TABLE I.

Summary of studies based on different entropic signal receivers defined for waveform $y=f(t)$ having density function $w_f(y)$: entropy, $H_f$, Renyi entropy, $I_f(r)$, and its asymptotic limiting form, $I_{f,\infty }$. The joint entropy $H_{f,g}$ is frequently much more sensitive than any of these.

“Entropic” receiver	Heuristic meaning	Scattering structure	Experimental system
$H_f=-{\int }_{f_{\mathit{m}\mathit{i}\mathit{n}}}^{f_{\mathit{m}\mathit{a}\mathit{x}}}{w}_f(y)\log \left[w_f(y)\right]dy$	“Information” contained	Materials characterization,	Graphite/epoxy laminates (Ref. 5)
$H_f=-{\int }_0^1\log \left[{f\prime }_{\uparrow }(t)\right]dt$	“Information” contained in backscattered RF $f(t)$.	Targeted nanoparticles, smooth muscle cells	MDA 435 (Ref. 16), B16
			VX2,MDx mice (Ref. 11)
			Precancer models (Ref. 7)
			Humans (Ref. 12)
$I_f(r)=1/1-r\text{log}{\int }_{f_{\mathit{min}}}^{f_{\mathit{max}}}{w}_f{(y)}^r\mathit{dy}$	“Weighted-information” contained in backscattered RF: $f(t)$ (note: $H_f=I_f(1)$).	Targeted nanoparticles, smooth muscle cells	MDA 435, B16 Precancer models (Ref. 17)
$I_{f,\infty }=\log \left[\left\{t_k\right|f\prime (t_k)=0\}1/\left|f^{″}\left(t_k\right)\right|\right]$	Limiting form of $I_f(r)$ as $r\to 2$. More sensitive than $H_f$, $I_f(r)$.	Targeted nanoparticles,	MDA 435 (Ref. 8), B16 (Ref. 10)
		smooth muscle cells	Humans
			Precancer models (Ref. 15)