Method and apparatus for encoding and decoding subband decompositions of signals

A computer-assisted method of preparing data for compression, capable of preparing the data in a single pass, the method including:

• receiving data corresponding to a subband decomposition of a signal, including coefficients, parent-child relationships among the coefficients, A-tree leading zeros values associated with the coefficients, and B-tree leading zeros values associated with the coefficients;
• visiting the coefficients, parent coefficients before their children coefficients;
• for the visited coefficients, translating a set of values for output, including:
• (a) translating a function of the A-tree leading zero value and the B-tree leading zero value, both associated with a grandparent coefficient of the visited coefficient, if the visited coefficient has any grandparent coefficient and the grandparent coefficient has not previously been translated;
• (b) translating a function of the A-tree leading zero value associated with a parent coefficient of the visited coefficient and of the B-tree leading zero value associated with the grandparent coefficient of the visited coefficient, if the visited coefficient has any parent coefficient and the parent coefficient has not previously been translated, where the B-tree leading zero value associated with the grandparent coefficient is assigned a predetermined value if the visited coefficient does not have any grandparent coefficient;
• translating part of the visited coefficient starting in a next place of the visited coefficient, if any, beyond a place indicated by the A-tree leading zero value of the parent coefficient, if the parent coefficient exists, or in a first place of the visited coefficient if the parent coefficient does not exist;
• and
• outputting the translated values.

A computer-assisted method of populating a data structure including coefficients, parent-child relationships among the coefficients, A-tree leading zeros value, and B-tree leading zeros value, the method including:

• receiving data derived from a subband decomposition of a signal;
• visiting coefficients in the data structure, parent coefficients before child coefficients, parsing one or more substrings from the data corresponding to the visited coefficient, and:
• for a visited coefficient that has a grandparent coefficient, translating a first substring into a function (a) of the A-tree leading zero value and the B-tree leading zero value both associated with a grandparent coefficient of the visited coefficient, calculating a B-tree leading zero value of the grandparent coefficient, and associating the B-tree leading zero value with the grandparent coefficient;
• for a visited coefficient that has a parent coefficient, translating a second substring into a function (b) of the A-tree leading zero value associated with the parent coefficient of the visited coefficient and of the B-tree leading zero value associated with the grandparent coefficient of the visited coefficient, where the B-tree leading zero value associated with the grandparent coefficient is assigned a predetermined value if the visited coefficient does not have any grandparent coefficient, calculating the A-tree leading zero value of the parent coefficient, and associating the A-tree leading zero value with the parent coefficient;
• translating a substring corresponding to the visited coefficient, utilizing the A-tree leading zero value of the parent coefficient, if any, to determine the number of leading zeros of the visited coefficient, and associating the coefficient value with the visited coefficient.

A machine readable data structure corresponding to coefficients of a subband decomposition of a signal, including:

• a machine readable memory;
• at least one array, located in the memory, containing coefficients of a subband decomposition, wherein parent-child relationships are defined among the coefficients;
• additional arrays, located in the memory, the additional arrays organized in parallel to one another, including
• an array of pointers to the coefficients, wherein the pointers are organized so that a pointer to a parent coefficient has a lower array index than a pointer to a child coefficient of the parent coefficient;
• an array of integers representing A-tree leading zero values associated with the coefficients;
• an array of integers representing B-tree leading zero values associated with the coefficients;
• an array of multiple flags associated with the coefficients representing
• a sign of a particular coefficient;
• whether the A-zero value of the particular coefficient has been translated for output;
• whether the B-zero value of the particular coefficient has been translated for output;
• and
• an array of integers representing array indexes of parent coefficients of the coefficients.

A machine readable data structure corresponding to coefficients of a subband decomposition of a signal, wherein parent-child relationships are defined among the coefficients, including:

• a machine readable memory;
• a plurality of arrays, located in the memory, the arrays organized in parallel, including
• an array of coefficients corresponding to the subband decomposition, wherein the coefficients are organized so that parent coefficients consistently have either higher or lower array indexes than their child coefficients;
• an array of integers representing A-tree leading zero values associated with the coefficients;
• an array of integers representing B-tree leading zero values associated with the coefficients;
• and
• an array of integers representing array indexes of parent coefficients of the coefficients.

A machine readable data structure corresponding to coefficients of a subband decomposition of a signal, wherein parent-child relationships are defined among the coefficients, including:

• a machine readable memory;
• a plurality of arrays, located in the memory, the arrays organized in parallel, including
• an array of coefficients corresponding to the subband decomposition,
• wherein the coefficients are organized so that parent coefficients consistently have either higher or lower array indexes than their child coefficients;
• an array of integers representing A-tree leading zero values associated with the coefficients;
• and
• an array of integers representing B-tree leading zero values associated with the coefficients.