Optimized quadtree for Karhunen-Loeve transform in multispectral image coding

A new multispectral image compression technique based on the Karhunen-Loeve transform (KLT) and the discrete cosine transform (DCT) is proposed. The quadtree for determining the transform block size and the quantizer for encoding the transform coefficients are jointly optimized in a rate-distortion sense. The problem is solved by a Lagrange multiplier approach. After a quadtree is determined by this approach, a one-dimensional (1-D) KLT is applied to the spectral axis for each block before the DCT is applied on the spatial domain. The eigenvectors of the autocovariance matrix, the quantization scale, and the quantized transform coefficients for each block are the output of the encoder. The overhead information required in this scheme is the bits for the quadtree, KLT, and quantizer representation.