This project will develop a dynamic, data-driven application system for signal and image processing under resource constraints. This system would lay a foundation for highly optimized implementations of fundamental signal and imaging processing computations that arise in many science and engineering problems, including image recognition, communications analysis, speech processing, querying, indexing, and retrieval from multimedia databases, and image segmentation of aerial, satellite, and astronomical images. The proposed multidisciplinary approach optimizes from algorithm specification, to mathematical representation, to software and hardware (FPGA) implementation, based on properties of data and unique requirements of the environment and the target hardware device. The novelty of the system is twofold: (1) it performs joint optimization across mathematical, software and hardware (system-on-a-chip FPGA) domains; and, (2) it is a dynamic, data-driven system in that signal-processing transforms are tailored to algorithm requirements and input signals, for reduced distortion and increased compression, and the system can be queried and steered during execution. Implementations are based on the best mathematical formulation of the problem coupled with automated selection of the best implementation among a space of alternatives, through the integration of models relating mathematical properties to implementation behavior. Both hardware and software optimization are treated in a unified way. It is anticipated that with these methods the design-time will be decreased by two orders of magnitude or more, compared to implementations derived in a traditional way. Because the proposed system can explore a broad range of implementations that exceed the capabilities of a human designer, the implementations derived by the approach pursued in the project may even exhibit lower resource costs and higher performance. This research will provide a foundation for signal processing at all scales, providing key building blocks for engineers to build complex, distributed networks of adaptive signal processing sensors.