.MCAD 303010000 1 87 37 0 .CMD PLOTFORMAT 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 NO-TRACE-STRING 0 2 1 0 NO-TRACE-STRING 0 3 2 0 NO-TRACE-STRING 0 4 3 0 NO-TRACE-STRING 0 1 4 0 NO-TRACE-STRING 0 2 5 0 NO-TRACE-STRING 0 3 6 0 NO-TRACE-STRING 0 4 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 2 2 0 NO-TRACE-STRING 0 3 3 0 NO-TRACE-STRING 0 4 4 0 NO-TRACE-STRING 0 1 5 0 NO-TRACE-STRING 0 2 6 0 NO-TRACE-STRING 0 3 0 0 NO-TRACE-STRING 0 4 1 0 NO-TRACE-STRING 0 1 21 15 0 3 .CMD FORMAT rd=d ct=10 im=i et=6 zt=15 pr=3 mass length time charge temperature tr=0 vm=65545 .CMD SET ORIGIN 0 .CMD SET TOL 0.001000000000000 .CMD SET PRNCOLWIDTH 8 .CMD SET PRNPRECISION 4 .CMD PRINT_SETUP 0.800000 0.500000 0.500000 0.500000 0 .CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty* .CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 .CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables .CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants .CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text .CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1 .CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2 .CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3 .CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4 .CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5 .CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6 .CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7 .CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 .CMD UNITS U=1 .CMD DIMENSIONS_ANALYSIS 0 0 .TXT 2 26 1 0 Cg a37.375000,48.000000,54 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Image Restoration with the Parametric Wiener Filter}} } .TXT 1 42 2 0 Cg a10.750000,21.000000,15 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {PWF_2D}{.MCD}} } .TXT 1 -32 22 0 Cg a17.500000,49.625000,25 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Ken Castleman, 3/24/94}} } .TXT 2 2 25 0 Cg a10.500000,47.625000,17 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Section 16.2.4}} } .EQN 4 -37 16 0 {0:Np}NAME~20 .EQN 0 9 3 0 {0:i}NAME:0;{0:Np}NAME .EQN 0 10 4 0 {0:j}NAME:0;{0:Np}NAME .EQN 0 9 32 0 ({0:u}NAME)[({0:i}NAME):({0:i}NAME)/({0:Np}NAME)-0.5 .EQN 0 12 33 0 ({0:v}NAME)[({0:i}NAME):({0:i}NAME)/({0:Np}NAME)-0.5 .EQN 5 -40 14 0 {0:\s}NAME~0.2 .EQN 0 10 15 0 {0:k}NAME~20 .EQN 0 10 31 0 {0:N}NAME~0.08 .EQN 0 11 19 0 {0:\g}NAME~.05 .EQN 0 10 5 0 {0:\m}NAME~0 .EQN 0 16 8 0 {0:G}NAME({0:\m}NAME,{0:\s}NAME,{0:x}NAME)~{0:if}NAME(|({0:x}NAME-{0:\m}NAME)<3*{0:\s}NAME,({0:e}NAME)^(-((((({0:x}NAME-{0:\m}NAME))^(2))/((2*{0:\s}NAME*{0:\s}NAME))))),0) .TXT 4 -57 28 0 Cg b86.500000,86.500000,99 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {The image, f(x,y), has been blurred by H(u,v) and corrupted by additive white noise of power Pn.}} } .EQN 5 4 6 0 ({0:H}NAME)[({0:i}NAME,{0:j}NAME):{0:G}NAME({0:\m}NAME,{0:\s}NAME,({0:u}NAME)[({0:i}NAME))*{0:G}NAME({0:\m}NAME,{0:\s}NAME,({0:v}NAME)[({0:j}NAME)) .EQN 0 26 7 0 ({0:Pf}NAME)[({0:i}NAME,{0:j}NAME):(2)/(1+{0:k}NAME*{0:k}NAME*(((({0:u}NAME)[({0:i}NAME)-{0:\m}NAME))^(2)+((({0:v}NAME)[({0:j}NAME)-{0:\m}NAME))^(2))) .EQN 0 35 9 0 ({0:Pn}NAME)[({0:i}NAME,{0:j}NAME):{0:N}NAME .TXT 6 -64 24 0 Cg a6.625000,83.625000,14 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {The filter:}} } .EQN 3 9 10 0 ({0:K}NAME)[({0:i}NAME,{0:j}NAME):(({0:H}NAME)[({0:i}NAME,{0:j}NAME))/(((({0:H}NAME)[({0:i}NAME,{0:j}NAME)))^(2)+{0:\g}NAME*((({0:Pn}NAME)[({0:i}NAME,{0:j}NAME))/(({0:Pf}NAME)[({0:i}NAME,{0:j}NAME)))) .EQN 0 37 12 0 ({0:H}NAME)[(0,0):0 .EQN 0 10 13 0 ({0:Pf}NAME)[(0,0):0 .EQN 0 10 11 0 ({0:K}NAME)[(0.,0):0 .EQN 0 10 34 0 {0:m}NAME:({0:Np}NAME)/(2) .EQN 7 -77 17 0 {0:H}NAME{30 45 0 60 50 30 40 1 2 1 0 -2013727972 @}{57} .EQN 0 44 18 0 {0:Pf}NAME{30 45 0 60 100 30 38 1 2 1 0 -2013727972 @}{57} .TXT 35 -33 37 0 Cg a15.375000,76.500000,22 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain Blurring function MTF} } .TXT 0 43 36 0 Cg a16.500000,34.500000,22 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain Signal power spectrum} } .EQN 1 -54 21 0 &&(_n_u_l_l_&_n_u_l_l_)&({0:K}NAME)[({0:i}NAME,{0:m}NAME),({0:Pf}NAME)[({0:i}NAME,{0:m}NAME),({0:H}NAME)[({0:i}NAME,{0:m}NAME),({0:Pn}NAME)[({0:i}NAME,{0:m}NAME)@&0&(8&_n_u_l_l_)&({0:u}NAME)[({0:i}NAME) 0 0 1 0 5 0 1 0 0 1 1 0 0 1 0 1 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 1 2 0 NO-TRACE-STRING 0 1 3 0 NO-TRACE-STRING 0 1 4 0 NO-TRACE-STRING 0 2 5 0 NO-TRACE-STRING 0 3 6 0 NO-TRACE-STRING 0 4 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 2 2 0 NO-TRACE-STRING 0 3 3 0 NO-TRACE-STRING 0 4 4 0 NO-TRACE-STRING 0 1 5 0 NO-TRACE-STRING 0 2 6 0 NO-TRACE-STRING 0 3 0 0 NO-TRACE-STRING 0 4 1 0 NO-TRACE-STRING 0 1 31 25 0 3 .EQN 1 44 20 0 {0:K}NAME{30 45 0 60 90 26 38 0 2 1 0 -2013727972 8}{57} .TXT 31 11 35 0 Cg a15.625000,31.500000,25 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain Filter transfer function} } .TXT 3 -25 26 0 Cg a20.750000,64.625000,31 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {The Parametric Wiener Filter}} } .TXT 3 -30 30 0 Cg b86.500000,86.500000,280 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {In this example the noise dominates the entire upper half of the spectrum, but the blurring is not excessive.\par The paremeters k, N and }{\f1 s}{ permit modeling the signal and noise spectra and the blurring MTF, respectively, \par and }{\f1 g}{ controls the degree of restoration.}} }