Reversible DCT for lossless-lossy compression

1. A method for creating a look up table for rounding offsets, said method comprising the steps of:

generating a first mapping of input values to transform output values using an initial rounding; and

for each row of collisions in the first mapping, wherein a collision is a mapping of inputs to the same transform output values,

determine the number of rows, each containing extras which are needed to provide a transform output value that would not be used with the initial rounding, wherein each extra comprises a transform output value that would not be used with an initial rounding,

select a number of extras evenly spaced within a row if a partial extra row is needed to provide one extra for each collision,

sort the extras in column order,

assign extras to collisions in column order so as to create a second mapping for use in the look up table.

2. The method defined in claim 1 further comprising the step of swapping pairs of input values and transform output values.

3. The method defined in claim 2 further comprising the step of rotating triplets of input values and transform output values.

4. A method for creating a look up table for rounding offsets, said method comprising the steps of:

for each collision in which there is a mapping of a plurality of inputs to the same transform output values,

for each extra in which there is a transform output value that would not be used with an initial rounding,

identify a swap with another extra based on predetermined criteria, and

perform the swap.

5. The method defined in claim 4 wherein the predetermined criteria comprises square error, and a swap is identified where the square error is reduced.