The design and successful fielding of sensors and detectors vital for homeland security can benefit greatly by the use of advanced signal and image processing techniques. The intent is to extract as much reliable information as possible despite noisy and hostile environments where the signals and images are gathered. In addition, the ability to perform fast analysis and response necessitate significant compression of the raw data so that they may be efficiently transmitted, remotely accumulated from different sources, and processed. Proper decompositions into compact representations allow fast pattern detection and pattern matching in real time, in situ or otherwise. Wavelets for signals and curvelets for images or hyperspectral data promise to be of paramount utility in the implementation of these goals. Together with statistical modeling and iterative thresholding techniques, wavelets, curvelets and multiresolution analysis can alleviate the severity of the requirements which today’s hardware designs can not meet in order to measure trace levels of toxins and hazardous substances. Photonic or electrooptic sensor and detector designs of the future, for example, must take into account the end game strategies made available by advanced signal and image processing techniques. The promise is the successful operation at lower signal to noise ratios, with less data mass and with deeper statistical inferences made possible than with boxcar or running averaging techniques (low pass filtering) much too commonly used to deal with noisy data at present. SPREE diagrams (spectroscopic peak reconstruction error estimation) are introduced in this paper to facilitate the decision of which wavelet filter and which denoising scheme to use with a given noisy data set.