Optical Imaging and Spectroscopy

CODING AND INVERSE PROBLEMS

In retrospect, I am guessing that my own innocent half-page letter in the June 1949 IRE Proceedings may have had a beneficial effect.

—M. Golay [95]

8.1 CODING TAXONOMY

Coding is the process of structuring data for transmission between a source and a receiver. This chapter considers transmission of information between an object and an optical sensor system as a coding problem. Coding is most advanced in the context of “algebraic coding theory,” which is the mathematical basis of modern communication systems. The system structure for a communications system is illustrated in Fig. 8.1. The goal of the system is to transmit data from a source to a receiver. In algebraic coding systems the source data is a set of algebraic symbols, such as a text file in ASCII symbols. In many cases, the source may encode its data for compression or encryption. The source-encoded data are transmitted over a channel, such as a telephone line or radio connection, to a receiver. Prior to transmission, a channel encoder writes the source data in a code specific to properties of the channel. The goal of channel encoding is to maximize the probability that the data will be received without error, loss, or interception. The encoding process is reversed by a channel decoder and source decoder at the receiving end of the channel.

Figure 8.2 is an analogous diagram for optical sensing. ...