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This Concept Map, created with IHMC CmapTools, has information related to: Dim_Reduc, Q is the source matrix, ∇F is the linearized Born scattering matrix, correlations between <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> A and </mtext> <mmultiscripts> <mtext> x </mtext> <none/> <mtext> t </mtext> </mmultiscripts> </mrow> </math>, the misfit can be Robust misfit, Subsampling by considering a fixed small number, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <munderover> <mtext> min </mtext> <mtext> m </mtext> <none/> </munderover> <mtext> φ(m) = ρ(D - F(m;Q)) </mtext> </mrow> </math> where m, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <munderover> <mtext> min </mtext> <mtext> δm </mtext> <none/> </munderover> <mtext> </mtext> <mmultiscripts> <mtext> ||δD- ∇F(m;Q) δm|| </mtext> <mtext> 2 </mtext> <mtext> 2 </mtext> </mmultiscripts> </mrow> </math> where ∇F, Simultaneous sources given by <math xmlns="http://www.w3.org/1998/Math/MathML"> <mmultiscripts> <mrow> <munderover> <mtext> q </mtext> <none/> <mtext> ~ </mtext> </munderover> </mrow> <mtext> j </mtext> <none/> </mmultiscripts> <mtext> = </mtext> <sum/> <mmultiscripts> <mtext> w </mtext> <mtext> ij </mtext> <none/> </mmultiscripts> <mmultiscripts> <mtext> q </mtext> <mtext> i </mtext> <none/> </mmultiscripts> </math>, gradient updates of the form <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mmultiscripts> <mtext> x </mtext> <none/> <mtext> t+1 </mtext> </mmultiscripts> <mtext> = </mtext> <mmultiscripts> <mtext> x </mtext> <none/> <mtext> t </mtext> </mmultiscripts> <mtext> + </mtext> <mmultiscripts> <mtext> A </mtext> <none/> <mtext> H </mtext> </mmultiscripts> <mtext> (b - A </mtext> <mmultiscripts> <mtext> x </mtext> <none/> <mtext> t </mtext> </mmultiscripts> <mtext> ) </mtext> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mmultiscripts> <mtext> R </mtext> <none/> <mtext> Σ </mtext> </mmultiscripts> <mtext> ⊗I </mtext> </mrow> </math> with <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mmultiscripts> <mtext> R </mtext> <none/> <mtext> Σ </mtext> </mmultiscripts> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <munderover> <mtext> min </mtext> <mtext> δm </mtext> <none/> </munderover> <mtext> </mtext> <mmultiscripts> <mtext> ||δD- ∇F(m;Q) δm|| </mtext> <mtext> 2 </mtext> <mtext> 2 </mtext> </mmultiscripts> </mrow> </math> where δD, Batching allows explicit control over the error, δD is the linearized data, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mmultiscripts> <mtext> w </mtext> <mtext> i </mtext> <none/> </mmultiscripts> </mrow> </math> are Uniform randomly selected columns of the scaled identity matrix, m is the vector of unknow medium parameters, Optimally sparse representation of wavefields in Curvelet frame, Non-linear Problem is given by <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <munderover> <mtext> min </mtext> <mtext> m </mtext> <none/> </munderover> <mtext> φ(m) = ρ(D - F(m;Q)) </mtext> </mrow> </math>, F is the forward operator, the misfit can be Least-Squares misfit, LASSO problem can be solved using <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mmultiscripts> <mtext> SPGL </mtext> <mtext> 1 </mtext> <none/> </mmultiscripts> </mrow> </math>
