Facsimile and static presentation processing – Facsimile – Recording apparatus
Patent
1993-12-09
1996-05-21
Tran, Thai O.
Facsimile and static presentation processing
Facsimile
Recording apparatus
358906, 348403, 364725, H04N 7133
Patent
active
055195032
DESCRIPTION:
BRIEF SUMMARY
TECHNICAL FIELD
This invention relates to an improvement in a picture reproducing device in which original picture data is restored from picture data compressed by orthogonal transform.
BACKGROUND ART
In general, picture data located at proximate positions exhibit strong correlation, so that, on orthogonal transform on the frequency domain, high-frequency components become approximately zero. The data volume can be diminished by taking advantage of this feature. That is, picture data are first formed into blocks, each made up of, for example, 8.times.8 pixels, and a discrete cosine transform (DCT) is performed for each block. The data on the frequency space, produced on DCT, is re-quantized and variable length coded for data compression.
For restoring picture data from the compressed data, the variable length encoded data are first decoded and subsequently the re-quantized data are decoded by way of an inverse operation of re-quantization. The picture data compressed by DCT are processed with inverse discrete cosine transform (IDCT) followed by block resolution.
Heretofore, 8-dimensional DCT is performed as a system of compressing picture data by orthogonal transform.
In an 8-dimensional DCT, picture data x.sub.i for respective pixels (i=0, 1, 2, . . . ) are formed into blocks at a period of 8 dots in the horizontal direction (X-direction) and at a period of 8 dots in the vertical direction (Y-direction) for generating matrices X each consisting of 64-dot picture data (elements) x.sub.ij in a real space, where 0.ltoreq.i , j.ltoreq.7. The picture data is transformed for each of the matrices X for producing matrices C each consisting of 64-elements c.sub.ij in a space of the spatial frequency, where 0.ltoreq.i, j.ltoreq.7. The matrix X in the real space and the matrix C in the space of the spatial frequency may be expressed by the following equations 1 and 2: ##EQU1##
In such case, DCT may be defined by the following equation (3), using a matrix of DCT transform matrix and a transposed matrix N.sup.t thereof: ##STR1##
The transform shown by the equation 3 may be resolved into multiplication of each of eight eight-element column vectors, divided from the matrix X, by a matrix N, and multiplication of each of eight eight-element row vectors, divided from a matrix resulting from the first-stated multiplication, with the transposed matrix N.sup.t.
For restoring the picture data compressed by the DCT, 8-dimensional IDCT is employed. With the IDCT, a matrix X in the real space is produced from the matrix C on the space of the spatial frequency, using the matrix of IDCT transform N' and a transposed matrix N'.sup.t thereof. The transform may be defined by the following equation (4): ##STR2##
The transform of the equation (4) may also be resolved into the multiplication of an eight-column column vectors on the space of the spatial frequency by the matrix of transform N' and the multiplication of an eight-row row vectors of a matrix resulting from the first-stated multiplication by the transposed matrix N'.sup.t.
With the above-described 8-dimensional DCT, 8-dot picture data on the coordinate x may be resolved into eight-component coefficients, namely a dc level not having a zero-crossing point and a cosine wave B having one zero-crossing point up to a cosine wave H having seven zero-crossing points, as shown in FIG. 1, The matrix of DCT transform according to the equation (3) is constituted by eight eight-element base unit vectors. These eight base unit vectors are constituted by data produced on sampling the dc level and cosine waves shown at A to H in FIG. 1 at eight points dividing the eight-dot width thereof into seven equal lengths.
Meanwhile, the elements of the matrix of the DCT transform N and the matrix of the IDCT transform N' are all irrational numbers, so that, if the above transform is to be executed with high accuracy, a multiplication circuit having a sufficiently long word length is required, and hence the circuit scale is increased on the whole. On the other hand, if picture data is compressed
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Kananen Ronald P.
Nguyen Huy
Sony Corporation
Tran Thai O.
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