Along with remarkable advances of computers and networks in recent years, many kinds of information such as text data, image data, audio data, and the like are stored or transmitted in the networks. Among these data, an image, especially, a multi-valued image contains a very large volume of information, and upon storing and transmitting such image, the image data size becomes huge. For this reason, storage and transmission of an image use high-efficiency coding that reduces the data size by removing redundancy of an image or changing the contents of an image to a degree at which deterioration of image quality is not visually recognizable.
As an example of the high-efficiency coding, JPEG recommended by ISO and ITU-T as an international standard coding scheme of still image is prevalently used. JPEG specifies several coding schemes in correspondence with use purposes of encoded data of images to be encoded, and roughly has two modes, i.e., a DCT use mode that uses discrete cosine transformation and aims at irreversible coding, and a spatial mode that aims at reversible coding on the basis of two-dimensional DPCM.
A detailed description of these modes will be omitted since these modes are described in ITU-T Recommendation T.81 | ISO/IEC 10918-1 and the like. The DCT mode controls the bit rate by changing the quantization step in quantization, and must give a large quantization step to set a low target bit rate. As a result, especially under a low-bit rate condition, the reproduced image is distorted beyond an allowable level due to quantization.
Also, JPEG specifies hierarchical coding. In hierarchical coding, a plurality of images having different resolutions are generated by reducing an input image in a plurality of scales like ½, ¼, . . . in both the horizontal and vertical directions, and an image having the lowest resolution is encoded and transmitted like a normal image.
In this hierarchical coding, the DCT and spatial modes can be used. If hierarchical coding is implemented as reversible coding, since the spatial mode is used for all the scales or only the last scale, and the DCT mode is used for all other scales, an apparatus must comprise a circuit or program that can implement both the two modes, resulting in a complicated apparatus.
As a scheme that can combat these problems, a coding scheme using discrete wavelet transformation has been proposed. Such coding scheme using discrete wavelet transformation is advantageous since it assures higher compression performance than the DCT mode, can implement hierarchical coding in JPEG in a single system, and so forth.
On the other hand, requirements for image compression coding are becoming increasingly stricter, and even for a binary image such as a text image which is conventionally encoded by another scheme, a decoded image is required to have higher image quality. However, with the conventional scheme, both natural and binary images or an image including these images cannot be restored, while assuring sufficiently high image quality of the decoded image.