A method for the detection and deconvolution of a statistically noisy spectral dataset comprising the steps of: a. placing a radiation detector system into suitable proximity with a test object, collecting radiation data emergent from the test object at the detector, resolving the radiation collected at the detector spectroscopically into a resolved dataset of measured flux at a plurality of energy bands, and thereby obtaining a spectroscopically resolved dataset of measured flux in which count data is resolved into values for each of a plurality of energy bands; b. generating an initial estimate of a true spectrum in which count data is resolved into values for each of the plurality of energy bands; c. operating on the estimate of the true spectrum using a response function of the detector used to collect the measured flux dataset so as to generate an estimate flux dataset; d. computing a merit value for statistical fit between the measured flux dataset and the estimate flux dataset; e. applying a perturbation to the value of each of the energy bands of the estimate of the true spectrum; f. repeating steps c and d to the estimate of the true spectrum so changed, accepting the change to the estimate of the true spectrum if the resultant merit value indicates an improvement or if the resultant merit value indicates a deterioration of less than a limit margin, and rejecting the change to the estimate of the true spectrum if the resultant merit value indicates a deterioration of more than a limit margin; g. repeating steps e and f for each further value of the estimate of the true spectrum to obtain a modified estimate of the true spectrum; and h. repeating steps c to g for successive modified estimates of the true spectrum while reducing the limit margin. a. placing a radiation detector system into suitable proximity with a test object, collecting radiation data emergent from the test object at the detector, resolving the radiation collected at the detector spectroscopically into a resolved dataset of measured flux at a plurality of energy bands, and thereby obtaining a spectroscopically resolved dataset of measured flux in which count data is resolved into values for each of a plurality of energy bands; b. generating an initial estimate of a true spectrum in which count data is resolved into values for each of the plurality of energy bands; c. operating on the estimate of the true spectrum using a response function of the detector used to collect the measured flux dataset so as to generate an estimate flux dataset; d. computing a merit value for statistical fit between the measured flux dataset and the estimate flux dataset; e. applying a perturbation to the value of each of the energy bands of the estimate of the true spectrum; f. repeating steps c and d to the estimate of the true spectrum so changed, accepting the change to the estimate of the true spectrum if the resultant merit value indicates an improvement or if the resultant merit value indicates a deterioration of less than a limit margin, and rejecting the change to the estimate of the true spectrum if the resultant merit value indicates a deterioration of more than a limit margin; g. repeating steps e and f for each further value of the estimate of the true spectrum to obtain a modified estimate of the true spectrum; and h. repeating steps c to g for successive modified estimates of the true spectrum while reducing the limit margin. <EOS>