deletions | additions       diff --git a/DeclareMathOperator_argmin_argmin_newcommand_reals__.tex b/DeclareMathOperator_argmin_argmin_newcommand_reals__.tex  index 1efcd8c..290d063 100644  --- a/DeclareMathOperator_argmin_argmin_newcommand_reals__.tex  +++ b/DeclareMathOperator_argmin_argmin_newcommand_reals__.tex 
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\newcommand{\nk}{n_k}  \paragraph{Sparse MRI Appendix A revisited}  Here we provide a detailed derivation of the 'complex' gradient of each term in the cost function as defined in Equation [A1]. Since by definition the 'complex' gradient is just the  transpose of the 'complex' derivative, we first find expressions in terms of derivatives. The cost function $f(m) : \complex^m \to \reals$ is given by  \begin{equation}  f(m) = \| \Fu m - y\|^2_{\ell_2} + \lambda \| \Psi m\|_{\ell_1}.