Reconstruction with Adaptive Feature-specific Imaging by ert554898

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									Reconstruction with Adaptive
  Feature-specific Imaging

     Jun Ke1 and Mark A. Neifeld1,2

    1Department   of Electrical and Computer Engineering,
              2College    of Optical Sciences
                     University of Arizona




          Frontiers in Optics 2007
                       Outline

 Motivation for FSI and adaptation.
 Adaptive FSI using PCA/Hadamard features.
 Adaptive FSI in noise.
 Conclusion.




                Frontiers in Optics 2007
                                  Motivation - FSI
Reconstruction with Feature-specific Imaging (FSI) :
 Sequential

                        Fmn  x n1  y m1
architecture:
      object
                                                                              M nm  y m1  x n1
                                                                                              ˆ
                                                            feature                         object estimate
                  Imaging
                   optics            Imaging
                                                            yi  x T f i   Reconstruction
                                      optics                               matrix M (nxm)
      x ( n1)                                      single
                                                   detector
                                                                                                   ˆ
                                                                                                   x
                      DMD
                              f i ( n1) (i  1,2,, M )
   Parallel                                                                    FSI benefits:
                                         y1  x T f1
 architecture:   f1
                                                                                 Lower hardware complexity
                 LCD
                                         y2  x T f 2                            Smaller equipment size/weight
                                                                                 Higher measurement SNR
     x ( n1)    LCD                                       M (nxm)
                 f2                                                              High data acquisition rate

                                         yM  x Tf M                             Lower operation bandwidth
                 fM
                                                                                 Less power consumption
                 LCD



                               Frontiers in Optics 2007
                       Motivation - Adaptation
   The design of projection vector effects reconstruction quality.
      Using PCA projection as example                            Well designed
                                                 Adaptive PCA   projection vectors
               Poorly designed
   Static PCA projection vectors
                                                                      Projection value

                                                                                  Training samples
       Projection
                           Testing sample
         axis 2                                                               for 2nd projection vector




                                            Projection
                                              axis 1
                     Training samples
Projection
  axis 1                           Estimation
                                                                                             Projection
                                                                                               axis 2


                                                         Estimation
    Acquire feature measurements sequentially
    Use acquired feature measurements and
   training data to adapt the next projection vector


                              Frontiers in Optics 2007
                                  PCA-Based AFSI
Adaptive FSI (AFSI) – PCA:                                                          K(1) nearest samples
                                                                                                               Projection axis 1
                                                 Selected samples
  K(1) nearest samples
                              Projection axis
                                                According to 1st feature




                                                                                                  Testing
                                                                                                  sample       Projection axis 2
                                                    According to   2nd   feature
                                                                                                           Object estimate
                      Testing sample
                                                                                   Object x                 x i   ym f m
                                                                                                            ˆ
                                                                                                                m 1...i


                                            Calculate R1 from A1
                                                                                                           Reconstruction
       i: adaptive step index
       Ai: ith training set                        Calculate f 1            Computational
                                                                               Optics                          yi = f iTx
       Ri: autocorrelation matrix of A i
       fi: dominate eigenvector of A i                                                                 Update Ai to Ai+1
                                                                             Calculate f i+1
       yi: feature value measured by                                                                    according to yi
       fi
   High diversity of training data helps adaptation                                            Ri+1


                                  Frontiers in Optics 2007
                          PCA-Based AFSI
Object examples (32x32):




 Feature measurements: y = Fx          where,   x : N 1 F: M  N
   M is the total # of features

                        ˆ
 Reconstructed object: x = F y
                                   T



 RMSE:         E{|| x - x ||2 }/ N
                       ˆ

 Number of training objects: 100,000

 Number of testing objects: 60


                          Frontiers in Optics 2007
                               PCA-Based AFSI
AFSI – PCA:




        K increases



Reconstruction from static FSI (M = 100)


                                            RMSE reduces using more features
                                            RMSE reduces using AFSI compare to static FSI
 Reconstruction from AFSI (M = 100)
                                            Improvement is larger for high diversity data
                                            RMSE improvement is 33% and 16% for high and
                                           low diversity training data, when M = 250.



                               Frontiers in Optics 2007
                              Hadamard-Based AFSI
 AFSI – Hadamard:                     Projection vector’s implementation order is adapted.
                                                  First 5 Hadamard basis
                                                ←Static FSI         AFSI→

                            projection axis 1                                     projection axis 2          projection axis 1
sample
 mean                                            Selected samples
                                              according to 1st feature

testing                                                                            testing sample
sample
                            K(1) nearest                                                                        K(1) nearest
                             samples                          according to 2nd feature                           samples

                                                                                                                          sample
                                                                                                                           mean




                                                      Object x                    Object estimate     Reconstruction

                 Sort
   x1(mean)                        Choose         Computational                                        yiL+j = f iL+jTx
               Hadamard
                                    f 1~f L          Optics                                              (j=1,…,L)
                bases
 xi(mean): average vector of A i                        Choose                                        Update Ai to Ai+1
                                                                           Sort          xi+1(mean)
 fi: dominant Hadamard vector for A i               f iL+1 ~ f (i+1)L                                 according to yiL+j


                                      Frontiers in Optics 2007
                       Hadamard-Based AFSI
AFSI – Hadamard:




                                                     L decreases




                                                                       L increases
      K increases



      Reconstruction from static FSI     RMSE reduces in AFSI compared with static FSI
                                         RMSE improvement is 32% and 18% for high
                                        and low diversity training data, when M = 500 and
                                        L = 10.
     Reconstruction from adaptive FSI    AFSI has smaller RMSE using small L when M is
                                        also small
                                         AFSI has smaller RMSE using large L when M is
                                        also large


                              Frontiers in Optics 2007
              Hadamard-Based AFSI – Noise
AFSI – Hadamard:
      Calculate x1(mean)                            Object estimate
                                 Object x
                                                     xi  m1...i ymfm
                                                     ˆ
                                                                                  y  y 0  n  Fx  n
      Sort Hadamard
           bases                                    Reconstruction

                            Computational          yiL+j = f iL+jTx+niL+j   Calculate
       Choose f 1~f L          Optics                  (j = 1,2,…L)         Ri for Ai

                           Choose f iL+1~f(i+1)L     ˆ
                                                     yiL  j from de-
                                                                                  M y  R y (R y  Rn )1
                                                       noising yiL+j
                                                                                  R y  E{yyT }
                                   Sort
  T : integration time
                                                                                         E{(Fx)(Fx)T }
  σ0 2 = 1                     xi+1(mean)          Update Ai to Ai+1
                                                                  ˆ
                                                     according to yiL  j                FR x FT

  Hadmard projection is used because of its good reconstruction performance
  Feature measurements are de-noised before used in adaptation
  Auto-correlation matrix is updated in each adaptation step
  Wiener operator is used for object reconstruction

                               Frontiers in Optics 2007
         Hadamard-Based AFSI – Noise
 T : integration time/per feature              detector noise variance σ2 = σ02 /T
 σ0 2 = 1
       High diversity training data; σ02 = 1                            High diversity training data; σ02 = 1




                                                          L decreases




                                                                                                     L increases
                                                                        K increases




 RMSE in AFSI is smaller than in static FSI
 RMSE is reduced further by modifying Rx in each adaptation step
 RMSE improvement is larger using small L when M is also small
 RMSE is small using large L when M is also large

                              Frontiers in Optics 2007
            Hadamard-Based AFSI – Noise
          High diversity training data; σ02 = 1             High diversity training data; σ0 2 = 1




      T : integration time/per feature;           M0: the number of features
      Total feature collection time = T × M0

 RMSE reduces as T increases
 High reconstruction quality requirement needs longer total feature collection time
 To achieve each RMSE requirement, there is a minimum total feature collection time.



                                 Frontiers in Optics 2007
                           Conclusion
Noise free measurements:
 PCA-based and Hadmard-based AFSI system are presented
 AFSI system presents lower RMSE than static FSI system


Noisy measurements:
 Hadamard-based AFSI system in noise is presented
 AFSI system presents smaller RMSE than static FSI system
 There is a minimum total feature collection time to achieve a reconstruction
quality requirement




                      Frontiers in Optics 2007

								
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