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LaTeX errors found:
! Undefined control sequence.
<recently read> \mathbb 
                        
l.55 ...nce between points in \eqn{\mathbb{R}^3}{}
                                                  .
! Undefined control sequence.
<recently read> \mathbb 
                        
l.72 ...inates of N points in \eqn{\mathbb{R}^3}{}
                                                  . Each row should correspo...
! Undefined control sequence.
<argument> T_{\mathfrak 
                        F} : \mathbb R^V \rightarrow \mathbb R^I
l.121 ... : \mathbb R^V \rightarrow \mathbb R^I}{}
                                                  . Given a function \eqn{f ...
! Undefined control sequence.
<argument> T_{\mathfrak F} : \mathbb 
                                     R^V \rightarrow \mathbb R^I
l.121 ... : \mathbb R^V \rightarrow \mathbb R^I}{}
                                                  . Given a function \eqn{f ...
! Undefined control sequence.
<argument> ...} : \mathbb R^V \rightarrow \mathbb 
                                                  R^I
l.121 ... : \mathbb R^V \rightarrow \mathbb R^I}{}
                                                  . Given a function \eqn{f ...
! Undefined control sequence.
<argument> f \in \mathbb 
                         R^V
l.121 ...iven a function \eqn{f \in \mathbb R^V}{}
                                                  , the analysis operation i...
! Undefined control sequence.
<argument> T_{\mathfrak 
                        F}f=(\langle f,r_i \rangle )_{i \in I}
l.122 ... F}f=(\langle f,r_i \rangle)_{i \in I}}{}
                                                  
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.421 ... scales, and \eqn{\lambda_{\text{max}}}{}
                                                   is the largest eigenvalue.
! Undefined control sequence.
<argument> \log (\lambda _{\text 
                                 {max}})
l.424 ...ext{max}})}{\log(b)} \right\rfloor + 2}{}
                                                   the wavelet coefficients ...
! Undefined control sequence.
<argument> k_{\text 
                    {max}}
l.440 The computation of \eqn{k_{\text{max}}}{}
                                                using \eqn{\lambda_{\text{ma...
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.440 ...x}}}{} using \eqn{\lambda_{\text{max}}}{}
                                                   and \eqn{b}{} applies pri...
! Undefined control sequence.
<argument> g : \mathbb 
                       R_+ \rightarrow \mathbb R_+
l.667 ... : \mathbb R_+ \rightarrow \mathbb R_+}{}
                                                  , the expectation of the g...
! Undefined control sequence.
<argument> g : \mathbb R_+ \rightarrow \mathbb 
                                               R_+
l.667 ... : \mathbb R_+ \rightarrow \mathbb R_+}{}
                                                  , the expectation of the g...
! Undefined control sequence.
<argument> k_{\text 
                    {max}}
l.743 The computation of \eqn{k_{\text{max}}}{}
                                                using \eqn{\lambda_{\text{ma...
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.743 ...x}}}{} using \eqn{\lambda_{\text{max}}}{}
                                                   and \eqn{b}{} applies pri...
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.868 ... scales, and \eqn{\lambda_{\text{max}}}{}
                                                   is the largest eigenvalue.
! Undefined control sequence.
<argument> \log (\lambda _{\text 
                                 {max}})
l.871 ...ext{max}})}{\log(b)} \right\rfloor + 2}{}
                                                   the reconstructed signal ...
! Undefined control sequence.
<argument> k_{\text 
                    {max}}
l.886 The computation of \eqn{k_{\text{max}}}{}
                                                using \eqn{\lambda_{\text{ma...
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.886 ...x}}}{} using \eqn{\lambda_{\text{max}}}{}
                                                   and \eqn{b}{} applies pri...
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.1353 ... eigenvalue \eqn{\lambda_{\text{max}}}{}
                                                   and the parameter \eqn{b}...
! Undefined control sequence.
<argument>  k_{\text 
                     {max}} = \left \lfloor \frac {\log (\lambda _{\text {ma...
l.1356 }{}
          
! Undefined control sequence.
<argument> \log (\lambda _{\text 
                                 {max}})
l.1356 }{}
          
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.1358 ...e range [0, \eqn{\lambda_{\text{max}}}{}
                                                  ] for each scale.
! Undefined control sequence.
<argument> k_{\text 
                    {max}}
l.1363 The computation of \eqn{k_{\text{max}}}{}
                                                 using \eqn{\lambda_{\text{m...
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.1363 ...}}}{} using \eqn{\lambda_{\text{max}}}{}
                                                   and \eqn{b}{} applies pri...
! Undefined control sequence.
<argument>  \mathbb 
                    E \left [\|\mathbf {F} - h(\widetilde {\mathbf {F}})\|_2...
l.1790 }{}
          
! Undefined control sequence.
<argument> ...thbf {F}})\|_2^2 \right ] = \mathbb 
                                                  E \left [-n\sigma ^2 + \|\...
l.1790 }{}
          
! Undefined control sequence.
<argument> T_{\mathfrak 
                        F}
l.1996 ...nalysis operator \eqn{T_{\mathfrak F}}{}
                                                   and is defined by the lin...
! Undefined control sequence.
<argument> T_{\mathfrak 
                        F}^\ast : \mathbb R^I \rightarrow \mathbb R^V
l.1996 ...: \mathbb R^I \rightarrow \mathbb R^V}{}
                                                  . For a vector of coeffici...
! Undefined control sequence.
<argument> T_{\mathfrak F}^\ast : \mathbb 
                                          R^I \rightarrow \mathbb R^V
l.1996 ...: \mathbb R^I \rightarrow \mathbb R^V}{}
                                                  . For a vector of coeffici...
! Undefined control sequence.
<argument> ...t : \mathbb R^I \rightarrow \mathbb 
                                                  R^V
l.1996 ...: \mathbb R^I \rightarrow \mathbb R^V}{}
                                                  . For a vector of coeffici...
! Undefined control sequence.
<argument> T^\ast _{\mathfrak 
                              F}(c_i)_{i \in I}=\sum _{i \in I} c_i r_i
l.1997 ...c_i)_{i \in I}=\sum_{i \in I} c_i r_i}{}
                                                  
! Undefined control sequence.
<argument> k_{\text 
                    {max}}
l.2074 The computation of \eqn{k_{\text{max}}}{}
                                                 using \eqn{\lambda_{\text{m...
! Undefined control sequence.
<argument> \lambda _{\text 
                           {max}}
l.2074 ...}}}{} using \eqn{\lambda_{\text{max}}}{}
                                                   and \eqn{b}{} applies pri...
! Undefined control sequence.
<argument> \omega : \mathbb 
                            R^+ \rightarrow [0,1]
l.2134 ...omega : \mathbb R^+ \rightarrow [0,1]}{}
                                                   be a function with suppor...
! Misplaced alignment tab character &.
<argument>  \omega (x) = \begin {cases} 1 &
                                            \text {if } x \in [0,b^{-1}] \\ ...
l.2141 }{}
          
! Undefined control sequence.
<argument>  \omega (x) = \begin {cases} 1 & \text 
                                                  {if } x \in [0,b^{-1}] \\ ...
l.2141 }{}
          
! Misplaced alignment tab character &.
<argument> ...frac {x}{1 - b} + \frac {b}{b - 1} &
                                                   \text {if } x \in (b^{-1}...
l.2141 }{}
          
! Undefined control sequence.
<argument> ...}{1 - b} + \frac {b}{b - 1} & \text 
                                                  {if } x \in (b^{-1}, 1] \\...
l.2141 }{}
          
! Misplaced alignment tab character &.
<argument> ...\text {if } x \in (b^{-1}, 1] \\ 0 &
                                                   \text {if } x > 1 \end {c...
l.2141 }{}
          
! Undefined control sequence.
<argument> ...if } x \in (b^{-1}, 1] \\ 0 & \text 
                                                  {if } x > 1 \end {cases} 
l.2141 }{}
          
! Undefined control sequence.
<argument>  \mathfrak 
                      F = \left \{ \sqrt {\psi _j}(\mathcal {L})\delta _i : ...
l.2158 }{}