Coding method and apparatus, and computer program and computer-readable storage medium

A encoding apparatus for encoding two-dimensional data f(m, n) including m×n elements into adaptive bases, each adaptive base including a one-dimensional array variable X(m) storing m data and a one-dimensional array variable Y(n) storing n data, comprising:

• initializing means for allocating i-th adaptive base in a memory and initializing the i-th adaptive base by setting random values into the one-dimensional array variable Xi( ) and the one-dimensional array variable Yi( ), where “i” is “1” in an initial stage;
• reconstruction means for reconstructing two-dimensional f′(m, n) data including m×n elements from the first to i-th adaptive bases represented by {X1( ), Y1( )}, . . . , {Xi( ), Yi( )}, using a predetermined conversion;
• error calculation means for calculating an error between the f(m, n) data to be encoded and the reconstructed f′(m, n) data by using a predetermined error evaluation function;
• correction means for correcting the i-th adaptive base by correcting the one-dimensional array variable Xi( ) and the one-dimensional away variable Yi( ) based on the error calculated by said error calculation means;
• first determination means for determining if the error calculated by said error calculation means has converged,
• first control means for, if said first determination means determines that the error has not converged, repeatedly controlling said reconstruction means, error calculation means, correction means and first determination means to perform each processing;
• second determination means for, if said first determination means determines that the error has converged, determining if the error is larger than a predetermined admissible error;
• output means for, if said second output means determines that the error is not larger than the predetermined admissible error, outputting away variables {X1( ), Y1( )}, . . . , {Xi( ), Yi( )} of the first to i-th adaptive bases stored in the memory as encoded data;
• and
• second control means for, if said second determination means determines that the error is larger than the predetermined admissible error, increasing the variable “i” to prepare a new adaptive base and repeatedly controlling said initializing means, reconstruction means, error calculation means, correction means, first determination means, first control means, second determination means and output means to perform each processing.