#### LARS Tech Report Number

050572

#### Abstract

Transform coding and block quantization techniques are applied to multispectral data for data compression purposes. Two types of multispectral data are considered, (1) aircraft scanner data, and (2) digitized satellite imagery. The multispectral source is defined and an appropriate mathematical model proposed.

Two error criteria are used to evaluate the performance of the transform encoder. The first is the mean square error between the original and reconstructed data sets. The second is the performance of a computer implemented classification algorithm over the reconstructed data set. The total mean square error for the multispectral vector source is shown to be the sum of the sampling (truncation) and quantization error.

The Karhunen-Loeve, Fourier and Hadamard encoders are considered and are compared to the rate distortion function for the equivalent gaussian source and to the performance of the single sample PCM encoder.

The K-dimensional linear transformation is shown to be representable by a single equivalent matrix multiplication of the re-ordered source output tensor. Consequences of this result relative to the K-dimensional Fourier and Hadamard transformations are presented.

Minimization of the total encoder system error over the number of retained transform coefficients and corresponding bit distribution for a fixed data rate and block size is considered and an approximate solution proposed. Minimization of the sampling error over the data block size for the continuous source is also considered.

The results of the total encoder system error problem are applied to both an artificially generated Markov source and to the actual multispectral data sets.

The Karhunen-Loeve transformation is applied to the spectral dimension of the multispectral source and the resulting principal components are evaluated as feature vectors for use in data classification.

Experimental results using the transform encoder and several different (i.e., one, two, and three dimensional) data blocks are presented for both the satellite and aircraft data sets. Performances of the encoders over the three test regions within the satellite data are evaluated and compared.

#### Date of this Version

January 1972