding step for rounding down the least significant bit, the predetermined value is 2Mi + Si (i = 0, 1, 2, 3), where Mi is an integer, Si = 0 or 1, S0 + S1 + S
2 + S3 = 1 or 3 is a Hadamard transform method. 23. An addition / subtraction step of performing an addition / subtraction process based on a Hadamard transform matrix on four integer input data; and after adding a predetermined value to a calculation result in the addition / subtraction step,
Rounding step for rounding down the least significant bit, the predetermined value is 2Mi + Si (i = 0, 1, 2, 3), where Mi is an integer, Si = 0 or 1, S0 + S1 + S
A program for executing the Hadamard transform method, wherein 2 + S3 = 1 or 3. 24. An addition / subtraction step of performing addition / subtraction processing based on a Hadamard transform matrix on four integer input data; and after adding a predetermined value to a calculation result in the addition / subtraction step,
Rounding step of rounding down the least significant bit, the predetermined value is 2Mi + Si (i = 0, 1, 2, 3), where Mi is an integer, Si = 0 or 1, S0 + S1 + S
A storage medium storing a program for executing the Hadamard transform method, wherein 2 + S3 = 1 or 3.