Image signal encoding method and decoding method, information source encoding method and decoding method, apparatuses therefor, programs therefor, and storage media which store the programs to process gaussian integer signal

An information source decoding method for decoding encoded data which is generated by transforming a signal value sequence of a Gaussian integer signal as an encoding target into integer pairs, each having two integers, arranged in the input order of the signal value sequence;

• regarding each of the integer pairs as a lattice point on two-dimensional coordinates, and obtaining integer values greater than or equal to zero by performing a two-dimensional-to-one-dimensional mapping in which the shorter the distance from each lattice point to the origin, the smaller the value assigned to the lattice point by the mapping;
• and encoding the integer values using codes which are used for encoding an information source that follows an exponential distribution, the method comprising the steps of:
• decoding the integer values by decoding the encoded data thereof;
• restoring the integer pairs by subjecting the decoded integer values to a one-dimensional-to-two-dimensional mapping, which is an inverse mapping of the two-dimensional-to-one-dimensional mapping;
• and
• outputting integers which form each restored integer pair from a first element to a second element thereof.

An information source encoding apparatus for encoding a Gaussian integer signal, the apparatus comprising:

• a device for inputting a signal value sequence of a Gaussian integer signal as an encoding target;
• a device for transforming signal values included in the input signal value sequence into integer pairs, each having two integers, arranged in the input order;
• a device for regarding each of the integer pairs as a lattice point on two-dimensional coordinates, and obtaining integer values greater than or equal to zero by performing a two-dimensional-to-one-dimensional mapping in which the shorter the distance from each lattice point to an origin of the two-dimensional coordinates, the smaller the value assigned to the lattice point by the mapping;
• and
• a device for encoding the integer values using codes which are used for encoding an information source that follows an exponential distribution.

An information source decoding apparatus for decoding encoded data which is generated by transforming a signal value sequence of a Gaussian integer signal as an encoding target into integer pairs, each having two integers, arranged in the input order of the signal value sequence;

• regarding each of the integer pairs as a lattice point on two-dimensional coordinates, and obtaining integer values greater than or equal to zero by performing a two-dimensional-to-one-dimensional mapping in which the shorter the distance from each lattice point to the origin, the smaller the value assigned to the lattice point by the mapping;
• and encoding the integer values using codes which are used for encoding an information source that follows an exponential distribution, the apparatus comprising:
• a device for decoding the integer values by decoding the encoded data thereof;
• a device for restoring the integer pairs by subjecting the decoded integer values to a one-dimensional-to-two-dimensional mapping, which is an inverse mapping of the two-dimensional-to-one-dimensional mapping;
• and
• a device for outputting integers which form each restored integer pair from a first element to a second element thereof.

An image signal encoding method for encoding an image signal which indicates a Gaussian integer signal, the method comprising the steps of:

• inputting a signal value sequence of an image signal as an encoding target;
• transforming signal values included in the input signal value sequence into integer pairs, each having two integers, arranged in the input order;
• regarding each of the integer pairs as a lattice point on two-dimensional coordinates, and obtaining integer values greater than or equal to zero by performing a two-dimensional-to-one-dimensional mapping in which the shorter the distance from each lattice point to an origin of the two-dimensional coordinates, the smaller the value assigned to the lattice point by the mapping;
• and
• encoding the integer values using Golomb codes.

An image signal decoding method for decoding encoded data which is generated by transforming a signal value sequence of an image signal, which is an encoding target and indicates a Gaussian integer signal, into integer pairs, each having two integers, arranged in the input order of the signal value sequence;

• regarding each of the integer pairs as a lattice point on two-dimensional coordinates, and obtaining integer values greater than or equal to zero by performing a two-dimensional-to-one-dimensional mapping in which the shorter the distance from each lattice point to the origin, the smaller the value assigned to the lattice point by the mapping;
• and encoding the integer values using Golomb codes, the method comprising the steps of:
• decoding the integer values by subjecting the encoded data thereof to Golomb decoding;
• restoring the integer pairs by subjecting the decoded integer values to a one-dimensional-to-two-dimensional mapping, which is an inverse mapping of the two-dimensional-to-one-dimensional mapping;
• and
• outputting integers which form each restored integer pair from a first element to a second element thereof.