Abstract:
An input digital video signal is encoded to produce at least first and second hierarchical data signals which respectively represent a first video signal and a lower resolution video signal. Each pixel data signal of the second hierarchical data signal is calculated as an average of N pixel data signals of the input digital video signal. The second hierarchical data signal is output together with first hierarchical pixel data signals representing only N−1 of the N pixel data signals of the input digital video signal. The first hierarchical pixel data signals may be differential signals produced by subtracting each of the N−1 pixel data signals from the average value of the N pixel data signals. During decoding the Nth pixel data signal is reconstructed from the N−1 pixel data signals and the average value provided as the corresponding second hierarchical pixel signal.

Description:
This application is a continuation of Ser. No. 08/251,173 filed May 31, 1994 abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to an hierarchical encoding apparatus which divides a digital image signal into a plurality of signals that represent images having different respective resolutions, and encodes such signals for transmission. The invention also relates to a corresponding hierarchical decoding apparatus. 
     2. Description of Related Art 
     There has been proposed a digital image signal encoding technique in which a high resolution image signal is received as a first hierarchical image signal, a second hierarchical image signal having a lower resolution than the first signal is formed therefrom, a third hierarchical image signal having a lower resolution than the second is formed, and so forth. This technique is referred to as a hierarchical encoding technique. According to this technique, a plurality of hierarchical image signals are transmitted through a single transmission path (one communication channel or one recording and reproducing process). on the receiving side, the transmitted image data can be reproduced by a television monitor corresponding to any one of the hierarchical levels. 
     More specifically, it is known to use video signals having various degrees of resolution, such as standard resolution, high resolution, and low resolution. Conventional television signals are an example of standard resolution video signals. High definition television signals are an example of high resolution video signals. Low resolution video signals may be used, for example, to retrieve image data at high speed from an image data base and to display the same on a computer display. The hierarchical encoding technique may be used for enlargement and reduction of images, as well as for providing video signals of varying degrees of resolution. Hierarchical encoding may be applied to reduction of images without changing the level of resolution. 
     FIG. 8 illustrates an example of an apparatus which carries out the above-described hierarchical encoding technique. According to this example, the apparatus outputs three levels of hierarchical signals, with the number of pixels in the second hierarchical image signal being one-quarter of the number of pixels in the first hierarchical image signal and the number of pixels in the third (highest) hierarchical image signal being one-sixteenth of the number of pixels in the first hierarchical image signal. As shown in FIG. 8, an input digital image signal, corresponding to the first hierarchical signal, is provided at an input terminal  41 . The input signal is supplied from the input terminal  41  to a thin-out circuit  42  and a subtracting circuit  43 . The output of the thin-out circuit  42  is provided to an encoding circuit  45  through another thin-out circuit  44 . The output of the encoding circuit  45  is provided at a third hierarchical output terminal  53 . The thin-out circuits  42  and  44  each reduce the number of pixels in the input signal supplied thereto by one half in both of the horizontal and vertical directions. Thus, the number of pixels in the output signal of each of the thin-out circuits  42  and  44  is one-quarter of the number of pixels in the respective input signal for those circuits. Accordingly, the number of pixels in the output signal of the thin-out circuit  44  is one-sixteenth of the number of pixels in the input signal for the thin-out circuit  42 . 
     The encoding circuit  45  encodes the signal output from the thin-out circuit  44  and provides a resulting encoded signal to the output terminal  53 . Typically, the thin-out circuits  42  and  44  are formed of thin-out filters. 
     In addition, the signal output from the thin-out circuit  42  is supplied to an interpolating circuit  46  and a subtracting circuit  47 . The interpolating circuit  46  performs interpolation to supply pixels that have been thinned out by the thin-out circuit  42 . The output signal from the interpolating circuit  46  is supplied to the subtracting circuit  43 , which calculates the difference, pixel by pixel, between the input image signal provided at input terminal  41  and the output signal from the interpolating circuit  46 . The resulting differential signal is supplied from the subtracting circuit  43  to an encoding circuit  48 , which is, in turn, connected to provide an encoded output signal to a first hierarchical output terminal  51 . 
     The output signal from the thin-out circuit  44  is supplied to a subtracting circuit  47  by way of an interpolating circuit  49 . In a similar manner to the subtracting circuit  43 , the subtracting circuit  47  calculates a differential value, pixel by pixel, between the output signal from the thin-out circuit  42  and the interpolated output signal from the interpolating circuit  49 . The differential signal provided by the subtracting circuit  47  is supplied to an encoding circuit  50 , which, in turn, supplies an encoded output signal to a second hierarchical output terminal  52 . In general, the interpolating circuits  46  and  49  are formed of interpolating filters. The encoding circuits  45 ,  50 , and  48  perform compression-encoding upon the input signals supplied thereto. 
     Encoded differential signals corresponding to the first and second hierarchies are respectively provided at the output terminals  51  and  52 , and an encoded signal (not a differential signal) corresponding to the third hierarchy is provided at the output terminal  53 . It will be seen that in the conventional hierarchical encoding apparatus of FIG. 8 higher-order hierarchical signals are obtained by thinning out lower-order hierarchical signals. With respect to each of the lower-order hierarchical signals, the apparatus forms differential data by subtracting an input signal from a higher-order interpolated signal. Then the highest-order signal, and the differential data in the other signals, are compression encoded. 
     A decoding apparatus which corresponds to the encoder of FIG. 8 is illustrated in block diagram form in FIG.  9 . As shown in FIG. 9, the transmitted first, second and third hierarchical signals are respectively received by the decoding apparatus at input terminals  61 ,  62  and  63 . A decoding circuit  64  is supplied with the third hierarchical signal received through the input terminal  63 , and a decoded output signal from the decoding circuit  64  is provided as a third hierarchical output signal at an output terminal  73 . The signal output from the decoding circuit  64  is also supplied to an interpolating circuit  67 . 
     The encoded differential signal corresponding to the second hierarchical level is supplied from the input terminal  62  to a decoding circuit  65  and the decoded differential signal output from the decoding circuit  65  is supplied to an adding circuit  68 . The adding circuit  68  adds the interpolated signal output from the interpolating circuit  67  and the differential signal received from the decoding circuit  65  to form a second hierarchical output signal which is provided at an output terminal  72 . The output signal from the adding circuit  68  is also provided as an input signal to an interpolation circuit  69 . 
     An encoded differential signal corresponding to the first hierarchical level is provided to a decoding circuit  66  from the input terminal  61 . The decoding circuit  66  outputs a decoded differential signal which is supplied to an adding circuit  70 . The adding circuit  70  adds an interpolated signal output from the interpolating circuit  69  and the decoded differential signal received from the decoding circuit  66  to form a first hierarchical output signal which is supplied to an output terminal  71 . 
     In the above-described conventional hierarchical encoding technique, as the number of hierarchical signal levels is increased, the amount of data to be transmitted also disadvantageously increases. For example, when two hierarchical signal levels are provided with thinning out at a rate of 1:4, the amount of data to be transmitted is increased by a factor of 1.25 (1+¼). With similar thinning out and three hierarchical levels, the amount of data is increased by a factor of about 1.31 (1+¼+{fraction (1/16)}). As the number of hierarchies increases, the number of pixels to be transmitted also continues to increase. Thus, it will be seen that there is a trade-off in conventional hierarchical encoding techniques between encoding efficiency and the number of hierarchical signal levels to be provided. 
     It should also be noted that according to the conventional encoding scheme described above, data compression is achieved by encoding differential values obtained with respect to input image data and reference image data formed by interpolating a thinned out signal. This interpolation process must then be duplicated on the decoder side to provide a reference image signal to which the transmitted differential value can be added. However, the need to interpolate at the decoder side results in delay and a relatively large hardware scale. 
     OBJECTS AND SUMMARY OF THE INVENTION 
     Accordingly, it is an object of the present invention to provide a method and apparatus for performing hierarchical encoding on a digital image signal without reducing encoding efficiency and with decreased delay and hardware scale on the decoding side. It is also an object to provide a decoding apparatus and method corresponding to the encoding apparatus and method. 
     In accordance with an aspect of the present invention, there is provided an apparatus for encoding an input digital video signal to produce at least first and second hierarchical data signals which respectively represent a first video signal and a second video signal having a resolution that is lower than a resolution of the first video signal, with the apparatus comprising means for receiving the input digital video signal and for generating the second hierarchical data signal by calculating each pixel data signal of the second hierarchical data signal as a linear combination of N pixel data signals of the input digital video signal, and means for outputting the generated second hierarchical data signal together with first hierarchical pixel data signals representing only N−1 of the N pixel data signals of the input digital video signal. 
     According to another aspect of the invention, the means for receiving and generating includes means for calculating an average value of four pixel data signals a, b, c, d of the input digital video signal to produce a pixel data signal m1 of the second hierarchical data signal. According to yet another aspect of the invention, the apparatus further includes means for subtracting the average value pixel data signal m1 from each of the input pixel data signals a, b, c to produce differential data signals Δa, Δb, Δc, with the average pixel data signal m1 being output as a pixel data signal of the second hierarchical data signal, and the differential data signals Δa, Δb, Δc being output as the first hierarchical pixel data signals representing only the N−1 pixel data signals of the input digital video signal. 
     In accordance with still another aspect of the present invention, there is provided an apparatus for decoding first and second hierarchical data signals which respectively represent a first video signal and a second video signal having a resolution that is lower than a resolution of the first video signal, with the apparatus including means for receiving a pixel data signal of the second hierarchical data signal and data signals representing N−1 pixels of the first hierarchical data signal, and means for calculating an Nth pixel data signal of the first hierarchical data signal from the received pixel data signal of the second hierarchical data signal and the received data signals representing N−1 pixels of the first hierarchical data signal. 
     According to still further aspects of the invention, N=4 and the means for calculating calculates the Nth pixel data signal by subtracting a sum of the received data signals representing the N−1 pixels from four times the received pixel data signal of the second hierarchical data signal; and, alternatively, the received data signals representing the N−1 pixels are differential signals, and the means for calculating calculates the Nth pixel data signal by subtracting a sum of the received data signals representing the N−1 pixels from the received pixel data signal of the second hierarchical data signal. 
     With the encoding technique in accordance with the present invention, a higher-order hierarchical signal is formed as an average value of lower-order signals, so that data representing a lower-order pixel (or corresponding differential data) can be omitted from transmission and then reconstructed on the receiving side. In this way, the number of pixels to be transmitted does not increase with provision of hierarchical signal levels. Further, the time required for calculation on the decoder side is decreased, thereby permitting high speed processing for decoding. Further, the hardware scale on the decoder side in relatively small. 
     The above, and other objects, features and advantages of the present invention will be apparent from the following detailed description thereof which is to be read in connection with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of an encoding apparatus according to a first embodiment of the present invention; 
     FIG. 2 is a block diagram of a decoding apparatus according to the first embodiment of the present invention; 
     FIG. 3 is a schematic illustration of hierarchical encoding performed according to the first embodiment of the invention; 
     FIG. 4 is a schematic illustration of hierarchical encoding performed according to a second embodiment of the present invention; 
     FIG. 5 is a block diagram of an encoding apparatus according to the second embodiment of the invention; 
     FIG. 6 is a block diagram of a decoding apparatus according to the second embodiment of the invention; 
     FIG. 7 schematically illustrates compression encoding techniques that may be used in the encoding apparatus according to the present invention; 
     FIG. 8 is a block diagram of a conventional hierarchical encoding apparatus; and 
     FIG. 9 is a block diagram of a conventional decoding apparatus corresponding to the encoding apparatus of FIG.  8 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A first preferred embodiment of the invention will now be described with reference to FIGS. 1-3. 
     As shown in FIG. 1, an encoder for providing four hierarchical image signals in accordance with the first embodiment includes an input terminal  1  to which an input digital image signal is supplied. An averaging circuit  2  is connected to receive the input digital image signal, and the input digital image signal is also supplied to an encoding circuit  8 . 
     According to the first embodiment, a first hierarchical signal is formed directly from the input signal, by encoding at the encoding circuit  8 , and is output via a first hierarchical output terminal  12 . 
     FIG. 3 schematically illustrates images corresponding to the first through fourth hierarchical signals. A portion (8 pixels by 8 pixels) of the image corresponding to the first hierarchy, which is also the input image, is shown in the lower-most portion of FIG.  3 . In FIG. 3, each square represents one pixel. 
     Thus, the averaging circuit  2  outputs an average value of four pixels (2 pixels by 2 pixels) to produce pixel data for the image corresponding to the second hierarchy. More specifically, the averaging circuit  2  forms a pixel value m1 for a pixel of the second hierarchical signal according to the formula m1=¼×(a+b+c+d). Accordingly, the averaging circuit  2  outputs a 4 pixel by 4 pixel portion of the image for the second hierarchy which corresponds to the 8 pixel by 8 pixel portion of the input image. 
     The signal output from the averaging circuit  2  is supplied to an averaging circuit  3  and also to an encoding circuit  7 . The encoding circuit  7  encodes the signal supplied thereto and outputs an encoded second hierarchical signal via a second hierarchical output terminal  11 . 
     The averaging circuit  3  calculates an average value of 4 pixels (2 pixels by 2 pixels) of the image corresponding to the second hierarchy. The resulting average value provided by the averaging circuit  3  corresponds to a pixel in the image corresponding to the third hierarchy. In other words, the averaging circuit  3  calculates the value of a pixel M1 of the third hierarchical signal according to the formula M1=¼×(m1+m2+m3+m4). As a result, the averaging circuit  3  generates a 2 pixel by 2 pixel portion of the image for the third hierarchy which corresponds to the 8 pixel by 8 pixel portion of the input signal. 
     The signal output from the averaging circuit  3  is supplied to an averaging circuit  4  and also to an encoding circuit  6 . The encoding circuit  6  encodes the signal supplied thereto and outputs an encoded third hierarchical signal via a third hierarchical output terminal  10 . 
     The averaging circuit  4  calculates an average value of 4 pixels (2 pixels by 2 pixels) of the third hierarchical signal. More specifically, the averaging circuit  4  calculates a pixel value M according to the formula M=¼×(M1+M2+M3+M4). Accordingly, the averaging circuit  4  outputs a fourth hierarchical pixel signal which corresponds to an 8 pixel by 8 pixel portion of the input image. The output signal from the averaging circuit  4  is supplied to an encoding circuit  5 , which, in turn, outputs an encoded fourth hierarchical output signal via a fourth hierarchical output terminal  9 . 
     As can be seen from FIG. 3, the number of pixels in the higher-order hierarchical signals is decreased with respect to the first hierarchical signal by factors of 1:4, 1:16 and 1:64, respectively. Thus, if the area of the image is maintained constant, the resolution correspondingly decreases as the number of pixels decreases. On the other hand, if the distance between pixels is kept constant, the size of the image correspondingly decreases. 
     The encoding circuits  5 ,  6 ,  7  and  8  perform compression-encoding on the data to be transmitted. In addition, the encoding circuits  6 ,  7  and  8  corresponding to the lower-order hierarchical signals suppress part of the data supplied thereto for transmission. More specifically, the encoding circuits  6 ,  7  and  8  each omit from transmission one of every four pixels, thereby preventing the amount of data to be transmitted from increasing due to the provision of the hierarchical signals. For example, the encoding circuit  7  receives average values m1, m2, m3 and m4 from the averaging circuit  2 . If data corresponding to all four of the average values were transmitted, the amount of data to be transmitted would increase, thus reducing transmission efficiency. To overcome this problem, the encoding circuit  7  omits from transmission one of the four average values, for example, m4. Similarly to encoding circuit  7 , the encoding circuits  6  and  8  also omit from transmission one of every four pixel values. In FIG. 3, the lower right-hand pixel of every group of four pixels (2 pixels by 2 pixels) is marked with a slant line to indicate that such pixel is omitted from transmission. It will be understood that with respect to the second and third hierarchical signals, the omitted pixel is an average value of pixels in the next lower-order hierarchical signal, whereas in the first hierarchy, the omitted pixel is a pixel of the input signal. 
     Thus, the total number of pixel signals to be transmitted in such a hierarchical encoding system can be calculated by adding 48+12+3+1 (proceeding from the lowest hierarchical level to the highest hierarchical level), yielding a total of 64 pixels, which is the same as the number of pixels in the input image. It will be noted that a hierarchical encoding system has been provided without increasing the total number of pixels to be transmitted. 
     There will now be described, with reference to FIG. 2, a decoding apparatus according to the first embodiment of the invention, and corresponding to the encoding apparatus of FIG.  1 . 
     In FIG. 2, fourth through first hierarchical data signals, transmitted from the above-described encoder, are respectively supplied to input terminals  21 - 24 . Decoding circuits  25 - 28  are respectively connected to receive the signals provided at the input terminals  21 - 24 . The decoding circuits  25 - 28  perform decoding that reverses the compression-encoding performed by the encoding circuits  5 - 8  of FIG.  1 . 
     Continuing to refer to FIG. 2, the decoded output signal provided by decoding circuit  25  is supplied to a fourth hierarchical output terminal  32 . The output signal from decoding circuit  25  is also supplied to a data reproducing circuit  29 . The data reproducing circuit  29  also receives a decoded output signal from the decoding circuit  26 . The data reproducing circuit  29  reconstructs data corresponding to pixels which were omitted from transmission on the encoder side. For example, if the data signal corresponding to pixel M4 was omitted from transmission, and consequently not received at the decoder of FIG. 2, the data reproducing circuit  29  calculates M4 according to the formula M4=4M−(M1+M2+M3) in order to reconstruct M4. It will be noted that the above formula is deriveable from the formula M=¼×(M1+M2+M3+M4), by which the corresponding fourth hierarchical pixel signal M was originally calculated on the encoder side. Thus the data reproducing circuit  29  outputs a third hierarchical output signal, including a reconstructed pixel signal, via a third hierarchical output terminal  33 . 
     The output signal from the data reproducing circuit  29  is also supplied to a data reproducing circuit  30  which also receives a decoded output signal from the decoding circuit  27 . The data reproducing circuit  29  reconstructs data which has not been transmitted in a similar manner to the processing performed by data reproducing circuit  29 . In particular, if data corresponding to a pixel m4 has been omitted from transmission, the data for such pixel is reconstructed at the data reproducing circuit  30  according to the formula m4=4M1−(m1+m2+m3). The resulting reconstructed signal, along with signals corresponding to data pixels which were transmitted, is output from the data reproducing circuit  30  via a second hierarchical output terminal  34 , and is also supplied to a data reproducing circuit  31 . 
     The data reproducing circuit  31  also receives a decoded output signal from the decoding circuit  28 . Again the data reproducing circuit  31  processes the data supplied thereto in a similar manner to the previously discussed data reproducing circuits  29  and  30 . Again, assuming that the signal corresponding to a pixel d was omitted from transmission, this signal is reconstructed in the data reproducing circuit  31  according to the formula d=4m1−(a+b+c). The reconstructed signal, together with signals representing pixels that were not omitted from transmission, is output by the data reproducing circuit  31  as a first hierarchical output signal via a first hierarchical output terminal  35 . 
     Thus, when a pixel signal in a desired hierarchical level is not directly represented in the received signal, the missing pixel signal can be reconstructed on the basis of a pixel signal in the next higher-order hierarchical signal. Where the pixel from the next hierarchical level also is not present, a pixel from still the next level can be used. In a worst case, the corresponding pixels in all levels except the highest level have not been transmitted, but even in this case the missing data can be reconstructed using the corresponding pixel in the highest hierarchical level. 
     A second preferred embodiment of the present invention will now be described with reference to FIGS. 4-6. In this second embodiment, as indicated by FIG. 4, three hierarchical signal levels are provided, rather than the four levels provided in the first embodiment shown in FIG.  1 . 
     FIG. 5 illustrates an encoding apparatus in accordance with the second embodiment. Elements of the encoding apparatus of FIG. 5 which correspond to those of the encoder of FIG. 1 have been assigned the same reference numerals as in FIG.  1 . An input digital image signal is provided at an input terminal  1  and this input signal is received from the input terminal  1  by an averaging circuit  2 , as well as a subtracting circuit  13 . The subtracting circuit  13  generates differential data by subtracting average values generated by the averaging circuit  2  from input image pixel signals (corresponding to first hierarchical signals). As in the embodiment of FIG. 1, averaging circuit  2  calculates a second hierarchical pixel signal value m1 as the average of four input pixels a, b, c, d, which form a 2 pixel by 2 pixel array in the input image. The subtracting circuit  13  forms differential data corresponding to three of the four pixels, omitting the fourth pixel, assumed in this case to be pixel d. In particular, the subtracting circuit  13  forms differential data according to the formulas Δa=a−m1, Δb=b−m1, and Δc=c−m1. 
     The resulting differential data output from the subtracting circuit  13  is supplied as a first hierarchical output signal to a first hierarchical output terminal  12  by way of an encoding circuit  8 . 
     The output signal from the averaging circuit  2  is also supplied to an averaging circuit  3  and a subtracting circuit  14 . In a similar manner to the subtracting circuit  13 , the subtracting circuit  14  forms differential data on the basis of average values corresponding to second hierarchical signal pixels, as calculated by averaging circuit  2 , as well as average value signals provided by averaging circuit  3 . It will be recognized that averaging circuit  3  generates its output signals by averaging four signals provided thereto from the averaging circuit  2 . The subtracting circuit  14  forms differential data according to the formulas Δm1=m1−M1, Δm2=m2−M1, and Δm3=m3−M1. As before, the subtracting circuit  14  does not form differential data corresponding to the fourth pixel value, m4. 
     Differential data output from the subtracting circuit  14  is supplied as a second hierarchical output signal to a second hierarchical output terminal  11  by way of an encoding circuit  7 . Finally, the highest (i.e., third level) hierarchical signal is obtained by encoding the signals output by the averaging circuit  3  at an encoding circuit  6 . The encoded third hierarchical signal is supplied to an output terminal  10  by the encoding circuit  6 . No data signals formed by the averaging circuit  3  are omitted from transmission in the third hierarchical signal. 
     As is shown in FIG. 4, in the second embodiment the total number of pixels to be transmitted is 48+12+4=64, which is the same number of pixels as were present in the input image, even though three hierarchical signal levels are provided in the transmitted signal. (In FIG. 4, as in FIG. 3, each small square represents a pixel, and pixels marked with a slant line are omitted from transmission.) 
     It should be noted that the compression encoding carried out in encoding circuits  5 ,  6 ,  7  and  8  (in FIGS. 1 and 5) may employ linear quantization, non-linear quantization, or an adaptive quantization technique such as ADRC (Adaptive Dynamic Range Coding). 
     The respective portions of FIG. 7 portray examples of quantizing techniques using linear quantizing units and non-linear quantizing units. Such techniques can reduce the number of bits transmitted per pixel, thereby compressing the total amount of data to be transmitted. These quantization-based compression coding techniques are well known to those who are skilled in the art, and so need not be further described. 
     FIG. 6 illustrates a decoding apparatus which corresponds to the encoding apparatus of FIG.  5 . As shown in FIG. 6, data signals corresponding to the third, second and first hierarchical levels are respectively provided at input terminals  22 ,  23  and  24 . Decoding circuits  26 ,  27  and  28  are respectively connected to the input terminals  22 ,  23  and  24  to decode the respective hierarchical signals. It will be appreciated that the decoding performed in the decoding circuits  26 - 28  reverses the compression-encoding performed in the encoding circuits  6 - 8 . 
     Decoded data output from the decoding circuit  26  is provided as a third hierarchical output signal at an output terminal  33 . 
     The decoding circuits  27  and  28  respectively output decoded differential data corresponding to the second and first hierarchical levels. The differential data are respectively supplied to differential value reproducing circuits  36  and  37 . The differential value reproducing circuits  36  and  37  each reconstruct a differential value that has been omitted from transmission on the basis of three differential values that have not been omitted. This can be done because, for example, Δa+Δb +Δc+Δd=a+b+c+d−4m1=0. Thus, when Δa, Δb and Δc are all known, the missing first hierarchical value Δd can be reconstructed at the differential value reproducing circuit  37  according to the formula Δd=−(Δa+Δb+Δc). A similar calculation can be made at the differential value reproducing circuit  36  to reconstruct second hierarchical differential data that has been omitted from transmission. The differential data output from the differential value reproducing circuit  36 , including transmitted differential values and reconstructed differential values, is supplied to an adding circuit  38 , at which the differential values are added to decoded third hierarchical average value data provided from the decoding circuit  26 . The resulting data signals output from the adding circuit  38  are provided as a second hierarchical output signal at an output terminal  34 . 
     Similarly, differential data, including both transmitted and reconstructed values, is output from the differential value reproducing circuit  37  to an adding circuit  39 , at which the first hierarchical output signal is formed by adding the differential data from the differential value reproducing circuit  37  to the second hierarchical signal data provided from the adding circuit  38 . Thus, the adding circuit  39  outputs a first hierarchical output signal to an output terminal  35 . 
     Completing the example given above with respect to the reproducing circuit  37 , it will be understood that the “non-transmitted” pixel d is, in effect, reconstructed according to the formula d=m1+Δd=m1−(Δa+Δb+Δc). 
     According to the second embodiment, if a data base of high definition television still images is provided, the first hierarchical output signal, available at the terminal  35 , provides reproduced data having the same resolution as the original images, i.e., high definition television images. The second hierarchical output signal provides a reproduced image with the resolution of standard television images, and the third hierarchical output signal provides a high speed retrieval image with low resolution. 
     It will be recognized that when compression-encoding is used to decrease the amount of information to be transmitted, the reproduced image data obtained upon decoding may not be exactly the same as the original input image. However, there are known techniques for hiding the differences so that deterioration in image quality is not perceived. Although it is preferred to provide the compression-encoding circuits  5 - 8  as described with respect to FIGS. 1 and 5, it is also within the contemplation of the invention to dispense with such compression-encoding. 
     It should also be recognized that a weighted average calculation or the like can be employed in averaging circuits  2 - 4  of FIGS. 1 and 5, rather than the simple arithmetic mean calculation described above. 
     By using the techniques described above, the present invention makes it possible to provide a plurality of hierarchical data signals without increasing the number of pixel data signals to be encoded and transmitted. Thus, encoding efficiency is not reduced. Further, in order to minimize delay upon decoding, reconstruction of a non-transmitted pixel in a particular hierarchical signal is performed on the basis of a pixel signal in the next higher hierarchical level. Moreover, because an averaging process is performed to generate higher-order hierarchical signals, interpolating filters are not required, thereby preventing the hardware scale from increasing. 
     Having described specific preferred embodiments of the present invention with reference to the accompanying drawings, it is to be understood that the invention is not limited to those precise embodiments, and that various changes and modifications may be effected by one skilled in the art without departing from the scope or spirit of the invention as defined in the appended claims.