DCT Computation with Minimal Average Number of Operations

The Discrete Cosine Transform (DCT) is widely used in all transform-based image and video compression standards due to its well-known decorrelation and energy compaction properties for typical images. Many fast algorithms available for the DCT optimize various parameters such as additions and multiplications but they are input independent and thus require the same number of operations for any inputs. In this paper we study the beneets of input-dependent algorithms for the DCT which are aimed at minimizing the average computation time by taking advantage of the sparseness of the input data. Here, we concentrate on the inverse DCT (IDCT) part since typical input blocks will contain a substantial number of zeros. We show how to construct an IDCT algorithm based on the statistics of the input data, which are used to optimize the algorithm for the average case. We show how, for a given input and a correct model of the complexity of the various operations, we can achieve the fastest average performance.