  The principal component analysis (PCA) is widely used for data decorrelation
and dimensionality reduction. However, the use of PCA may be impractical in
real-time applications, or in situations were energy and computing constraints
are severe. In this context, the discrete cosine transform (DCT) becomes a
low-cost alternative to data decorrelation. This paper presents a method to
derive computationally efficient approximations to the DCT. The proposed method
aims at the minimization of the angle between the rows of the exact DCT matrix
and the rows of the approximated transformation matrix. The resulting
transformations matrices are orthogonal and have extremely low arithmetic
complexity. Considering popular performance measures, one of the proposed
transformation matrices outperforms the best competitors in both matrix error
and coding capabilities. Practical applications in image and video coding
demonstrate the relevance of the proposed transformation. In fact, we show that
the proposed approximate DCT can outperform the exact DCT for image encoding
under certain compression ratios. The proposed transform and its direct
competitors are also physically realized as digital prototype circuits using
FPGA technology.
