MRI gradient waveform design using convex optimization
First Claim
Patent Images
1. 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, ande) 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 fTx 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.
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Abstract
A time-optimal MRI gradient design method utilizes constrained optimization to design minimum-time gradient waveforms that satisfy gradient amplitude and slew-rate limitations. Constraints are expressed as linear equations which are solved using linear programming, L1-norm formulation, or second-order cone programming (SOCP).
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Citations
25 Claims
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1. A method of rapid magnetic resonance imaging using constrained optimization comprising the steps of:
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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 fTx 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. - View Dependent Claims (2, 3, 4, 5, 6)
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7. A method of rapid magnetic resonance imaging using constrained optimization comprising the steps of:
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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, wherein steps c), d), and e) include adding slack variables to the optimization, 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. - View Dependent Claims (8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24)
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25. A method of rapid magnetic resonance imaging using constrained optimization comprising the steps of:
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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 a second-order cone programming (SOCP) to find said shortest solution x that minimizes a linear pulse function fTX subject to a second order cone constraint
∥
Ax+b∥
2≦
Cx+d
which is a superset of the linear constraints in linear programming where matrices A and B and vectors b and d are formed by combining all linear constraint equations for 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.
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Specification