Abstract Continuous developments in cardiovascular imaging, software, and hardware have led to technological advancements that open new ways for assessing myocardial mechanics, hemodynamics, function. The technical shift from clinical ultrasound machines rely on conventional line-per-line beam transmissions ultrafast imaging based plane or diverging waves provides very high frame rates of up 50...

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

in this paper, g-dual function-valued frames in l2(0;1) are in-troduced. we can achieve more reconstruction formulas to ob-tain signals in l2(0;1) by applying g-dual function-valued framesin l2(0;1).