An apparatus and methods for efficiently processing signal and image data are described. The invention provides a representation of signal and image data that can be used as a figure of merit to compare and characterize different signal processing techniques. The representation can be used as an intermediate result that is may be subjected to further processing, and/or may be used as a control element for processing operations. As a provider of an intermediate result, the invention can be used as a step in processes for the transduction, storage, enhancement, refinement, feature extraction, compression, coding, transmission, or display of image, audio and other data. The invention improves manipulation of data from intrinsically unpredictable, or partially random sources. The result is a concise coding of the data in a form permitting robust and efficient data processing, a reduction in storage demands, and restoration of original data with minimal error and degradation. The invention provides a system of coding source data derived from the external environment, whether noise-free or contaminated by random components, and regardless of whether the data are represented in its natural state, such as photons, or have been pre-processed.