A Framework for Linear Transform Approximation Using Orthogonal Basis Projection

Abstract—This paper aims to develop a novel framework to systematically trade-off computational complexity with output distortion in linear multimedia transforms, in an optimal manner. The problem is important in real-time systems where the computational resources available are time-dependent. We solve the real-time adaptation problem by developing an approximate transform framework. There are three key contributions of this paper – (a) a fast basis projection approximation framework that allows us to store signal independent partial transform results to be used in real-time, (b) estimating the complexity distortion curve for the linear transform approximation using a given basis projection approximation set and searching for optimal transform approximation which satisfies the complexity constraint with minimum distortion and (c) determining optimal operating points on complexity distortion function and a meta-data embedding algorithm for images that allows for real-time adaptation. We have applied this approach on the FFT approximation for images with excellent results. Index Terms—linear transform approximation, basis projection, complexity distortion function, metadata encoding I