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The present invention relates to a thermal recording apparatus, and more particularly to an apparatus and a method for performing an image processing process (or image data processing process) of recorded images with high efficiency. As an example of an apparatus for recording (printing) an image on a recording medium such as recording paper, there is a thermal recording apparatus. This type of thermal recording apparatus is provided with a thermal head having a plurality of heat generating members, a platen for supporting a recording medium, and a plurality of driving cams for driving the thermal head. By activating the driving cams, the thermal head makes a reciprocating motion for feeding in a predetermined direction while pressing the recording medium, thereby recording an image on the recording medium. The thermal recording apparatus in this type can have a good heat response and can also record a high quality image with only one operation. The thermal recording apparatus can also be applied to an ink jet printer and a laser beam printer. This type of thermal recording apparatus usually has a maximum recording speed of about 240 mm/sec in the case of printing on A4-size recording paper. It is considered that the recording speed will increase to about 320 mm/sec in the near future. Also, in the case of printing on recording paper having a width of about 500 mm, the recording speed will increase to about 350 mm/sec. The thermal recording apparatus should be provided with an image processing (data processing) circuit for image processing in order to improve the recording speed. For the thermal recording apparatus, an image processing speed of a commercially available microprocessor (MC6800 manufactured by MOTOROLA) is insufficient, and an improvement in the image processing speed is required. Since the development cost of the image processing circuit is higher than the development cost of hardware, it is desirable that the image processing is performed by the hardware. However, it is necessary that the image processing be accomplished in a short time, in order to implement the high speed recording. As an example of the conventional technology, Japanese Patent Laying-Open No. 1-283243 (1989) discloses a method in which the memory circuit for image data storage is provided for each of colors of red (R), green (G) and blue (B) in a memory having a capacity of several kilo-bytes. More specifically, the image data is divided into portions of a predetermined length and temporarily stored in the memory, thus constituting the data buffer. Thereafter, the data stored in the buffer is read out at a specified speed and output to the recording head. In this manner, the data is printed out continuously, and thereby the continuous image is formed on the recording paper. In this method, image data for each color is temporarily stored in the memory in a single operation, and therefore it is necessary to provide the memory having a capacity for a number of bits of the image data corresponding to the number of pixels on a line. FIG. 14 shows a block diagram of the image processing circuit, provided with a central processing unit (CPU) 1, a data buffer 2 and a control circuit 3 for controlling the data buffer 2. The data buffer 2 is formed by connecting a main memory to a cache memory. When image data is input to the buffer 2, it is temporarily stored in the data buffer 2. The image data for each color stored in the data buffer 2 is read out at a specified timing in accordance with a color synchronization signal or the like. Thus, an output port of the data buffer 2 is coupled with a head driver and a driving section, as will be described later. The CPU 1 reads the image data from the data buffer 2, performs data processing, and thereafter writes the image data in the data buffer 2. However, the image data is stored once in the data buffer 2 when it is read out from the data buffer 2. Accordingly, in the case where the image data is for one line, one operation in which all the data is written into the data buffer 2 is completed. Therefore, a processing time can be considerably reduced by adopting the buffer 2 having a capacity of several kilo-bytes, in comparison with a case where the buffer having a capacity of about 100 bytes. However, it is difficult to further reduce the time for data processing, and thus the CPU 1 should read the image data and write the data in the data buffer 2 again. The memory structure for storing the image data is not taken into consideration in this case. In a recording apparatus, an image processing speed depends on an amount of data processed per unit time. For example, a processing time required for reading and writing image data is given by an equation: EQU T=L.times.R/(F.times.B) (1) wherein T is the processing time; L is a length of data per pixel in a direction of a carriage traveling in the recording apparatus; R is a resolution in a main scanning direction (which is a direction of the carriage traveling in the recording apparatus); F is a resolution in a sub-scanning direction (which is a direction perpendicular to the main scanning direction); and B is a recording speed. An increase of the image data processing time (T) is derived from the increase of the number of pixels. Therefore, in order to realize the high speed recording, it is required that the length of the data per pixel is shortened (L). For example, if it is attempted to realize a high speed recording in a laser beam printer having a resolution of 100 dpi and a recording speed of 10 mm/sec, since B=10 mm/sec.times.100 dpi, L=6 .mu.s is obtained from Equation (1). If it is assumed that data processing time T is 100 ms, the length of data per pixel becomes shorter than one bit. Since the time for an analog-to-digital conversion (to be referred to as an A/D conversion hereinafter) in a D/A converter is considerably greater than one bit, a required data length L becomes shorter than one bit. For this reason, a data conversion method called a multi-level data conversion method is required. This data conversion method is not limited to the case of the laser beam printer, and applies also to other recording apparatuses such as a thermosensitive recording apparatus. Therefore, the following description is given only for the laser beam printer. In a case of the multi-level data conversion method, it is required that an A/D converter be provided corresponding to each of the several bits in the data per pixel, for each of colors. If a resolution R and a recording speed B are fixed, the following expressions hold in a color mode having four colors: ______________________________________ 1 bit converter: 1.5 bits/sec (T/F=30 ms/10 mm) 4 bits converter: 1.2 bits/sec (T/F=60 ms/10 mm) 8 bits converter: 2 bits/sec (T/F=120 ms/10 mm) ______________________________________ Conversely, in the laser beam printer using the multi-level data conversion method, if a color mode having four colors is used, the recording speed B can be increased to: EQU B=8(mm/sec).times.8(dpi)=64 mm/sec. Therefore, in the case where the resolution is high and the color mode is used, the color recording speed is increased considerably. However, in the case of the foregoing conventional example, although the recording speed is increased to 64 mm/sec, this speed cannot be effectively used because a data processing time T is not considerably reduced. This is because the time for an A/D conversion (1 bit converter) corresponding to one bit of data is not considered, and therefore the recording speed is determined by the maximum processing speed. FIG. 15 shows an example of a time required for processing one pixel in the case of the 1 bit converter, wherein T.sub.D represents a time required for an A/D conversion of a data. On the other hand, in the case of the multi-level data conversion method, the following can be achieved: ______________________________________ 1 bit converter: 1.5 bits/sec (T/F=30 ms/10 mm) 4 bits converter: 1.2 bits/sec (T/F=60 ms/10 mm) 8 bits converter: 2 bits/sec (T/F=120 ms/10 mm) ______________________________________ In this case, the data processing time T is not considered. From the above description, the present applicant has proposed a method in which an image data processing speed is increased by controlling the data processing time T according to the number of colors used. FIG. 16 is a flowchart showing the method in which the data processing time T is controlled. In this method, when image data is written to a data buffer, data is read out from the data buffer, and the write address in the data buffer is determined based on the data read out. Then, data is read from the data buffer at a constant rate to convert it into multi-level data. If a CPU is constituted by a general purpose microcomputer, an A/D conversion circuit can be constituted by the microcomputer. Therefore, in order to control the data processing time T, it is sufficient to determine the address for writing the data. Also, if it is required to change the timing of the reading of the data, it is sufficient to start reading the data at a position of a start address read out from the data buffer. Accordingly, it is possible to realize a high speed image processing in accordance with the number of colors used, using a general purpose microcomputer. In this case, however, data may be written to the data