A fast modified signed Discrete Cosine Transform for image compression

The Discrete Cosine Transform (DCT) is widely used in image compression for its high power compaction property. The Signed DCT (SDCT) and its modifications approximate the DCT and proceed faster. This paper introduces an efficient and low complexity 8 point transform. The proposed algorithm is derived by applying the signum function operator to an existing SDCT modification transform with good power compaction capabilities. Consequently, the elements of the proposed transform are only zeroes and ones. No multiplications or shift operations are required. The introduced transform keeps the high power compaction capabilities of its originating transform and, in the same time, provides a saving in computational complexity. A flow diagram is provided for the fast implementation of the transform. Only 17 additions are required for both forward and backward transformations. Simulation experiments are provided to justify the efficiency and improved performance of the proposed transform in image compression compared to other transforms.