Abstract: The inverse problem of object detection in a turbid medium such as breast tissue has been studied extensively recently using advanced optical techniques and high power laser. We propose an alternative approach to using photon migration statistics and Bayesian decision procedure in analyzing the transmitted speckle profile provided by low power lasers. The non-uniform turbid medium was imitated by an oil colloidal system embedded with millimeter size tubes simulating the connective ducts as observed in x-ray breast mammograms. Therefore, the tube depth positions of the colloidal system were intentionally left as an unknown quantity with prior probability. The object is a ceramic particle mimicking the calcified object in the tissue that is undetectable by x-ray mammograms. Bayesian decision procedure, using object size as action, was applied to a region of interest. The expected loss for each action was taken as the departure of the observed data from the predicted results obtained from the migration statistics with respect to the tube's prior probabilities. It appears that the proposed Bayesian decision procedure is viable for detecting small objects embedded in non-uniform turbid media and would be a supplement to the current x-ray mammography. !10
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