Digital image recording apparatus and method

Abstract: In a digital image recording apparatus, an image processing is carried out on a first digital image signal obtained by sampling at a predetermined density an image signal representing an original image. The image processing is for increasing the amount of information carried by the first digital image signal and reducing frequency components of the first digital image signal which are higher than the Nyquist rate of the first digital image signal, thereby obtaining a second digital image signal. The second digital image signal is reproduced on a recording medium at a density higher than the predetermined density, thereby forming an image which is higher in resolution than that obtained from the first digital image signal and equal to that obtained from the first digital image signal in size.

Description: Field of the Invention This invention relates to a digital image recording apparatus and a digital image recording method according to the preamble of claim 1 and claim 2, respectively, particularly to those for visually completely restoring on a recording medium image information components at frequencies not higher than the Nyquist rate included in digital image information. Description of the Related Art There have been known an image recording apparatus such as laser printers, thermal printers and the like for recording a digital image in an actual size or to an enlarged or reduced scale. In such an image recording apparatus, a digital image signal obtained by sampling an analog image signal is subjected to a predetermined image processing, as required, for instance, to an interpolation processing in the case where the image is to be enlarged and then reproduced on an image recording medium. Recording by the image recording apparatus is equivalent to restoring a digital image signal as an analog image signal. As a theorem for restoring such a digital signal, there has been known a sampling theorem. The sampling theorem defines a condition on sampling intervals for completely restoring the digital signal as an analog signal. For example, in a one-dimensional sampling theorem, it has been proven that when an analog signal is sampled at a sampling frequency N (sampling intervals of N/2), the signal components at frequencies not higher than N/2 included in the analog signal can be completely restored. The frequency of N/2 is generally referred to as "the Nyquist rate". Further it has been known that when a digital signal including therein frequency components higher than the Nyquist rate is restored to an analog signal, error due to folding of a high frequency side part toward a low frequency side (aliasing error) occurs and the shape of the analog signal restored is greatly deformed. As for an image signal, a two-dimensional sampling theorem shows that the signal components at frequencies not higher than the Nyquist rate can be completely restored and that when a digital signal includes frequency components higher than the Nyquist rate, the digital signal cannot be completely restored. Accordingly it seems that signal components at a frequency not higher than the Nyquist rate can be visually completely restored by the image recording apparatus if sampling or recording of an image is carried out on the basis of the sampling theorem. However in conventional image processing systems, signal components at frequencies not higher than the Nyquist rate actually cannot be visually completely restored in conformity with the theorem. This is because of the following fact. That is, since the sampling theorem assumes that the original waveform can be restored by convoluting a sinc function ((sin x)/x) in sampled values, the response to recording of the recording medium must be a sinc function in order to record an image according to the sampling theorem. In other words, the recording medium must be such that a picture element is recorded on the recording medium at a density corresponding to a value which is obtained by convoluting the sinc function in a value of a given digital signal component. However since the sinc function can take a negative value whereas the response of recording cannot be negative, the sinc function cannot be actually convoluted. That is, it is actually impossible to visually completely restore the signal components at frequencies not higher than the Nyquist rate on a recording medium. However since the sampling theorem has been wide known and various systems other than the recording system are designed according to the sampling theorem, the image recording apparatus has been expected, as if natural, to be able to visually completely restore the signal components of frequencies not higher than the Nyquist rate according to the sampling theorem. In accordance with the pre-characterizing part of each of claims 1 to 4, EP-A-440 794 discloses an apparatus and a method for recording an image having the double size of an original image. The method includes the step of interpolation to enlarge an image. Then, a response which has been deteriorated by the interpolation processing is amplified with an inverse function filter. Thereby, the response before the interpolation can be maintained after the interpolation. The reference does not mention to cut off values of frequency components higher than the Nyquist rate. US-A-5 253 043 discloses a digital image processing method and apparatus in which upsampling is carried out with zero insertion and filtering. US-A-5 383 144 disclosed subsampling method and interpolation method for digital signals, wherein an input signal is subsampled such that the number of samples of the input signal is halved so as to produce an output signal. This output signal is received by an interpolation circuit, which adds new samples obtained by interpolation, thereby restoring the original number of samples of the input signal. SUMMARY OF THE INVENTION In view of the foregoing observations and description, the primary object of the present invention is to provide a digital image recording apparatus and method which can visually completely restore digital image signal components of frequencies not higher than the Nyquist rate included in a digital image signal. The digital image recording apparatus of the present invention comprises the features of claim 1. Specifically, the image processing means comprises an image information increasing means which increases the amount of information carried by the first digital image signal by interpolating predetermined values into the first digital image signal according to a predetermined rule, a frequency analysis means which analyzes the frequency components of the first digital image signal by carrying out a first transformation processing on the first digital image signal increased with the amount of information carried thereby and developing the first digital image signal in a frequency space, a high frequency component removing means which replaces the values of the frequency components higher than the Nyquist rate of the first digital image signal with 0 in the frequency space in which the first digital image signal is developed by the frequency analysis means and obtains said second digital image signal, and an inverse transformation means which carries out a second transformation processing inverse to the first transformation processing on the second digital image signal obtained by the high frequency component removing means in said frequency space. The method of the present invention is a digital image recording method having the features of claim 2. Specifically, the image processing comprises the steps of increasing the amount of information carried by the first digital image signal by interpolating predetermined values into the first digital image signal according to a predetermined rule, analyzing the frequency components of the first digital image signal by carrying out a first transformation processing on the first digital image signal increased with the amount of information carried thereby and developing the first digital image signal in a frequency space, obtaining said second digital image signal by replacing the values of the frequency components higher than the Nyquist rate of the first digital image signal with 0 in the frequency space in which the first digital image signal is developed, and carrying out a second transformation processing inverse to the first transformation processing on the second digital image signal. In this specification, the expression "reducing frequency components of the first digital image signal which are higher than the Nyquist rate of the first digital image signal" should be broadly interpreted to include complete removal of such frequency components in addition to reduction of such frequency components. Further the expression "interpolating predetermined values into the first digital image signal according to a predetermined rule" means a processing, for instance, for interpolating a predetermined value (e.g., 0) into the first digital image signal every other picture element and line and the processing may be carried out according to any rule and by use of any value so long as it can increase the amount of information carried by the first digital image signal. These factors may be determined as matter of design. The term "transformation processing" means an orthogonal transformation processing such as a Fourier transformation wide known as a method of frequency analysis, and accordingly the expression "developing the first digital image signal in a frequency space" means to obtain a Fourier transformation image by carrying out Fourier transformation on the first digital image signal. The expression "second transformation processing inverse to the first transformation processing" means, for instance, an inverse Fourier transformation. However since the first transformation processing is carried out in order to visually clear the frequency components of the first digital image signal, any transformation known as a method of frequency analysis may be employed without limiting to the Fourier transformation. On a Fourier transformation image, the value of each frequency component of the digital image signal is given as a value of a coordinate (position) and the expression "replacing the values of the frequency components higher than the Nyquist rate of the first digital image signal with 0" means to replace the values of the positions with 0. Further the expression "interpolating 0 into the first digital image signal so that values of the frequency components higher than the Nyquist rate of the first digital image signal become 0" means to make 0 the values of positions representing frequency components higher than the Nyquist rate of the first digital image signal on a Fourier transformation image. However the "interpolation of 0" differs from the "replacement with 0" described above in that by interpolation of 0 into a given position, the original value for the position is shifted to another position representing a frequency component not higher than the Nyquist rate and as a result, an enlarged Fourier transformation image is obtained. That is, by "replacement with 0", the amount of information carried by the first digital image signal is left unchanged whereas by "interpolation of 0", the amount of information carried by the first digital image signal is increased. Further the expression "carrying out an interpolation processing on the first digital image signal by use of a filter" means to carry out, in addition to a normal filtering processing for obtaining values corresponding to picture elements originally contained in the first digital image signal, a processing for obtaining values to be interpolated among the original picture elements by the similar filtering and interpolating the values among the original picture elements. By this processing, the amount of information carried by the first digital image signal is increased. In accordance with the present invention, the amount of information carried by the first digital image signal is increased and the frequency components higher than the Nyquist rate of the first digital image signal are removed from the first digital image signal, and the second digital image signal thus obtained is reproduced on a recording medium at a density higher than sampling density in a size substantially equal to that of the original image though the amount of information carried by the second digital image signal is larger than that carried by the first digital image signal. Accordingly, image information among the sampling points which has conventionally been lost can be compensated without involving the frequency components higher than the Nyquist rate, which makes it feasible to precisely restoring the digital image signal on a recording medium. When the amount of information carried by the first digital image signal is increased by interpolating predetermined values into the first digital image signal according to a predetermined rule and then the first digital image signal increased with the amount of information carried thereby is developed in a frequency space by a Fourier transformation or the like, the frequency components in the digital image signal can be visually cleared, and accordingly the frequency components higher than the Nyquist rate can be easily removed. By thereafter carrying out an inverse Fourier transformation or the like, a digital image signal with supplemented information can be obtained. The same effect can be obtained by enlarging the Fourier transformation image so that no frequency component higher than the Nyquist rate is included therein. In this case, since the Fourier transformation is carried out before the amount of information carried by the digital image signal is increased, the amount of operation for the Fourier transformation is less, whereby load on the system can be reduced. Further when values to be interpolated among the original picture elements are obtained and interpolated among the original picture elements by carrying out a filtering processing on the digital image signal without developing the digital image signal in a frequency space, the same effect can be obtained and at the same time, load on the system can be further more reduced. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a view for briefly illustrating an image recording apparatus in accordance with a first embodiment of the present invention, Figure 2 is a view for illustrating the operation of the image processing means employed in the first embodiment, Figure 3 is a view for briefly illustrating an image recording apparatus not falling within the scope of the claims, Figure 4 is a view for illustrating the operation of the image processing means employed in the apparatus of Fig. 3, Figure 5 is a view for briefly illustrating an image recording apparatus using a filter, Figure 6 is a view for illustrating the operation of the image processing means shown in Fig 5, Figure 7 is a view showing the properties of the filter F1 shown in example 1 of the filter, Figure 8 is a view for illustrating an example of interpolation processing with a filter, Figure 9 is a view for illustrating the operation of the image recording apparatus of fig. 5, Figure 10 is a view showing the properties of the filter F4 shown in Figure 8, Figure 11 is a view showing an example of original image signal, Figure 12 is a view showing a digital image signal obtained by sampling the original image signal shown in Figure 11, Figure 13 is a view showing an example of second digital image signal in the first embodiment, Figure 14 is a view showing a result of the first embodiment, Figure 15 is a view showing a result of the apparatus of fig 5, Figure 16 is a view showing an example of image signal recorded by a conventional image recording apparatus, and Figure 17 is a view showing an example of image signal recorded in accordance with the method using a filter which does not satisfy the condition of the present invention. DESCRIPTION OF THE PREFERRED EMBODIMENTS Figures 1 to 10 are for illustrating three embodiments of the present invention, and Figures 11 to 17 show image signals to be processed or processed by the image recording apparatuses in accordance with the embodiments of the present invention or in accordance with a prior art. In Figures 11 to 17, the abscissa represents the position on a line of an image and the ordinate represents the density of the image. Figure 11 shows an example of original image signal whose frequency is 3.4 cycle/mm, and Figure 12 shows a digital image signal obtained by sampling the image signal shown in Figure 11 at 10 pixel/mm (10 sampling points per 1mm). Description will be made on the case where the digital image signal shown in Figure 12 is subjected to an image processing and the processed digital image signal is reproduced on a recording medium. Reproduction of the digital image signal shown in Figure 12 by a conventional image recording apparatus will be described first. Since the sampling frequency of the digital image signal is 10 pixel/mm as described above, the Nyquist rate of this digital image signal is 5 cycle/mm. Accordingly the original image signal whose frequency is 3.4 cycle/mm does not contain frequency components higher than the Nyquist rate of the digital image signal and theoretically can be completely restored. However as described above, since-the recording response cannot be a sinc function to light (in the case of a laser printer) nor heat (in the case of a thermal printer), actually the original image signal cannot be completely restored. The signal shown in Figure 16 is an example where the digital image signal shown in Figure 12 is reproduced in the same size as the original image by the conventional image recording apparatus. As can be seen from Figure 16, even the digital image signal which does not contain frequency components higher than the Nyquist rate is reproduced as a signal far from the original image signal. Figure 1 is a view for illustrating an image recording apparatus and an image recording method in accordance with a first embodiment of the present invention. As shown in Figure 1, the image recording apparatus of this embodiment comprises an image processing means 4 which carries out a predetermined image processing on a first digital image signal 1 obtained by sampling an original image signal representing an original image at a predetermined sampling density and thereby obtains a second digital image signal 2, and a high density recording means 5 which reproduces the second digital image signal 2 at a density higher than the sampling density as a printed image 3. The predetermined image processing carried out by the image processing means 4 includes a processing for increasing the amount of information to be carried by the first digital image signal 1 and a processing for reducing frequency components of the first digital image signal 1 higher than the Nyquist rate of the first digital image signal 1. In this particular embodiment, the image processing means 4 comprises an image information increasing means 6a, a frequency analysis means 7, a high frequency component removing means 8 and an inverse transformation means 9 as shown in Figure 2. In this embodiment, the image information increasing means 6a increases the amount of information carried by the first digital image signal 1 by interpolating 0 into the first digital image signal 1 every other picture element and every other line, which results in double increase in each of the transverse and longitudinal directions, i.e., four-fold increase in total. This is equivalent to doubling the sampling points, and accordingly the Nyquist rate of the resultant digital image signal 10 is twice as large as the Nyquist rate N/2 of the first digital image signal 1 and equal to N. At the same time, by the interpolation processing, the frequency components of the digital image signal vary. That is, even if the first digital image signal 1 does not contain frequency components higher than the Nyquist rate N/2, the resultant digital image signal 10 can contain such frequency components. Since the frequency components higher than the Nyquist rate adversely affect restoring the digital image signal as described above, such frequency components should be removed. Then the frequency components in the resultant digital image signal 10 are visually made clear by carrying out a Fourier transformation on the resultant digital image signal 10 and obtaining a Fourier transformation image 11a thereof by the frequency analysis means 7 and the frequency components higher than the Nyquist rate N/2 of the first digital image signal 1 are removed by replacing values of the frequency components with 0 by the high frequency component removing means 8, thereby obtaining a Fourier transformation image 12a shown in Figure 2 free from the high frequency components. In this particular embodiment, a discrete Fourier transformation (DFT) is carried out using an algorism of a fast Fourier transformation (FFT) as the relevant Fourier transformation. A discrete Fourier transformation image has been known to be represented by repetition of Fourier transforms of a continuous signal, and in accordance with this method of representation, the blacked portion of the Fourier transformation image 12a represents the frequency components higher than the Nyquist rate N/2 of the first digital image signal 1. When an inverse Fourier transformation is subsequently carried out on the Fourier transformation image 12a free from the high frequency components by the inverse transformation means 9, a second digital image signal 2, that is, the digital image signal 10 increased with the amount of information carried thereby minus the frequency components higher than the Nyquist rate of the first digital image signal 1, is obtained. Finally by reproducing the second digital image signal 2 at the double density by the high density recording means 5, a printed image 3 at a high resolution can be obtained. In order to prove the effect of the present invention, a case where the original image signal shown in Figure 11 is processed by the image recording apparatus on this embodiment will be described, hereinbelow. A second digital image signal 2 obtained by carrying out the aforesaid processing on the digital image signal shown in Figure 12 obtained by sampling the original image signal shown in Figure 11 is as shown in Figure 13, and the signal obtained by recording the second digital image signal 2 at a high density is as shown in Figure 14. From comparison of the original image signal shown in Figure 11, the image signal shown in Figure 14 and the image signal shown in Figure 16 which is restored by the conventional image recording apparatus, it can be seen that the image signal restored by the image recording apparatus of this embodiment is closer to the original image signal than that restored by the conventional image recording apparatus and is free from fluctuation which is seen in the image signal restored by the conventional image recording apparatus. The image signal restored by the image recording apparatus of this embodiment may be considered to be complete restoration of the original image signal. Figure 3 is a view for illustrating an image recording apparatus and an image recording method not falling within the scope of the claims of the present invention, and Figure 4 shows a processing by the image processing means 4 in this apparatus. The image processing means 4 comprises a frequency analysis means 7, an image information increasing means 6b and an inverse transformation means 9 as shown in Figure 3. The frequency analysis means 7 and the inverse transformation means 9 will not be described in detail here since they are the same as those in the first embodiment except that the object of processing differs from that in the first embodiment. This apparatus is characterized in that the processing for increasing the amount of information carried by the digital image signal is carried out after a Fourier transformation. That is, as shown in Figure 4, a Fourier transformation is first carried out on the first digital image signal 1, thereby obtaining a Fourier transformation image 11b, and then the amount of information is increased by interpolating 0 into positions representing the frequency components higher than the Nyquist rate of the first digital image signal 1 in the Fourier transformation image 11b. Thereafter, as in the first embodiment, a second digital image signal 2 is obtained by carrying out an inverse Fourier transformation by the inverse transformation means 9 and the second digital image signal 2 is reproduced at the double density by the high density recording means 5, whereby a printed image 3 at a high resolution is obtained. The printed image 3 obtained by the second embodiment is equivalent to that obtained by the first embodiment in quality. However, since the Fourier transformation is carried out before the amount of information carried by the digital image signal is increased, the amount of operation for the Fourier transformation is greatly reduced. Generally, when operation for a Fourier transformation is executed by a computer, the computing time is not always proportional to the size of the image. That is, in the case where memories and the like are limited, processing for delivery of image information is carried out between the memory and the disk in addition to operation of the Fourier transformation and accordingly as the size of the image to be processed increases, the computing time for additional processing increases. An image recording apparatus and an image recording method not falling within the scope of the claims of the present invention will be described with reference to Figures 5 to 10, hereinbelow. Though carrying out the Fourier transformation as described above is adequate as an image processing method, it is not always preferable from the viewpoint of performance of the apparatus. Here, the amount of image information is increased and the frequency components higher than the Nyquist rate is reduced without carrying out a Fourier transformation. Figure 6 shows the image processing carried out by the image processing means 4 shown in Figure 5. As shown in Figure 5, the image processing means 4 of this embodiment carries out an interpolation processing by use of a filter. The filter should satisfy the condition R(f)≦0.2 in at least 80% of the region where N/2<f≦N, wherein N/2 represents the Nyquist rate of the first digital image signal, f represents the frequency and R(f) represents the properties of the filter. It is preferred that the region where R(f)≦0.2 be as close to 100% of the region where N/2<f≦N as possible and R(f) be as close to 0 as possible for each frequency in the region. Examples of filters which satisfy the condition described above and examples of interpolation processing using such filters will be described hereinbelow. In the example 1 shown in Figure 6, convolution is carried out by use of a filter F1 on an image interpolated with 0 every other picture element, that is, values are obtained by addition with weighting through the filter F1 while shifting the filter F1. By interpolation of 0, the amount of information obtained by the filtering processing becomes twice as large as that of the original information. In the case of the filter F1, the original picture elements and the picture elements obtained by this processing are alternate with each other. The filter F1 has response properties shown in Figure 7 and accordingly, the image signal obtained has less frequency components higher than the Nyquist rate as compared with the original digital image signal. The same effect can be obtained by carrying out filtering alternately using filters F2 and F3 (example 2), which are obtained by dividing the filter F1 into two pieces, without interpolation of 0. Another example of the filter which satisfies the aforesaid condition will be described, hereinbelow. Figure 8 shows an example of an interpolation processing using a filter F4 whose response properties are as shown in Figure 10. In the case of processing using the filter F4, by carrying out filtering on sampling points of the original image (digital image signal components) represented by Amn (m and n stand for integers representing positions) in Figure 8 with the filter F4, that is, by carrying out operations according to formulae (a), (b) and (c), the values of interpolated points Bmn, Cmn and Dmn are obtained. In Figure 8, only a part of the interpolated points Bmn, Cmn and Dmn is shown. Figure 9 shows a concrete processing carried out by the image processing means 4 which carries out the interpolation processing using the filter F4 shown in Figure 8. The digital signal components for the respective picture elements A01 to A09, A10 to A19 ······ of the first digital image signal 1 to be processed are input into the image processing means 4 scanning line by scanning line in this order. The image processing means 4 calculates Bmn on the basis of the digital image signal components for the last ten picture elements out of the signal components input into the image processing means 4 in sequence and outputs to buffers in sequence each allotted to one line. The capacity of the buffer is such that digital image signal components for picture elements twice as many as the picture elements in one scanning line, that is, digital image signal components for twenty picture elements in this particular embodiment, can be stored therein. The values Bmn which are obtained in sequence in the manner described above and output to the buffers and the values Amn for the original picture elements alternate with each other in this example. When the buffers for 10 scanning lines are filled, the image processing means 4 obtains Cmn and Dmn on the basis of digital image signal components stored in the corresponding positions of the buffers, that is, digital image signal components for picture elements on the same column in Figure 8. The picture element values Amn, Bmn, Cmn and Dmn thus obtained are output in sequence in the scanning line direction. Thereafter the image processing means 4 clears the image signals in the buffer in which digital image signal components are stored first in the 10 buffers. Then digital image signal components for another line are stored in the buffer and the image processing means 4 repeats the processing described above. The digital image signal subjected to the interpolation processing using the aforesaid filter is recorded as an image signal shown in Figure 15. The image signal shown in Figure 15 is more close to the original image signal than an image signal recorded by a conventional image recording apparatus (Figure 16) and an image signal recorded in accordance with the method similar to the third embodiment but by use of a one-dimensional filter which does not satisfy the condition of the present invention (Figure 17). The image recording apparatus and the image recording method in accordance with the present invention need not be limited to the embodiments described above but the embodiments may be variously modified. For example, the transformation carried out by the frequency analysis means 7 may be any of transformations known as a method of frequency analysis. Further the filter need not be a one-dimensional filter but may be of any type so long as it satisfies the aforesaid condition. Further though description has been made on the result of the invention using a simple sine wave signal, all image signals are of a superposition of sine waves and accordingly the result of the present invention described above can also be applied to more complicated image signals.

Claims: A digital image recording apparatus comprising an image processing means (4) which carries out an image processing on a first digital image signal (1) obtained by sampling at a predetermined sampling frequency an image signal representing an original image, the image processing being for reducing frequency components of the first digital image signal which are higher than the Nyquist rate of the first digital image signal (1), thereby obtaining a second digital image signal (2), and a high density recording means (5) which reproduces the second digital image signal (2) on a recording medium characterized in that the high density recording means reproduces the second digital image signal at a density higher than said predetermined density, thereby forming an image (3) which is higher in resolution than that obtained from the first digital image signal (1) and equal to that obtained from the first digital image signal (1) in size, and that the image processing means (4) comprises an image information increasing means (6a) which increases the amount of information carried by the first digital image signal (1) by interpolating "0"-values into the first digital image signal according to a predetermined rule, a frequency analysis means (7) which analyzes the frequency components of the first digital image signal (1) by carrying out a first transformation processing on the first digital image signal increased with the amount of information carried thereby and developing the first digital image signal in a frequency space, a high frequency component removing means (8) which replaces the values of the frequency components higher than the Nyquist rate of the first digital image signal (1) with 0 in the frequency space in which the first digital image signal is developed by the frequency analysis means (7) and obtains said second digital image signal (2) and an inverse transformation means (9) which carries out a second transformation processing inverse to the first transformation processing on the second digital image signal obtained by the high frequency component removing means in said frequency space. A digital image recording method comprising the steps of carrying out an image processing on a first digital image signal (1) obtained by sampling at a predetermined sampling frequency an image signal representing an original image, the image processing being for reducing frequency components of the first digital image signal which are higher than the Nyquist rate of the first digital image signal, thereby obtaining a second digital image signal, and reproducing the second digital image signal (2) on a recording medium characterized in that the second digital image signal is reproduced at a density higher than said predetermined density, thereby forming an image (3) which is higher in resolution than that obtained from the first digital image signal and equal to that obtained from the first digital image signal in size, and that the image processing comprises the steps of increasing the amount of information carried by the first digital image signal (1) by interpolating "0" values into the first digital image signal (1) according to a predetermined rule, analyzing the frequency components of the first digital image signal by carrying out a first transformation processing on the first digital image signal increased with the amount of information carried thereby and developing the first digital image signal in a frequency space, obtaining said second digital image signal by replacing the values of the frequency components higher than the Nyquist rate of the first digital image signal with 0 in the frequency space in which the first digital image signal is developed, and carrying out a second transformation processing inverse to the first transformation processing on the second digital image signal.

Inventors: ITO WATARU, ITO, WATARU
Applicants: FUJI PHOTO FILM CO LTD, FUJI PHOTO FILM CO., LTD.
Application year: 1997
Main classification: H04N1
IPC codes: G06T3, H04N1