Abstract:
Where a quantized data value is produced by a first quantization of an input data value, followed by a first inverse quantization and subsequently by a second quantization and the first quantization has first quantization intervals and the second quantization has second quantization intervals, third quantization intervals are generated by displacing interval boundaries of the second quantization intervals, respectively, to the next interval boundaries of the first quantization intervals. A third reconstruction value is determined for the third quantization intervals such that the third reconstruction value lies within the associated third quantization intervals. A corrected data value is generated by a third inverse quantization of the quantized data value and the third inverse quantization is affirmed by the third quantization intervals containing the associated third reconstruction value.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is based on and hereby claims priority to German Application No. 10 2005 038 295.9 filed on Aug. 12, 2005, the contents of which are hereby incorporated by reference. 
     BACKGROUND 
     During transcoding of quantized digital signals, such as a video signal, for example, a digital input signal is converted into a new digital output signal. A method for transcoding can be used to adapt the input signal for different transmission requirements and/or various terminal device functionalities. In so doing, the adaptation of a data rate of the input signal can be carried out by new quantization. More complex transcoding methods modify further parameters, such as a refresh rate or a screen resolution in cases of transcoding a video signal. 
     With the aid of  FIG. 1 , a coding chain with transcoding of digital signals is described in more detail. An uncoded image signal features a plurality of brightness and color values which are edited in the spectral range, for example. These uncoded values are labeled as uncoded data values X 0 . 
     An uncoded data value X 0 , i.e. an input data value X 0 , is coded in a first coder C 1  to a first intermediate data value X 1 . The coding takes place with the aid of a first quantization Q 1 . The first intermediate data value X 1  is decoded into the second intermediate data value X 2  using the first decoder D 1 . In this connection, a first inverse quantization IQ 1  is carried out. The second intermediate data value X 2  corresponds to the uncoded data value X 0  apart from a quantization error. This second intermediate data value X 2  is coded into a third intermediate data value X 3  with the aid of a second coder C 2 . The second coder C 2  uses a second quantizer C 2  for coding. Subsequently, the third intermediate data value X 3  is decoded into a final data value X 4  using a second decoder D 2 . The decoding takes place in the second decoder D 2  by the application of a second inverse quantization IQ 2 . The final data value X 4  corresponds to the uncoded data value X 0  apart from a quantization error, whereby this quantization error is caused both by the first quantization Q 1  or first inverse quantization IQ 1  and by the second quantization Q 2  or second inverse quantization IQ 2 . 
     If, for example, a video distribution service is observed, then for a plurality of video images, having a plurality of uncoded data values X 0 , a plurality of first intermediate data values X 1  are generated with the aid of the first coder. These first intermediate data values X 1  are, for example, filed on a hard disk for later organized transmission to a terminal device. In order to transfer the video images to a terminal device in the suitable form, e.g. with a low data rate, the first intermediate data values X 1  can be decoded into the second intermediate data values X 2  with the aid of the first decoder. Subsequently, the second intermediate data values X 2  are coded into the third intermediate data values X 3  using the second coder, and can subsequently be transmitted to the desired terminal device in this form. The terminal device receives the third intermediate data values X 3 , decodes these with the aid of the second decoder D 2  and displays the decoded end data values X 4  on a screen, for example. In  FIG. 1  a transcoding device TR is described with the aid of the first decoder and the second coder which transcoding device, for example, conducts a reduction of the data rate in the form of a code conversion of the first intermediate data values X 1  (=input signal) into the third intermediate data value X 3  (=output signal). 
     Digital signals, such as digital video signals, are coded or compressed for transfer with the aid of known coding standards, for example MPEG4 (MPEG—Motion Picture Expert Group) or H.264. These coding standards or video coding methods break the video signal down into blocks and introduce a motion compensation for predictive coding. The individual blocks are thereby broken down into spectral components by a mathematical map. For better compression the spectral components are quantized, such that components are removed from the signal which are not or only insignificantly recognizable for an observer. These removed components are also no longer accessible or reproducible within the transcoder. 
     The removal of signal components leads to additional quantization losses or quantization errors arising through a high quantizer level while carrying out an additional new quantization within the transcoder with the aid of the second quantization Q 2 . This means that, through the use of the first and second quantization, higher quantization errors arise than with the use of an individual quantizer. A loss in quality arising through the transcoding due to the new quantization leads to a visible deterioration of the image quality. 
     In  FIG. 2 , an image quality in PSNR (PSNR—Peak Signal to Noise Ratio) can be seen in exemplary form from the quantization level using one and two quantizations when used in a video coding method. The quantization level indicates a number of amplitudes of data values which are summarized within a quantization interval to a reconstruction value. For example, with a quantization level of 15 the amplitudes from 0 to 14 or from 15 to 29 etc. are each summarized to a reconstruction value, e.g. 7, 23 etc. The larger the quantization level, the stronger the compression by the quantization. The curve marked with squares is a first reference curve R 1  and describes the image quality when using an individual quantizer, whereby quantization is performed with the quantization level indicated in  FIG. 1 . A second reference curve R 2 , marked with circles, shows the image quality with the use of two quantization levels according to  FIG. 1  connected to each other in series, whereby quantization takes place in the first quantization Q 1  with a first quantization level of 12 and in the second quantization Q 2  with the quantization level indicated in  FIG. 2 , e.g. 20. It can thereby clearly be seen that the second reference curve lies underneath the first reference curve. So the difference in image quality PSNR at a quantization level of 20 is around 2 dB (dB—decibels). This means that with the use of more than one quantization the image quality is significantly reduced as compared to that with the use of an individual quantization. 
     Today, known video transcoders typically consist of the series connection of a decoder and a coder. A good overview can be gained from A. Vetro et al., “Video Transcoding Architectures and Techniques: An Overview”, IEEE Sig. Proc. Mag., March 2003, pp. 18-29. The decoder decodes the input signal either completely or up to a specific level, such that at least the amplitudes of the spectral coefficients from the quantized values are calculated in order to be able subsequently to conduct a new quantization. For the sake of a reduction in complexity, both these decoded data values and peripheral information, like for example prediction modes and/or motion vectors, can be assigned to the second coder. In the second coder the rate adaptation by new quantization can be conducted with a higher quantization level than in the first quantization Q 1 . In O. H. Werner, “Generic Quantiser for Transcoding Hybrid Video”, Proc. Pict. Cod. Symp. (PCS), 1997, a method is presented which adjusts the quantization in terms of the coefficients of the input data values and the additionally developed drift. Methods are known from P. A. Assuncao et al., “Optimal Transcoding of Compressed Video”, IEEE Proc. Int. Conf. Image Proc. (ICIP), Vol. 1., 1997, pp. 739-742, and W.-N. Lie et al., “Rate-Distortion Optimized DCT-Domain Video Transcoder for Bit-Rate Reduction of MPEG Video; IEEE, Proc. Int. Conf. Aud. Sp. and Sig. Proc. (ICASSP), Vol. V., 2004, pp. 969-972, which use a Lagrange approach, in which the quantization is chosen in such a way that the distortion is minimal in terms of a predetermined rate, for the adjustment of the new quantization. We will, however, not go into the choice of a new reconstruction value in this connection. 
     SUMMARY 
     An aspect is to specify a method and a device which in a simple fashion reduces a quantization error during a transcoding with two quantizers, in particular within the scope of an image coding. 
     Described below is a method for correcting a quantized data value, whereby the quantized data value is generated by a first quantization of an input data value, followed by a first inverse quantization and subsequently by a second quantization; and a first quantization features first quantization intervals and the second quantization second quantization intervals, in which third quantization intervals are generated by displacement of each of the interval boundaries of the second quantization intervals to the nearest-located interval boundaries of the first quantization intervals; in which for each of the third quantization intervals a third reconstruction value is established in such a way that the third reconstruction value is located within the associated third quantization interval; in which a corrected data value is generated by a third inverse quantization of the quantized data value, whereby the third inverse quantization is formed by the third quantization intervals with the third associated reconstruction value. 
     A reduction in quantization error is achieved by the method, whereby the determination of the third quantization interval and of the third reconstruction values can be carried out with a low computational effort. 
     Furthermore, the method can be put to use for intervals of the first and/or second (inverse) quantization of the same or different sizes. 
     In addition, the method can be used within the scope of a decoding in a terminal device and/or in a transcoding unit. 
     If the third reconstruction value of the third quantization interval is preferably generated from at least one of those first reconstruction values of each of the first quantization intervals which are located within the observed third quantization interval, then the third reconstruction value can be determined simply. 
     If the third reconstruction value in an alternative embodiment is generated from two neighboring first reconstruction values by a weighted mean value, then individual properties of each of the first reconstruction values, such as a frequency distribution of the emergence of the first reconstruction values, can be considered for the generation of the third reconstruction value. 
     Preferably, the third reconstruction value is generated in such a way that the third reconstruction value is located in the middle of the associated third quantization interval. Hence the third reconstruction value can be determined in an especially simple way and with a very low degree of complexity. 
     In one extension, the third reconstruction value of the third quantization interval is generated in such a way that, on the basis of a relative frequency distribution of data values, in particular of data values according to the first inverse quantization, the most frequently occurring data value is reassigned to the third reconstruction value. In this way the quantization error is further reduced. 
     Preferably, that data value within the third quantization interval which, in the mean, produces the lowest quantization error under consideration of the relative frequency distribution of data values, is reassigned to the third reconstruction value of the third quantization interval, so the quantization error is additionally reduced and hence the image quality is visibly improved. 
     If the third inverse quantization is carried out in such a way that an intermediate value is generated by the second inverse quantization of the quantized data value, and this generated intermediate value is replaced by that third reconstruction value lying in the same third quantization interval as the generated intermediate value, then the method described herein can be simply integrated into an existing method. This is because the allocation of the third reconstruction values takes place after the second inverse quantization, through which merely a conversion of the second reconstruction values into the third reconstruction values is required. A replacement of existing components of the existing method, such as the second quantization, is thereby not required. 
     The method for correcting within the scope of a decoding method, especially an image coding method, is preferably adopted on those quantized data values which remain unconsidered for handling other quantized data values. Through this, a faultless decoding, e.g. in a terminal device, is made possible and at the same time a reduction of the quantization error and hence an improvement of the image quality is achieved. 
     In an alternative extension, the method for correcting preferably within the scope of a decoding method, in particular an image coding method, is only applied to the quantized data values after the latter remain unconsidered for the handling of other quantized data values. For this reason the method described herein can also be adopted in decoding methods which conduct a predictive coding. 
     If the method for correction within the scope of a transcoding method is adopted preferably with a first decoder and a second coder in a feedback loop of the second coder, then the method described herein can also be used for a transcoder. Through this an improvement of the image quality comes about. 
     Furthermore, a device implementing the method described herein can be used for correcting a quantized data value generated by a first quantization of an input data value followed by a first inverse quantization and subsequently by a second quantization, and a first quantization features first quantization intervals and the second quantization second quantization intervals, from which first by shifting each of the interval boundaries of the second quantization intervals to the nearest-located interval boundaries of the first quantization intervals, third quantization intervals are generated. Second, for each of the third quantization intervals a third reconstruction value is established in such a way that the third reconstruction value is located within the associated third quantization interval. Third, a corrected data value is generated by a third inverse quantization of the quantized data value, whereby the third inverse quantization is built by the third quantization intervals with the associated third reconstruction vale. In addition, extensions and variants can be implemented and carried out. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other aspects and advantages will become more apparent and more readily appreciated from the following description of the exemplary embodiments, taken in conjunction with the accompanying drawings of which: 
         FIG. 1  is a block diagram of a device for generating an output data value from an input data value using two quantization levels; 
         FIG. 2  is a graph for a comparison of the image quality between the use of a single and two quantization levels; 
         FIG. 3  is a data transmission diagram for an exemplary embodiment of the method described below; 
         FIG. 4  is a data transmission diagram illustrating an assignment of third interval boundaries and third reconstruction values; 
         FIG. 5  is a graph for a comparison of an image quality in the use of a single quantization level, two quantization levels and two quantization levels, taking into consideration the method described below; 
         FIG. 6  is a block diagram of a device for carrying out the method; 
         FIG. 7  is a block diagram illustrating use of the device within the scope of a fixed-image decoding method; 
         FIG. 8  is a block diagram illustrating use of the method described below within the scope of a transcoding device; 
         FIG. 9  are graphs for determination of the third reconstruction value, taking into consideration the relative frequency of data values for minimizing a quantization error; 
         FIG. 10  is a graph for comparison of the image quality when using the method, taking into consideration the choice of the third reconstruction value by a relative frequency. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Reference will now be made in detail to the preferred embodiments, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout. 
     Elements with the same function and mode of operation are provided with the same reference numbers in the figures. 
     In a transcoding of digital signals, such as video signals or audio signals, a quality of an output signal or end data values X 4  is substantially reduced by the use of two quantizers. This has already been illustrated in more depth in the introduction to the description with reference to  FIGS. 1 and 2 , and therefore this will not be examined in more detail below. In the following exemplary embodiment the method is described in greater depth by a video signal. The method or the device can be used not only for video signals, however, but also any kind of signals in which an inverse quantization and a new quantization downstream take place within the scope of a transcoding. This is prevalent in the coding of speech signals, music signals or fixed images, for example. 
       FIG. 3  goes into greater detail regarding the method for a concrete numerical example. An uncoded data value X 0 , i.e. an input data value X 0 , is X 0 =90, for example. Within the scope of a first quantization Q 1 , a range of figures from 0 to 255 is separated out into eight first quantization intervals QI 1  of equal size, i.e. a first quantization level of the first quantization comes to 32. In  FIG. 3  a value is indicated on the lower and on the upper interval boundary for every first quantization interval Q 11 , as well as a first reconstruction value R 1  corresponding to the respective first quantization interval. This is indicated analogously for the second and third quantization intervals QI 2 , QI 3 . This first reconstruction value R 1 , for example 144, is achieved if a quantized data value is transferred using a first inverse quantization IQ 1  in the numerical range from 0 to 255. In the present example the uncoded data value X 0 =90 is quantized into the value 2, i.e. a first intermediate value X 1 =2. If the first inverse quantization QI 1  is applied to the first intermediate data value X 1 , then a second intermediate data value X 2 =80 comes about, whereby this corresponds to the first reconstruction value R 1 =80 of the associated first quantization interval QI 1 . 
     The second intermediate data value X 2 =80 is subjected to a second quantization Q 2 . In this the range of values from 0 to 255 is divided up into five second quantization intervals QI 2  of equal size, i.e. the quantization level of the second quantization comes to 51. Analogously to the first quantization Q 1 , a value is indicated in each case for the upper and lower interval boundary of every second quantization interval QI 2  in addition to a second reconstruction value R 2 . The second intermediate data value X 2 =80 is quantized by the second quantization Q 2  in a third intermediate data value X 3 =1. The third intermediate data value X 3  is also labeled as quantized data value X 3 . 
     Subsequently, a corrected data value XR is formed from the third intermediate data value X 3  using the method. The third intermediate data value X 3 =1 is thereby displayed on a third quantization interval QI 3  with the interval boundaries 64 to 95, whereby because of a third inverse quantization IQ 3  the third intermediate data value X 3  is reassigned to the third reconstruction value R 3 =80. This third reconstruction value R 3 =80 corresponds to the corrected data value XR. In  FIG. 3  the five third quantization intervals QI 3  are displayed on the right hand side. Furthermore, for every one of the third quantization intervals QI 3  an associated third reconstruction value R 3 , for example R 3 =32 or R 3 =224, can be seen. 
     For generating the third quantization intervals QI 3 , the interval boundaries of the second quantization intervals QI 2  are shifted in such a way that each of them corresponds to the nearest-located interval boundaries of the first quantization intervals QI 1 . If the second quantization interval QI 2  is observed from 204 to 255, for example, then the upper interval boundary of this second quantization interval QI 2  corresponds to the interval boundary of one of the first quantization intervals QI 1 . The lower interval boundary 204, however, lies within the interval boundaries 192 to 223 of one of the first quantization intervals QI 1 . Hence this interval boundary 204 of the second quantization interval QI 2  is displaced to the nearest-located interval boundary of the first quantization interval QI 1  with the lower interval boundary 192. This mode of operation can be adopted for all second upper and lower interval boundaries, and to determine the interval boundaries of the third quantization intervals QI 3 . 
     In order to establish the third reconstruction value R 3 , a value can be selected from within the respective third quantization interval QI 1 . So the third reconstruction value R 3  of the third quantization interval QI 3  with the interval boundaries comes to 192 to 255 just like R 3 =224. In the present exemplary embodiment according to  FIG. 3 , the third reconstruction values of each of the third quantization intervals QI 3  are laid out in the middle of each of the quantization intervals QI 3 , whereby through rounding up or down as appropriate only whole number values are allowed for the third reconstruction values R 3 . 
     In  FIG. 3  the third intermediate values X 3  are used e.g. as an index for choosing the third reconstruction values R 3  from a first list. This list goes e.g.: 
     
       
         
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 X3 
                 0 
                 1 
                 2 
                 3 
                 4 
               
               
                   
                   
               
             
             
               
                   
                 R3 
                 32 
                 80 
                 128 
                 176 
                 224 
               
               
                   
                   
               
             
          
         
       
     
     So for the third intermediate value X 3 =2 the third reconstruction value R 3 =128 is chosen. 
     In an alternative embodiment, after the second quantization Q 2  the second inverse quantization IQ 2  is initially carried out. The second reconstruction values R 2  gained therefrom, i.e. the fourth intermediate values X 4 , can then serve as an index for a second list, in order to determine therefrom the third reconstruction values. This second list looks, for example, like: 
     
       
         
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 R2, X4 25 
                 76 
                 127 
                 178 
                 229 
               
               
                   
                   
               
             
             
               
                   
                 R3 
                 32 
                 80 
                 128 
                 176 
                 224 
               
               
                   
                   
               
             
          
         
       
     
     So for the second reconstruction value R 2 =229 the third reconstruction value R 3 =224 is selected. The mode of operation according to the first list has the advantage that an organized saving and editing of the first list is easier, as the index of the first list X 3  is ascending linearly from 0 to 4. 
     The method is explained by way of example by equally large first and second quantization intervals. In general, the method described herein can also be adopted for first and/or second quantization intervals of differing sizes. Furthermore, the method can also be used for quantization intervals which instead of positive (data) values include negative and/or positive and negative (data) values. 
     In  FIG. 4  the method is displayed graphically in an alternative display format. In the first row there are displayed several first quantization intervals QI 1  and the associated first reconstruction values R 1 . Underneath that there follows in the second row the second quantization intervals QI 2  and the associated second reconstruction values R 2 , as well as in the third row the third quantization intervals QI 3  and the associated third reconstruction values R 3 . After the inverse first quantization IQ 1 , the first reconstruction values R 1  are each displayed on one of the second reconstruction values R 2 . Next to a bijective drawing from R 1  to R 2 , two or more, especially neighboring, first reconstruction values R 1  can also be displayed on an individual second reconstruction value R 2 . 
     For generating the third quantization intervals QI 3 , the interval boundaries of the second quantization intervals QI 2  are shifted in such a way that they correspond to their neighboring interval boundaries of the first quantization Q 1 . Furthermore, the third reconstruction values R 3  are generated in such a way, for example, that a value lying in the middle of the respective third quantization interval QI 3  is selected. As is shown according to  FIG. 4 , a third reconstruction value R 3  is thereby reassigned to each second reconstruction value R 2 . In addition to the use of equally large first or second quantization intervals QI 1 , QI 2 , the method or device is also applicable should the first quantization intervals QI 1  and/or second quantization intervals QI 2  be of different sizes. As can be seen from  FIG. 4 , for example, the second quantization intervals QI 2  are not exactly the same length. 
     In  FIG. 6  a device for carrying out the method is depicted. The third intermediate data value X 3 , which is generated because of the first or second quantization, is conveyed to the device V. In the device V, third quantization intervals QI 3  are generated with a first unit M 1  by shifting the interval boundaries of each of the second quantization intervals QI 2  to the nearest-located interval boundaries of the first quantization intervals QI 1 . Furthermore, with the aid of a second unit M 2  for the third quantization intervals QI 3 , the respective third reconstruction values R 3  are established in such a way that the third reconstruction value R 3  is located within the associated third quantization interval QI 3 , for example in the middle of the respective third quantization interval QI 3 . Subsequently, through a third unit M 3  of the device V, the corrected data value XR is generated by a third inverse quantization IQ 3  of the third intermediate value, or rather of the quantized data value X 3 , whereby the third inverse quantization IQ 3  is represented by the third quantization intervals QI 3  with the associated third reconstruction values R 3 . 
     The processing carried out through the first and the second units M 1 , M 2  are carried out only a single time at the initialization of the device V, for example. In contrast, further processing, carried out through the third unit M 3 , is adopted for every new quantized data value X 3 . The device V delivers on each output a corrected data value XR per quantized data value X 3 . With the aid of a fourth unit M 4 , extensions of the method can be implemented and carried out. 
     The device, or the method, be used within the scope of a fixed image decoding method VID. This is shown in  FIG. 7 . The coded data value {tilde over (X)} is thereby subjected to an inverse entropy coding E −1 . From this the quantized data value X 3  is generated, which represents e.g. a spectral coefficient. The device V carries out the method and generates the corrected data value XR, which is processed further within the scope of the fixed image decoding method VID, e.g. by an inverse transformation T −1 . The image reconstructed by the fixed image coding method VID can finally be returned to an image screen D. In the example envisaged according to  FIG. 7 , the quantized data value X 3  corresponds to a spectral coefficient coded within an 8×8 image block, within an image coded e.g. according to JPEG standard (JPEG—Joint Picture Expert Group). The mode of operation according to  FIG. 7  can also be usable in a video coding method, whereby only those quantized data values X 3  which are not made on the basis of a prediction of other pixels or images are edited with the aid of the device or method described herein. 
     The introduction of the method or the device within the scope of a hybrid video transcoder is described in more detail with the aid of  FIG. 8 . The first intermediate data value X 1 , L A  is calculated, with the aid of an inverse entropy coding E A   −1 , from an entropy-coded data value BS A ; and the second intermediate data value X 2 , Ŝ A  is calculated from the first intermediate data value X 1  by the first inverse quantization IQ 1 , Q A   −1 , and the second intermediate value X 2 , Ŝ A  undergoes the inverse transformation T A   −1 . To the data value obtained from this is added a predictor P from one of the preceding images, through which a modified second intermediate value X 2 ′ is generated. This predictor P is 0 is cases of non-predicted (intra-) images. Additional to motion vectors MV, a piece of information about the first quantizer level HQ 1  used in the first quantization Q 1  is delivered to the coder B (not shown). 
     To generate the third intermediate data value X 3 , an arrangement of the second coder C 2  according to  FIG. 8  is used. An arrangement of this kind is known to someone skilled in the art, for example from the video coder standard H.263 or H.264. After an optional subtraction of a data value—calculated by a predictor from one of the previous images—from the modified second intermediate data value X 2 ′, this subtracted data value ê TC  is coded with the aid of a transformation T A  into a transformed second intermediate value X 2 ″, S B , this transformed second intermediate value X 2 ″ is coded using the second quantization Q 2 , Q B  into the quantized data value X 3 , L B , and this is coded by an entropy coding E B  to a coded end value BS B . The second quantization Q 2  has the second quantization level HQ 2 . As can be seen from  FIG. 8 , the method is carried out on an identical basis, e.g. on transformed data values. This means that the second data value X 2  is inverse transformed and transformed again before the second quantization Q 2 . In order to achieve the identical data basis, the transformation T A  and the inverse transformation T A   −1  are inverse to one another. 
     In the feedback loop of the second coder, which grips the quantized data value X 3 , L B  after the second quantization Q 2 , the device V is introduced instead of the inverse second quantization otherwise conventional in the standard H.263. This, under consideration of the first and second quantizer levels HQ 1 , HQ 2 , generates an inverse quantized value Ŝ B , which is introduced for the further coding, e.g. the inverse transformation T A   −1 . 
     In this exemplary embodiment according to  FIG. 8 , the device or rather the method is used in the feedback loop. In order to ensure that the second decoder D 2 , e.g. integrated in a terminal device (not shown), can accomplish an error-free decoding of the quantized data values X 3 , the quantizer levels HQ 1 , HQ 2  of the first and second quantization Q 1 , Q 2  are transmitted e.g. to the second decoder D 2 . 
     With the aid of  FIG. 5 , the improvement achieved in the image quality will be explained in more detail using the method.  FIG. 5  shows, as has already been explained in more detail in  FIG. 2 , the first and second reference curves R 1 , R 2 . The curves XR, R* labeled “x” and “*” represent the image quality when using the method. If the method is merely adopted on one decoder (variant  2 ), as is explained for example with the aid of  FIG. 7 , then the second curve XR marked “x” is generated. This variant  2  shows a clear improvement as compared with the second reference curve R 2 . If the method is additionally carried out in a transcoder unit, as for example is explained in more detail with the aid of  FIG. 8  (variant  1 ), then a further quality improvement can be achieved. This can be seen in  FIG. 5  by the “*”s in the first curve R*. 
     In an extension to the method, the third reconstruction value R 3  of the third quantization interval QI 3  can be generated from at least one of those first reconstruction values R 1  of the respective first quantization intervals which are located within the observed third quantization interval QI 3 . Reference is made to  FIG. 4  for explanation in greater detail. If the first and third quantization intervals QI 1 , QI 3  on the left side of  FIG. 4  are observed, the respective interval boundary of the first and third quantization interval QI 1 , QI 33  is identical. In order to determine the third reconstruction value R 3  of this third quantization interval QI 3 , the third reconstruction value R 3  can e.g. be chosen identically to the first reconstruction value R 1 . 
     On the other hand, the right hand third quantization interval QI 3  in  FIG. 4  includes two first quantization intervals QI 1 . In order to determine a third reconstruction value R 3  for this third quantization interval QI 3 , either one of the two first reconstruction values R 13 , R 14  of the two right quantization intervals QI 1  can be selected. In an alternative embodiment to this, the third reconstruction value R 3  can be generated from a combination of the first two reconstruction values R 13 , R 14 . For example, the third reconstruction value R 3  is calculated through a weighted mean. Formally, this looks like e.g.:
 
 R 3=0.5*( R 13+ R 14)=0.5*(240+208)=224
 
     The values for R 13 =208 and R 14 =240 were taken from  FIG. 3 . As can also be taken from  FIG. 3 , R 3 =224 is generated. Instead of determining a mean, each of the first reconstruction values R 1  can be charged with an individual factor, and by addition of the weighted first reconstruction values R 13 , R 14  the third reconstruction value R 3  is determined. 
     In an alternative extension of the method, the third reconstruction values of every third quantization interval are generated in such a way that the third reconstruction value R 3  corresponds to a value with a highest probability of appearing within the associated third quantization interval QI 3 . 
     Moreover, the third reconstruction value R 3 , as is shown in greater detail with reference to  FIG. 9 , can be calculated on the basis of a relative frequency of appearance of a value of a data value, for example of the uncoded data value X 0 , and of the quantization error associated with the respective value. In the left half of  FIG. 9  there is a relative frequency LPF(.) for the appearance of a value of an uncoded data value for a selected third quantization interval QI 3 . If a mean quantization error MQF for the selected third quantization interval QI 3  is calculated, then the third reconstruction value R 3 * can be placed in the position within the third quantization interval QI 3  which generates the smallest mean quantization error MQF. The mean quantization error MQF for every possible value R 3 ′ of a data value within the observed third quantization interval QI 3  is calculated e.g. by the following equation: 
                     MQF   ⁡     (     R   ⁢           ⁢     3   ′       )       =       ∫     i   =     UI   ⁡     (     QI   ⁢           ⁢   3     )           OI   ⁡     (     QI   ⁢           ⁢   3     )         ⁢     [       LPF   ⁡     (   i   )       *       (       R   ⁢           ⁢     3   ′       -   i     )     2       ]               (   1   )               
whereby the lower interval boundary is UI and the upper interval boundary OI, and the quadratic (quantization) error is expressed by the term (R 3 ′−i) 2 . Furthermore, the value R 3 ′ takes values between the lower and the upper interval boundary UI, OI. If only discrete values are used, then in equation (1) a summation is made from the integral.
 
     Subsequently, the mean quantization errors MQF are analyzed depending on value R 3 ′, see e.g. the right graph of  FIG. 9 , and that value R 3 ′ for the third reconstruction value R 3 * is chosen which gives the smallest mean quantization error MQF. This is expressed mathematically as:
 
 R 3*=min[MQF( R 3′)]  (2)
 
     Alongside this mode of operation there are further alternatives for calculating the smallest mean quantization error MQF known to those skilled in the art, such as calculating the quantization error with a norm formula |R 3 ′−i| instead of the mean quadratic quantization error (R 3 ′−i) 2 . 
     Instead of using a relative frequency LPF calculated by measurement of the uncoded data values X 0 , a predetermined statistic can also be used. A good approximation for a relative frequency LPF for uncoded data values X 0  is generated by the use of a Laplace distribution. A Laplace function or Laplace distribution is known from the prior art to those skilled in the art. The mode of operation for calculating the smallest mean quantization error by adopting a Laplace function is analogous to the above embodiment. 
     By the use of a relative frequency, the quantization error can be further reduced. Attention is drawn to this in  FIG. 10 , in which next to the first and the second reference curves R 1 , R 2  and the curve R* according to variant  1  a further results curve Rxx is displayed which introduces the Laplace distribution as relative frequency (variant  3 ). Variant  3  is related to the introduction of the method in the transcoder TR and the second decoder D 2 . As can be taken from  FIG. 10 , through the introduction of the relative frequency to determine the third reconstruction value R 3 * a raising of the PSNR and hence an improvement of the image quality, or rather a reduction of the quantization error, is achieved. With the aid of the fourth mean M 4 , extensions to the method, such as the use of the relative frequency for calculating the third reconstruction value R 3 *, can be implemented and carried out. 
     The system also includes permanent or removable storage, such as magnetic and optical discs, RAM, ROM, etc. on which the process and data structures of the present invention can be stored and distributed. The processes can also be distributed via, for example, downloading over a network such as the Internet. The system can output the results to a display device, printer, readily accessible memory or another computer on a network. 
     A description has been provided with particular reference to preferred embodiments thereof and examples, but it will be understood that variations and modifications can be effected within the spirit and scope of the claims which may include the phrase “at least one of A, B and C” as an alternative expression that means one or more of A, B and C may be used, contrary to the holding in  Superguide v. DIRECTV,  358 F3; d 870, 69 USPQ2d 1865 (Fed. Cir. 2004).