A method of producing blood flow velocity vector imagery, comprising: emitting N unfocused plane wave acoustic signals at each of M angles Θ m to a transducer array into a medium over substantially an entire field of measurement, wherein M is at least 1, N is at least 2 and m ∈{1,..., M}; receiving scattered and reflected ultrasonic signals on the transducer array in response to the emission; processing the received ultrasonic signals to extract for each image point of an image of the medium information in the form of ensembles of observations r m = [ r m,..., r m ( N - 1)] T,where r m is an image point signal for the angle Θ m and N is the number of unfocused plane wave acoustic signals emitted per angle Θ m, to construct a blood flow velocity vector signal, by: wall filtering the extracted information, wherein for each image point the wall filtered signal data vector is Ŝ, with the angle index m suppressed; using the wall-filtered information to form compressed format conjugate-lagged products, wherein the conjugate-lagged products F(p, t, l) of a vector of time samples s(t), at pixel image point p, of signal data vector Ŝ are computed in compressed amplitude format, for one or more lags l - 0, l - 1,... as F p t l = s ^ t s ^ t − l * s ^ t s ^ t − l * − 1 / 2 wherein the terms ŝ(t)ŝ(t-I)* are summands of the sample autocorrelation at lag l; forming a vector velocity measurement model by using space-time gradient operation on the products, and solving said model by a weighted least squares scheme; detecting the presence of blood flow at a pixel by qualifying blood flow vector velocity signals through a series of tests on values of quality metrics produced as byproducts of the blood flow vector velocity estimation procedure; and generating on a display device blood flow vector velocity imagery from the blood flow vector velocity signal. emitting N unfocused plane wave acoustic signals at each of M angles Θ m to a transducer array into a medium over substantially an entire field of measurement, wherein M is at least 1, N is at least 2 and m ∈{1,..., M}; receiving scattered and reflected ultrasonic signals on the transducer array in response to the emission; processing the received ultrasonic signals to extract for each image point of an image of the medium information in the form of ensembles of observations r m = [ r m,..., r m ( N - 1)] T,where r m is an image point signal for the angle Θ m and N is the number of unfocused plane wave acoustic signals emitted per angle Θ m, to construct a blood flow velocity vector signal, by: wall filtering the extracted information, wherein for each image point the wall filtered signal data vector is Ŝ, with the angle index m suppressed; using the wall-filtered information to form compressed format conjugate-lagged products, wherein the conjugate-lagged products F(p, t, l) of a vector of time samples s(t), at pixel image point p, of signal data vector Ŝ are computed in compressed amplitude format, for one or more lags l - 0, l - 1,... as F p t l = s ^ t s ^ t − l * s ^ t s ^ t − l * − 1 / 2 wherein the terms ŝ(t)ŝ(t-I)* are summands of the sample autocorrelation at lag l; forming a vector velocity measurement model by using space-time gradient operation on the products, and solving said model by a weighted least squares scheme; detecting the presence of blood flow at a pixel by qualifying blood flow vector velocity signals through a series of tests on values of quality metrics produced as byproducts of the blood flow vector velocity estimation procedure; and wall filtering the extracted information, wherein for each image point the wall filtered signal data vector is Ŝ, with the angle index m suppressed; using the wall-filtered information to form compressed format conjugate-lagged products, wherein the conjugate-lagged products F(p, t, l) of a vector of time samples s(t), at pixel image point p, of signal data vector Ŝ are computed in compressed amplitude format, for one or more lags l - 0, l - 1,... as F p t l = s ^ t s ^ t − l * s ^ t s ^ t − l * − 1 / 2 wherein the terms ŝ(t)ŝ(t-I)* are summands of the sample autocorrelation at lag l; forming a vector velocity measurement model by using space-time gradient operation on the products, and solving said model by a weighted least squares scheme; detecting the presence of blood flow at a pixel by qualifying blood flow vector velocity signals through a series of tests on values of quality metrics produced as byproducts of the blood flow vector velocity estimation procedure; and are summands of the sample autocorrelation at lag l; forming a vector velocity measurement model by using space-time gradient operation on the products, and solving said model by a weighted least squares scheme; detecting the presence of blood flow at a pixel by qualifying blood flow vector velocity signals through a series of tests on values of quality metrics produced as byproducts of the blood flow vector velocity estimation procedure; and generating on a display device blood flow vector velocity imagery from the blood flow vector velocity signal.