Method for encoding wavelet coefficients

A method for encoding wavelet transform coefficients in an image encoding method in which image data is converted and quantized into coefficients by a two-dimensional wavelet transform and the coefficients having the same spatial position are collected to form a block so as to encode the coefficients on an individual block basis, the method comprising the steps of:

• defining a layered quad-tree structure of the coefficients included in each block with respect to each of a set of coefficients representing a vertical component, a set of coefficients representing a horizontal component and a set of coefficients representing a diagonal component, each quad-tree structure having a root corresponding to a coefficient of a lowest frequency band;
• searching for a zero tree of which all descendant nodes lack a significant coefficient;
• encoding positional information of the zero-tree;
• scanning the coefficients other than descendants of the zero-tree so as to form a one-dimensional coefficient string of the scanned coefficients;
• encoding the one-dimensional coefficient string according to a two-dimensional encoding method based on (1) run lengths of zero runs immediately preceding significant coefficients and (2) the significant coefficients;
• producing a zero-tree map having a layered quad-tree structure corresponding to the coefficient tree, each node of the zero-tree map indicating whether or not a corresponding coefficient is a root of the zero tree, each node being represented by one-bit data;
• scanning the zero-tree map according to the depth-first method so as to change the zero-tree map into a one-dimensional string of the nodes;
• and
• producing encoded data of the positional information of the zero-tree map by encoding the one-dimensional string of the nodes.