The processing of compressed imagery exhibits computational advantages due to the processing of fewer data, as well as the advantage of low-level data security afforded by the encoding format. We have elsewhere discussed the general theory of compressive processing, and have presented complexity analyses which support the claim of computational speedup. In this introductory paper, general methods are described for the processing of signals and imagery encoded via transform-, block-, runlength-, and derivative-coding schemes. Operations of interest include unary and binary pointwise operations, the global reduce operation, and neighborhood operations, such as morphological erosion and dilation. Implementational analyses emphasize the relationship between the compression ratio and the time complexity of compressive computation.