Transformation of image parts in different domains to obtain resultant image size different from initial image size

A method, comprising the steps of:

• receiving first and second image parts through receiving a first plurality of image parts,
• applying sparse matrix multiplication to each of the first and second image parts through applying sparse matrix multiplication to each image part of the first plurality of image parts to obtain a second plurality of image parts;
• applying sparse matrix multiplication to each image part of the second plurality of image parts to obtain a third plurality of image parts;
• and
• applying simple linear processing to the third plurality of image parts to obtain low-frequency image parts in a transform domain and obtaining a value of zero for high-frequency image parts in the transform domain.

A system comprising:

• a transform component that receives first and second image parts through receiving a first plurality of image parts;
• a transform component that applies sparse matrix multiplication to each of the first and second image parts to obtain a second plurality of image parts;
• a transform component that applies sparse matrix multiplication to each image part of the second plurality of image parts to obtain a third plurality of image parts;
• and
• a transform component that applies simple linear processing to the third plurality of image parts to obtain low-frequency image parts in a transform domain and to obtain a value of zero for high-frequency image parts in the transform domain.

An article, comprising:

• a computer-readable signal-bearing medium;
• means in the medium for receiving first and second image parts;
• and
• means in the medium for applying sparse matrix multiplication to each of the first and second image parts through utilization of matricies represented by k1·((TLTts)+(TRTts)) and k2·((TLTts)−(TRTts)), wherein superscript t denotes transpose of a matrix, k1 and k2 are scalar constants, TL and TR are N/2 leftmost and N/2 rightmost columns respectively of an N×N non-identity matrix T=[TLTR] such that T Tt is an identity matrix and Ts is an N/2×N/2 non-identity matrix such that TsTts is an identity matrix.

An article, comprising:

• a computer-readable signal-bearing medium;
• means in the medium for receiving first and second image parts through receipt of a first plurality of image parts;
• means in the medium for applying sparse matrix multiplication to each of the first and second image parts which comprises means in the medium for applying sparse matrix multiplication to each image part of the first plurality of image parts to obtain a second plurality of image parts;
• means in the medium for applying sparse matrix multiplication to each image part of the second plurality of image parts to obtain a third plurality of image parts;
• and
• means in the medium for applying simple linear processing to the third plurality of image parts to obtain low-frequency image parts in a transform domain and for obtaining a value of zero for high-frequency image parts in the transform domain.