Patent ID: 11965949
Assignee: STEPHAN MAIER
Field: Measurement (Instruments)
Classification: CPC G  A | IPC A  G

Claim 5:
6. The method according to claim 1, wherein the first estimation of noise σg for each pixel in step 1f) is made by performing the following computation:, σ
   g
  
  =
  
   
    1
    
     N
     f
    
   
   ⁢
   
    
     ∑
     1
     N
    
    
     
      
       (
       
        
         
          s
          ˆ
         
         i
        
        -
        
         s
         i
        
       
       )
      
      2
     
     
      
       2
       ⁢
       
        
         
          s
          ˆ
         
         i
        
        
         θ
         i
        
       
      
      +
      
       2
       ⁢
       
        θ
        i
       
       ⁢
       
        (
        
         
          
           s
           ˆ
          
          i
         
         -
         
          
           
            θ
            i
            2
           
           
            2
            ⁢
            
             
              s
              ˆ
             
             i
             2
            
           
          
          ⁢
          
           (
           
            
             exp
             (
             
              -
              
               
                θ
                i
                2
               
               4
              
             
             )
            
            ⁢
            
             
              π
              2
             
            
            ⁢
            
             
              
               
                s
                ˆ
               
               i
              
              
               θ
               i
              
             
             [
             
              
               
                
                 
                  
                   (
                   
                    
                     
                      s
                      ˆ
                     
                     i
                     2
                    
                    +
                    
                     2
                     ⁢
                     
                      
                       
                        s
                        ˆ
                       
                       i
                       2
                      
                      
                       θ
                       i
                       2
                      
                     
                    
                   
                   )
                  
                  ⁢
                  
                   I
                   0
                  
                  ⁢
                  
                   (
                   
                    
                     θ
                     i
                     2
                    
                    4
                   
                   )
                  
                 
                 +
                
               
              
              
               
                
                 
                  
                   s
                   ˆ
                  
                  i
                  2
                 
                 ⁢
                 
                  I
                  1
                 
                 ⁢
                 
                  (
                  
                   
                    θ
                    i
                    2
                   
                   4
                  
                  )
                 
                
               
              
             
             ]
            
           
           )
          
         
        
        )
       
      
     
    
   
  
 

wherein N equals the number of b-factors, and
wherein Nf=N−Np, and
wherein Np equals the number of free fit parameters, and
wherein θi is an estimated signal-to-noise ratio obtained in step 1e;
wherein ŝi is the best fit equation result, and
wherein si is the measured signal.