The problem of detecting a defect inside the material in an ultrasonic nondestructive testing (NDT) session is addressed in this dissertation. What makes this problem a difficult one is the presence of clutter noise, which is signaldependent noise. The clutter noise in the material is caused by the microstructure of the material under test. When an ultrasonic wave travels through a coarsegrained material, the traveled pulse hits the grain boundaries, which will cause some of its energy to propagate back to the transducer and mask the echo from the defect if it exists. We tackle the problem by first establishing the statistical framework (using the hypothesis testing approach). Then, we propose a new physically motivated model for the clutter noise. We construct the physically motivated clutter model as the output of a random linear time-invariant (LTI) filter, whose impulse response can be assumed to be a realization of a Gaussian wide sense stationary (WSS) random process. Next, we determine the model mean, vii

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