Patent ID: 7301341

Claim:
A method of rapid magnetic resonance imaging using constrained optimization comprising the steps of: A) applying a magnetic gradient to an object, comprising the steps of: a) selecting a number N of discrete-time waveforms with a sampling period, τ, and time T=Nτ, b) expressing constraints as equations, c) identifying if a solution exists for T, and if not, increasing T until a solution exists, d) decreasing T to find a shortest solution, and e) solving the equations to identify said shortest solution, utilizing linear programming to identify said shortest solution, wherein the linear programming finds the vector x that minimizes a cost function f T x subject to the constraint Ax=<b, where matrix A and vector b are formed by combining all of the linear constraint equations for an amplifier and pulse sequence constraints, wherein said shortest solution is used for generation of said magnetic gradient; B) detecting imaging signals; and C) providing an image based on the detected image signals.