JP5035926B2 - Image coding apparatus, image coding method, and image coding program - Google Patents

Description

  The present invention relates to a high-efficiency image signal encoding method, and more particularly to an image encoding device, an image encoding method, and an image encoding program that improve energy compaction in noise shaping and improve encoding efficiency.

  One of the important elemental techniques in image coding is transform coding represented by Discrete Cosine Transform (DCT). The role of transform coding in image coding is to remove spatial correlation between pixels. This is because, as a whole position of the encoder, information is concentrated on a small number of transform coefficients by transform coding, and the transform coefficient with low information concentration is rounded down by quantizing the transform coefficients, so that Is intended to reduce the amount of information.

  FIG. 8 shows an example of a general encoding apparatus 100 that encodes a video signal. When the video signal is input, the encoding apparatus 100 obtains a prediction residual signal from the difference from the prediction signal predicted by the prediction unit 106, and the transform unit 101 performs orthogonal transform on the prediction residual signal. The output transform coefficient is quantized by the quantization unit 102, and the quantized value is variable-length encoded by the entropy encoding unit 107 and output as an encoded stream. On the other hand, the output of the quantization unit 102 is inversely quantized by the inverse quantization unit 103 and further inversely orthogonally transformed by the inverse transform unit 104. A decoded signal is generated by adding a prediction signal to the conversion result. The decoded signal is subjected to noise removal processing by the distortion removal filter 105 and input to the prediction unit 106 as a reference decoded signal. The prediction unit 106 generates a prediction signal for encoding the next video signal by motion search or the like.

  Up to now, in application to image coding, many transform coding schemes such as discrete cosine transform (DCT) and overlapping orthogonal transform discrete wavelet transform (DWT) have been studied.

  For example, as transform coding, discrete cosine transform (DCT) is adopted in JPEG, and discrete wavelet transform (DWT) is adopted in JPEG2000. In addition, since orthogonal transformation uses a complete basis, the number of data before and after the transformation is unchanged. For this reason, the orthogonal transform is a non-redundant transform. In the moving image encoding apparatus, the conversion unit 101 in FIG. 8 corresponds to the above technique.

  On the other hand, there is a transform called a redundant transform using an overcomplete basis in which the number of bases is larger than the number of samples of the original signal. For this reason, the redundant transformation cannot be an orthogonal transformation, but by giving redundancy to the data after the transformation, it is possible to have characteristics that cannot be realized by the non-redundant transformation. For example, a discrete stationary wavelet transform (SWT) that is a DWT that does not perform downsampling processing can establish shift invariance lost in the DWT due to redundancy after the transformation.

  In the field of image processing, “conversion with direction separation characteristics” has attracted attention. Such conversion is generally redundant conversion, and a typical example is Curvelet conversion. A parallel tree complex wavelet transform (DTCWT) is a transform having similar characteristics.

  The conversion having the direction separation characteristic is a conversion in which a curve such as an edge included in the image signal is expressed using a direction base defined in two dimensions. Since a two-dimensional structure is approximated with high accuracy using a direction basis, it is more effective for noise removal and feature extraction than a transformation with poor direction separation characteristics such as DWT.

  However, conversion with direction separation characteristics has a problem that the number of data after conversion increases. When x is an input signal to transform coding and Ψ is a transform matrix, a transform coefficient y obtained by the transform is expressed as follows.

y = Ψx (1)
In the case of DTCWT, if x is an n-dimensional vector, the conversion coefficient y obtained by the conversion is a 2n-dimensional vector. For this reason, when the transformation is applied to image coding, it is necessary to appropriately select a transformation coefficient from the viewpoint of reducing the number of data. This selection of transform coefficients can be formulated as the following constrained minimization problem.

min _y ‖y‖ ₀ subject to Φy = x (2)
Here, min _y is a function for obtaining the minimum value of the following expression. ‖ · ‖ ₀ is an L ⁰ norm and represents the number of non-zero coefficients. Φ is a matrix representing the inverse transformation of the transformation consisting of an overcomplete basis set. The above minimization problem with constraints is reduced to the following minimization problem by Lagrange's undetermined multiplier method.

min _y ‖y‖ ₀ + λ‖Φy−x‖ ₂ ² (3)
Here, λ is a weight parameter given from the outside. ‖ · ‖ ₂ ² is the square value of the L ² norm and represents the sum of squares. The first term is the number of selected transform coefficients, and is an approximate value of the information amount of transform coefficients. The second term represents the reconstruction error associated with the selection of the transform coefficient and represents the coding distortion. However, since the above minimization problem is difficult to NP, conventionally, a method of approximating the following L ¹ norm as a minimization problem has been adopted.

min _y ‖y‖ ₁ + λ‖Φy−x‖ ₂ ² (4)
Here, ‖ · ‖ ₁ is an L ¹ norm, and represents the sum of absolute values of vector elements.

  As a technique for giving a suboptimal solution to the minimization problem of Equation (4), a technique called noise shaping processing shown in FIG. 9 has been proposed (see Non-Patent Document 1).

  Organize the symbols used. The conversion coefficient after forward conversion for the input signal x (N pixels) is defined as follows.

y ₀ = Ψx
Using I as a unit matrix, two types of projections P ^s ≡ΨΦ and P⊥≡I−ΨΦ are defined (note that ⊥ is a subscript attached to the right shoulder of P).

The output obtained by the former projection is called the effective component, and the output obtained by the latter projection is called the invalid component. An index representing the number of repetitions in the noise shaping process is represented by i, and the i-th output in the noise shaping process is represented by y _i . For y _i , a clipping process is performed in which the coefficient whose absolute value is equal to or smaller than the threshold θ _i is rounded down to zero. The output after clipping processing for y _i is represented as ｙy _i (＾ is a symbol on y) as follows:

^ Y _i (θ _i ) = y _i + ε _i (θ _i )
Here, ε _i (θ _i ) is an error (referred to as a clipping error) to be superimposed in accordance with the clipping process.

In FIG. 9, w _i (θ _i ) is an error feedback signal in the noise shaping process and is given by the following equation.

w _i (θ _i ) = ky ₀ −kΨΦ ^ y _i (θ _i )
Using this ^ y _i (θ _i ) and w _i (θ _i ), y _{i + 1} is expressed as the following equation.

y _{i + 1} (θ _i , ^ y _i (θ _i )) = ^ y _i (θ _i ) + w _i (θ _i )
The operation of the noise shaping processing apparatus 200 shown in FIG. 9 will be briefly described. The conversion unit 201 performs conversion using a redundant conversion basis on the input signal x to calculate a conversion coefficient y ₀ . The clipping processing unit 202, transform coefficients y _i (initial value i = 0) performs a comparison between a predetermined threshold theta _i, if y _i is less than theta _i, replacing y _i to zero. Assume that the output after this clipping process is y _i . The inverse transform unit 203, ^ inversely convert y _i seek ^ x _i of the inverse transform results. The difference between the input signal x and ^ x _i is the error e _i in the pixel region.

The weight coefficient multiplication unit 204 multiplies e _i by a predetermined weight coefficient k, and forward-converts the multiplication result in the conversion unit 205, thereby calculating an error feedback signal w _i . An update conversion coefficient y _{i + 1} is calculated by adding an error feedback signal w _i to the output ^ y _i of the clipping processing unit 202. After being delayed for a certain time by the delay unit 206, the update conversion coefficient y _{i + 1} is input to the clipping processing unit 202 and the process is repeated in the same manner for the update conversion coefficient y _{i + 1} . The end condition judging unit 207 checks whether or not the difference between e _{i + 1} and e _i is smaller than a certain minute value, and when the difference becomes smaller than the minute value, the ^ y _i is output as a conversion result.

T. Reeves and N. Kingsbury, “Overcomplete image coding using iterative projection-based noise shaping”, Proc. IEEE Conf. On Image Processing, vol.3, pp.597-600, 2002.

  The error feedback processing in noise shaping is intended to reduce the clipping error power included in the reconstructed signal. For this reason, although the clipping error is reduced compared to the signal before feedback processing, it is not processing that directly optimizes the energy compaction for the conversion coefficient after feedback processing, so there is room for improvement in improving this energy compaction. leave.

  The present invention has been made in view of such circumstances, and in a redundant conversion using an overcomplete basis, a conversion coefficient that realizes an improvement in energy compaction in a noise shaping process for removing redundancy between conversion coefficients. An object of the present invention is to establish an image encoding method based on the above configuration method.

  In order to solve the above-described problems, the present invention performs a correction process for reducing the coding error for the obtained transform coefficient by performing transform using a redundant transform base on the input video signal. The most important feature is to set a transform coefficient that maximizes energy compaction by recalculating the transform coefficient while maintaining the same coding error. .

  When setting the transform coefficient by recalculating the transform coefficient, obtain the decoded signal (vector value) by inverse transform of the transform coefficient, and select the basis function to use that has the closest approximation to the decoded signal. When approximating the decoded signal and repeating the process of approximating the approximate error while increasing the number of basis functions used one by one for the approximate error, and the approximate error is less than the given error In addition, the transformation coefficients of the basis functions that are not used for approximation at that time are set to zero.

  According to the present invention, it is possible to improve encoding efficiency by improving energy compaction in noise shaping processing and consolidating information into specific components.

It is a figure explaining a redundant signal expression and a reconstruction error. It is a figure explaining the efficient signal representation in the case of using the basis of an Overcomplete system. It is a figure explaining the method of calculating | requiring the coefficient vector with which information content becomes small among several coefficient vectors. It is a figure which shows the structural example of the encoding apparatus which concerns on embodiment of this invention. It is a flowchart of the calculation process of an update conversion coefficient. It is a flowchart of the recalculation process of a conversion coefficient. It is a system block diagram when implement | achieving from a software program. It is a block diagram of a general encoding apparatus. It is a figure which shows the example of the conventional noise shaping processing apparatus.

Prior to describing embodiments of the present invention, an outline of the basic technique of the present invention will be described. The effective component and the invalid component of the clipping error ε _i (θ _i ) to be superimposed in accordance with the clipping processing in the noise shaping processing described in [Background Art]
ε _i (θ _i ) ^s = P ^s ε _i (θ _i )
ε _i (θ _i ) ⊥ = P⊥ε _i (θ _i )
(⊥ is a subscript on the upper right). The conversion coefficient y _{i + 1} (θ _i , ^ y (θ _i )) obtained as a result of i + 1 iterations is expressed as ε _j (θ _j ) ⊥ and ~ ε _{j, i} (θ _j ) ^s (note that ~ Is represented by the following equation using ε).

Here, ~ ε _{j, i} (θ _j ) ^s is defined as follows.

~ Ε _{j, i} (θ _j ) ^s = (1-k) ^{i-j + 1} ε _j (θ _j ) ^s (5)
When k = 1, ˜ε _{j, i} (θ _j ) ^s = 0
Therefore, the conversion coefficient y _{i + 1} (θ _i , ^ y (θ _i )) is expressed by the following equation.

The conversion coefficient y _{i + 1} (θ _i , ^ y (θ _i )) is not optimally configured with respect to energy compaction. Therefore, a conversion coefficient that improves the energy compaction is calculated while maintaining the same reconstruction error as the conversion coefficient y _{i + 1} (θ _i , ^ y (θ _i )).

First, y _{i + 1} (θ _i , ^ y (θ _i )) is inversely transformed to calculate a reconstructed pixel signal.

x _{i + 1} = Φy _{i + 1} (θ _i , ^ y (θ _i ))
Next, the conversion base of DTCWT is set as ψ _n (n = 1,..., 2N), and the construction method of the conversion coefficient using the base will be described below. Note that ψ _n is the n-th row vector of ψ. In the following, for simplicity, x _{i + 1} is abbreviated as x. The inner product of x and ψ _n (n = 1,..., 2N) is calculated, and the basis ψ _m1 having the maximum inner product is obtained from 2N bases. Next, assuming that the conversion coefficient for ψ _m1 is c _m1 = <x, ψ _m1 >, an error r ₁ in the case of approximating x using ψ _m1 ,
r ₁ = x−c _m1 ψ _m1
And Note that <x, ψ _m1 > represents the inner product of x and ψ _m1 .

For this r ₁ , an inner product with ψ _n (n = 1,..., 2N, n ≠ m ₁ ) is calculated, and a basis ψ _m2 having the maximum inner product is obtained from 2N−1 bases. . Assuming that the conversion coefficient for ψ _m2 is c _m2 = <r _1, ψ _m2 >, an error r ₂ when r ₁ is approximated using ψ _m2 ,
r ₂ = r ₁ −c _m2 ψ _m2
The same process is repeated.

  The repetition end condition differs depending on whether k ≠ 1 or k = 1.

  If k ≠ 1,

Or until n = 2N.

If k = 1, repeat until r _n = 0 (n = 1,..., 2N) is satisfied or n = 2N.

  The reason why the conversion coefficient is converted into a conversion coefficient having a large energy compaction while maintaining the same reconstruction error by the above processing will be briefly described.

  FIG. 1 is a diagram for explaining redundant signal expressions and reconstruction errors. A redundant conversion will be described by taking DTCWT as an example.

  In DTCWT, as shown in FIG. 1A, 2N conversion coefficients are output by DTCWT for N input pixels. As shown in FIG. 1B, the pixel area is X and the CWT coefficient area is Y. A vector representing the original image is converted into a coefficient vector in the CWT coefficient region by the CWT. Since this conversion is a redundant transformation, there are a plurality of coefficient vectors representing one image as shown in the inverse CWT conversion example. Will exist. That is, the same decoded image is generated by inverse CWT regardless of which coefficient vector in the dotted frame in the Y region is used, and the error between the decoded image and the original image becomes constant.

  Therefore, if a coefficient vector that minimizes the amount of information can be obtained from among a plurality of coefficient vectors that can generate the same decoded image, the coding efficiency can be improved. A strategy to achieve this goal is to construct the coefficient vector so that the bias between the coefficients is large. That is, by configuring the coefficient vector so that the deviation between the coefficients is large, the energy compaction is increased and the coding efficiency is improved.

  FIG. 2 is a diagram for explaining an efficient signal representation when an Overcomplete base is used. When the vector x is expressed using two basis functions (basis vectors) ψ 1 and ψ 2, it is as shown in FIG. Note that δ indicates a value that is rounded due to quantization.

  In the case of Overcomplete basis sets, more basis functions than the number of signal dimensions are prepared. An example is shown in FIG. As is clear from a comparison between FIG. 2A and FIG. 2B, it can be seen that FIG. 2B can be expressed with a smaller amount of information than in the case of FIG.

  FIG. 3 is a diagram for explaining a method for obtaining a coefficient vector having a small amount of information among a plurality of coefficient vectors.

In the present invention, while maintaining the same reconstruction error as the transformation coefficient y _{i + 1} (θ _i , ^ y (θ _i )) calculated by the conventional noise shaping process as described in FIG. In order to calculate a conversion coefficient that improves energy compaction, first, the conversion coefficient y _{i + 1} (θ _i , ^ y (θ _i )) is inversely transformed, and the inverse transformation result is used as a vector x, and The inner product with the transformation basis ψ _n (n = 1,..., 2N) corresponding to the n-row vector is calculated. This is to obtain an approximate vector when x is projected in the ψ direction and x is expressed using ψ.

The process of taking the inner product of two vectors x and ψ is equivalent to projecting the original signal vector x in the ψ direction and obtaining the amplitude in the ψ direction. That is, the inner product c can be said to be a component in the ψ direction of x. From this, an approximate vector of x is obtained as shown in FIG. In the figure, ψ is a unit vector. The length of the vector obtained by projecting x in the ψ direction is the inner product of x and ψ, and c = <x, ψ> if this is c. This vector is cψ. In such ψ _n , obtaining the basis ψ having the maximum inner product is most approximate to x in the projection of the original signal vector x in each ψ _n direction (n = 1,..., 2N). This corresponds to obtaining the vector cψ.

An error vector r between the approximated vector cψ and the original signal vector x is a vector r (r = x−cψ) as shown in FIG. Assuming that ψ _m1 having the maximum inner product is ψ _m1 , the error vector r (r ₁ ) is most approximated among the transformation bases ψ _n (n = 1,..., 2N) excluding ψ _m1. In order to obtain a thing, an inner product of r ₁ and ψ _n (excluding ψ _m1 ) is calculated, and a basis ψ _m2 that maximizes the inner product is obtained. The inner product is c _m2 = <r _1, ψ _m2 >, and the error r ₂ when r ₁ is approximated using ψ _m2 is
r ₂ = r ₁ −c _m2 ψ _m2
It becomes. Similarly, by repeating the process of approximating this approximation error using one basis of ψ _n until the predetermined end condition such as the approximation error being 0 or smaller than a certain value is satisfied, the same decoded image is obtained. Among the plurality of coefficient vectors that can be generated, the coefficient vector that increases the bias between the coefficients is selected, and the energy compaction is improved.

  Hereinafter, specific examples of embodiments of the present invention will be described with reference to the drawings. FIG. 4 is a diagram illustrating a configuration example of the encoding device according to the embodiment of the present invention.

  An encoding apparatus according to an embodiment of the present invention includes, for example, an encoding apparatus 100 as shown in FIG. The coefficient recalculation unit 3 is replaced.

  The redundant conversion unit 1 and the update conversion coefficient calculation unit 2 in FIG. 1 are parts that implement the processing functions of the noise shaping processing device 200 as described in FIG. That is, the redundant conversion unit 1 converts the encoding target signal into a conversion coefficient using a redundant conversion basis. The update conversion coefficient calculation unit 2 performs clipping with the clipping processing unit 20 using a conversion coefficient smaller than a predetermined threshold as a zero value, and updates the conversion coefficient so that the clipping error is reduced by feedback processing of the clipping error.

  The transform coefficient recalculation unit 3 is a characteristic part of the present invention, and the update transform coefficient calculated by the update transform coefficient calculation unit 2 is regenerated so as to increase the energy compaction while maintaining the same coding error. calculate.

  The inverse conversion unit 30 in the conversion coefficient recalculation unit 3 performs inverse conversion on the update conversion coefficient output from the update conversion coefficient calculation unit 2 and stores the reconstructed pixel signal as a result of the inverse conversion in the buffer 31.

The inner product maximum basis calculation unit 32 calculates the inner product of the signals (vectors) stored in the buffer 31 and the conversion basis ψ _n, and 2N−i (i increases sequentially as 0, 1, 2,...). Among the bases, the base ψ _m having the maximum inner product is obtained, and the base ψ _m and the inner product (transform coefficient c _m ) at that time are stored in the transform coefficient / base storage unit 33.

The buffer update unit 34 calculates an error when approximating the signal vector stored in the buffer 31 using the conversion base ψ _m stored in the conversion coefficient / base storage unit 33, and stores the error value in the buffer 31 is overwritten.

  The inner product maximum base calculation unit 32 calculates the inner product of the error vector written in the buffer 31 with the transformation base excluding the base already used for calculating the error vector, and similarly calculates the maximum one. repeat. The buffer update unit 34 also repeats the update of the buffer 31 from the calculation result of the inner product maximum base calculation unit 32.

The end condition determination unit 35 determines a repetitive end condition. The repetition termination condition is, for example, as follows. When the predetermined weight coefficient k (see FIG. 9) for the error feedback signal is 1, all the elements r _{n of the} error vector stored in the buffer 31 have become 0, or the processing for all the conversion bases ψ _n has been completed. Sometimes. If the weighting factor k is not 1, and when the square sum of the elements r _n of the error vectors or falls below the sum of squares S of the active ingredient of the clipping error, processes have been performed for all the transformation bases [psi _n.

  When the above end condition is satisfied, the transform coefficient output unit 36 outputs the transform coefficient stored in the transform coefficient / base storage unit 33 as a reconstructed transform coefficient.

  The reconstructed transform coefficient is quantized by the quantization unit 4, variable-length encoded by the entropy encoding unit 5, and output as an encoded stream.

  FIG. 5 is a flowchart of the update conversion coefficient calculation process. The update conversion coefficient calculation unit 2 shown in FIG. 4 executes steps S1 to S7 shown in FIG. 5, and the conversion coefficient recalculation unit 3 executes step S8. Details of step S8 are shown in FIG.

  The update conversion coefficient calculation unit 2 reads a conversion coefficient obtained as a result of converting the encoding target signal by the redundant conversion unit 1 (step S1). Further, the clipping threshold used in the clipping processing unit 20 is read (step S2).

  The clipping processing unit 20 performs a clipping process in which the value of the conversion coefficient equal to or less than the threshold is set to zero to obtain a corrected conversion coefficient (step S3). Next, the modified transform coefficient obtained by the clipping process is inversely transformed to obtain a decoded signal (step S4). Subsequently, a difference signal between the decoded signal and the original signal is calculated. This difference signal is stored in a register (step S5).

  The difference signal is forward converted to obtain a correction coefficient (step S6). This correction coefficient is added to the modified conversion coefficient, and an updated conversion coefficient is written (step S7). The above processing is the same as the update of the transform coefficient by the noise shaping processing described with reference to FIG. 9, and is repeated until the change in the difference signal between the decoded signal and the original signal becomes a minute value or less.

  Next, the transform coefficient recalculation unit 3 inversely transforms the update transform coefficient calculated by the update transform coefficient calculation unit 2 in order to improve the energy compaction of the transform coefficient, obtains a decoded signal, The conversion coefficient is recalculated (step S8). Details of this processing will be described below with reference to FIG.

  FIG. 6 is a flowchart of transform coefficient recalculation processing. The transform coefficient recalculation unit 3 inversely transforms the updated transform coefficient by the inverse transform unit 30 and stores the decoded signal of the inverse transform result in the buffer 31 (step S10). Hereinafter, the signal stored in the buffer 31 is represented by r.

Next, the reference map M [n] (n = 1, 2,..., 2N) is initialized to 1 (step S11). This reference map M [n] indicates whether or not the projection of r on the transformation basis (also referred to as a basis function) ψ _n (n = 1,..., 2N) has been performed. “0” represents processed.

  First, among n = 1, 2,..., 2N, the processing from step S13 is executed on n satisfying M [n] = 1 (step S12). When all M [n] are 0, the process is terminated.

An inner product of the signal r in the buffer 31 with a basis function ψ _n with M [n] = 1 is calculated, and a basis function that maximizes the inner product is obtained. The maximum value of the inner product and the basis function for realizing the maximum value of the inner product are stored in the transform coefficient / base storage unit 33 as c _{mi + 1} and ψ _{mi + 1} (step S13). c _{mi + 1} means the component in the ψ _{mi + 1} direction of the vector of the signal r.

The buffer update unit 34 calculates a difference (error) between the signal r in the buffer 31 and c _{mi + 1} ψ _{mi + 1} and stores the result in the buffer 31 as a new signal r (step S14). Then, M [m _{i + 1} ] in the reference map M [n] is updated to 0 (step S15).

Next, in order to determine the termination condition, and calculates the square sum ‖r‖ elements r _n of the signal r (step S16). It is determined whether or not the weighting factor k for the error feedback signal is 1 (step S17). If it is 1, the process proceeds to step S18, and if it is not 1, the process proceeds to step S20.

When k = 1, it is determined whether or not the square sum ‖r‖ of the element of the signal r is 0 (step S18). If not, the process returns to step S12 and the process is repeated in the same manner. If 0, among n = 1, 2,..., 2N, n satisfying M [n] = 1 is set to conversion coefficient c _n = 0 (step S19), and the process is terminated.

If k ≠ 1, the square sum S of the effective components of the clipping error is calculated (step S20), and it is determined whether the square sum ‖r‖ of the elements of the signal r is equal to or less than S (step S21). If not less than S, the process returns to step S12 and the process is repeated in the same manner. If it is less than or equal to S, among n = 1, 2,..., 2N, the conversion coefficient c _n = 0 is set for _n satisfying M [n] = 1 (step S22), and the process ends.

  The above-described image encoding processing can be realized by a computer and a software program, and the program can be recorded on a computer-readable recording medium or provided through a network.

  FIG. 7 shows an example of the system configuration when the present invention is implemented using a software program. The memory 52 stores an image encoding program 53 for performing the image encoding process of the present invention. The CPU 50 sequentially fetches and executes the instructions of the image encoding program 53 stored in the memory 52. The video storage device 51 is a device that stores a video signal to be encoded. The video signal may be input from a camera or the like (not shown). The encoded stream generated by the image encoding program 53 is stored in the encoded stream storage device 54. Alternatively, the encoded stream may be output to an external device via an interface such as a network adapter. The system bus 55 is a bus that connects the CPU 50, the video storage device 51, the memory 52, and the encoded stream storage device 54.

DESCRIPTION OF SYMBOLS 1 Redundant conversion part 2 Update conversion coefficient calculation part 20 Clipping process part 3 Conversion coefficient recalculation part 30 Inverse conversion part 31 Buffer 32 Inner product maximum base calculation part 33 Conversion coefficient and base memory | storage part 34 Buffer update part 35 End condition determination part 36 Conversion Coefficient output unit 4 Quantization unit 5 Entropy coding unit

Claims (5)

An image encoding device that performs conversion using a redundant conversion basis on an input video signal and encodes a conversion coefficient of a conversion result,
An update conversion coefficient calculation means for calculating an update conversion coefficient by a clipping process in which a conversion coefficient equal to or less than a predetermined threshold is zero among conversion coefficients obtained by conversion using the conversion base of the redundant system;
The update conversion coefficient calculated by the update conversion coefficient calculation means is inversely converted, the inner product of the obtained decoded signal and the conversion base of the redundant system is calculated, the conversion base that maximizes the inner product is selected, and the conversion base The transform coefficient for is set to the maximum value of the inner product, the decoded signal is approximated by the transform base and the transform coefficient, and the inner product of the remaining transform base in the transform base of the redundant system is calculated for the approximation error. Then, a conversion coefficient recalculating means for recalculating the updated conversion coefficient by repeating the process of approximating the approximation error with the maximum value and the conversion base that gives the maximum value until a predetermined termination condition is satisfied,
An image encoding apparatus comprising: encoding means for encoding the recalculated transform coefficient. The image encoding device according to claim 1,
One of the termination conditions in the transform coefficient recalculating means is a case where the approximation error is less than or equal to a predetermined error, and the transform coefficient recalculating means performs approximation when the termination condition is satisfied. An image coding apparatus, wherein a transform coefficient of a transform base that is not used is set to a zero value. An image encoding method for converting an input video signal using a conversion base of a redundant system and encoding a conversion coefficient of a conversion result,
An update conversion coefficient calculation step of calculating an update conversion coefficient by a clipping process in which the conversion coefficient obtained by the conversion using the conversion base of the redundant system is zero with a conversion coefficient equal to or less than a predetermined threshold;
The update transform coefficient calculated by the update transform coefficient calculation process is inversely transformed, an inner product of the obtained decoded signal and the transform base of the redundant system is calculated, a transform base that maximizes the inner product is selected, and the transform base The transform coefficient for is set to the maximum value of the inner product, the decoded signal is approximated by the transform base and the transform coefficient, and the inner product of the remaining transform base in the transform base of the redundant system is calculated for the approximation error. Then, the process of approximating the approximation error with the maximum value and the conversion base that gives the maximum value is repeated until a predetermined termination condition is satisfied, and the conversion coefficient recalculation process for recalculating the updated conversion coefficient,
An image encoding method comprising: an encoding process for encoding the recalculated transform coefficient. The image encoding method according to claim 3, wherein
One of the termination conditions in the transform coefficient recalculation process is when the approximation error is less than or equal to a predetermined error, and the transform coefficient recalculation process is approximated when the termination condition is satisfied. An image encoding method, wherein a transform coefficient of a transform base that is not used is set to a zero value.   An image encoding program for causing a computer to execute the image encoding method according to claim 3 or 4.

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