Encoding of pictures using the singular value decomposition (SVD) and 1-D discrete cosine transform (DCT)

Abstract

We propose an efficient encoding algorithm which decomposes a picture matrix A to singular values and eigen vectors of AA/sup T/ and A/sup T/A, and then encodes the singular values and DCT coefficients of eigen vectors by PCM. We transform the eigen vectors of the first decomposed term, which are flat and do not have higher frequency components, to 1 dimensional DCT coefficients. The magnitude of the coefficients is small when the vector is flat, allowing us to encode the coefficients efficiently using this characteristic. For decomposed terms other than the first decomposed term, we are able to encode the singular values and eigen vectors by PCM with a small number of bits without increasing quantization noise, since the singular values are very small.