engleski

Karhunen-Loeve Transform and its Theoretical Importance for Video Compression

For the block transform compression of data, orthogonal transform coding schemes are useful to reduce effectively the redundancy of data. The Karhunen-Loeve transform (KLT) method is considered as an optimal one in the sense that it makes the transformed data completely uncorrelated and minimizes the mean square error (MSE) of the reconstructed data after the compression. The KLT constructs the image-specific set of basis functions that correspond to the normalized eigenvalues of the autocorrelation matrix of the image, and, thus provides a maximum decorrelation and redundancy reduction. However, the KLT is seldom used in practice because it is difficult to compute and there is no fast algorithm for it. But, the KLT function approaches asymptotically to the discrete cosine transform (DCT) function when the input data in a sequence are strongly correlated as is usually the case for the image data. The DCT has decorrelation properties very close to the KLT and can be fast implemented by means of a Fast Fourier Transform algorithm. Therefore, the DCT is available in practice and has been widely used in the coding of image data.

Video Signal; Image; Compression; Redundancy; Karhunen-Loeve Transform; Discrete Cosine Transform

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