Efficient Computation of the 8-point DCT via Summation by Parts

TL;DR

This paper presents a novel fast algorithm for the 8-point DCT using summation-by-parts, achieving minimal multiplicative complexity and adaptable to various input signal types for applications like image processing.

Contribution

The paper introduces a new summation-by-parts based algorithm for the 8-point DCT that is both scaled and exact, with minimal multiplicative complexity and adaptable to different input signals.

Findings

Achieves theoretical minimal multiplicative complexity for 8-point DCT

Can be applied to various input signal types including null mean and accumulated signals

Potential applications in harmonic detection and image enhancement

Abstract

This paper introduces a new fast algorithm for the 8-point discrete cosine transform (DCT) based on the summation-by-parts formula. The proposed method converts the DCT matrix into an alternative transformation matrix that can be decomposed into sparse matrices of low multiplicative complexity. The method is capable of scaled and exact DCT computation and its associated fast algorithm achieves the theoretical minimal multiplicative complexity for the 8-point DCT. Depending on the nature of the input signal simplifications can be introduced and the overall complexity of the proposed algorithm can be further reduced. Several types of input signal are analyzed: arbitrary, null mean, accumulated, and null mean/accumulated signal. The proposed tool has potential application in harmonic detection, image enhancement, and feature extraction, where input signal DC level is discarded and/or the signal is required to be integrated.