Qualitative properties of an entropy-based signal detector

Detection of molecular epitopes associated with neovasculature in a growing tumor presents a unique challenge for ultrasonic clinical imaging systems. In this study, we attempt to solve the problem of detection of site-specific contrast through the use of signal receivers i.e., mathematical operations that reduce an entire radio frequency (RF) waveform or a portion of it to a single number) based on information-theoretic quantities, such as Shannon Entropy (H), or its counterpart for continuous signal (H_f). These receivers appear to be sensitive to diffuse, low amplitude features of the signal that often are obscured by noise, or else lost in large specular echoes and, hence, not usually perceivable by a human observer. Qualitative and quantitative properties of the finite part, H_f, of the Shannon entropy of a continuous waveform f(t) in the continuum limit are derived in order to illuminate its use for waveform characterization.