Phase Retrieval Based on Fractional Order Total Variation Algorithm

Fig. 4. Reconstruction results of different orders of Cameraman with an oversampling rate of 3.34. (a) Original image; (b) α=1.0; (c) α=1.2; (d) α=1.4; (e) α=1.6; (f) α=1.8

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Fig. 5. Comparison of reconstruction results of different algorithms under noiseless conditions. (a)‒(c) Original images; (d)‒(f) HIO algorithm; (g)‒(i) RAAR algorithm; (j)‒(l) RAARL1 algorithm; (m)‒(o) FOTVPR algorithm with α=1.0; (p)‒(r) FOTVPR algorithm with α=1.6

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Fig. 6. Comparison of reconstruction results of different algorithms under noise conditions. (a)‒(c) Original images; (d)‒(f) OSS algorithm; (g)‒(i) RAAR algorithm; (j)‒(l) RAARL1 algorithm; (m)‒(o) FOTVPR algorithm with α=1.0; (p)‒(r) FOTVPR algorithm with α=1.6

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Fig. 7. Convergence curves of Fruits image reconstruction with 10% Gaussian noise. (a) PSNR iteration curves; (b) relative residues iteration curves

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Table 0. [in Chinese]

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Table 0. [in Chinese]

Algorithm 1 FOTVPR algorithm step

Input：observation amplitude b； non-negative support constraint set $s_{+}$ ； random initial value $u^{(0)}$ ； parameter settings： $λ = 100$ ， $ρ = 0.75$ ， $x^{(0)}, t^{(0)}, φ^{(0)}$ all set to 0， $μ_{1} = 0.05$ ， $μ_{2} = 0.5$

$μ_{3} = 1$ ， scale dual variable $d_{1}^{(0)}, d_{2}^{(0)}, d_{3}^{(0)}$ all set to 0， $i t e r$ =2000；

for k=0： $i t e r$ -1

（1） according to （23）， update dual variable $x^{(k + 1)}$

（2） according to （24）， update dual variable $t^{(k + 1)}$

（3） according to （26）， update image $u^{(k + 1)}$

（4） according to （27）， update auxiliary variable $φ^{(k + 1)}$

update scale dual variable $d_{1}, d_{2}, d_{3}$ ，according to（20）‒（22）

end

Output： reconstruct image $u^{k + 1}$

Table 1. Comparison of PSNR reconstruction results with different oversampling rates and orders

View table

Table 1. Comparison of PSNR reconstruction results with different oversampling rates and orders

Image

Oversampling rate

α

=1.0

α

=1.2

α

=1.4

α

=1.6

α

=1.8

Cameraman

3.88

3.34

2.91

2.56

55.39

53.03

50.63

48.81

54.41

52.68

50.08

47.97

53.01

51.12

48.63

47.02

50.99

49.71

47.29

45.79

49.68

48.21

46.72

45.28

Lena

3.88

3.34

2.91

2.56

42.79

42.82

41.74

41.43

41.75

42.07

40.79

40.06

40.53

40.38

39.66

24.15

39.27

28.36

38.37

38.11

38.41

36.23

28.22

Fruits

3.88

3.34

2.91

2.56

47.39

47.92

45.60

42.75

48.55

46.92

46.49

44.59

47.57

45.19

45.06

43.27

44.95

44.98

43.09

42.36

43.61

42.85

42.36

41.25

Table 2. Comparison of PSNR for noiseless reconstruction results of different algorithms

View table

Table 2. Comparison of PSNR for noiseless reconstruction results of different algorithms

Image

Oversampling rate

HIO

RAAR

RAARL1

α=1.0

α=1.6

Cameraman

3.88

3.34

2.91

2.56

36.30

33.12

25.52

23.82

33.51

33.68

24.12

23.97

43.52

43.56

43.52

43.44

54.67

52.58

51.17

48.92

51.44

49.02

47.26

45.44

Lena

3.88

3.34

2.91

2.56

37.89

38.88

32.38

23.22

36.83

38.03

27.71

23.25

42.88

43.37

37.78

37.67

42.87

43.03

42.46

41.46

38.98

39.31

32.39

38.29

Fruits

3.88

3.34

2.91

2.56

35.13

33.82

29.59

23.79

37.83

31.53

28.78

21.67

43.61

38.88

38.20

38.06

50.49

47.24

45.89

46.69

45.74

44.63

43.32

42.41

Table 3. Comparison of running times of different algorithms
View table
Table 3. Comparison of running times of different algorithms
Algorithm HIO RAAR RAARL1 α=1.0 α=1.6
Runtime /s 13.93 12.52 254.45 19.32 20.88

Table 4. Comparison of PSNR for noise reconstruction results of different algorithms

View table

Table 4. Comparison of PSNR for noise reconstruction results of different algorithms

Image

Noise intensity/%

OSS

RAAR

RAARL1

α=1.0

α=1.6

Cameraman

26.28

23.39

21.74

21.47

24.58

24.31

22.74

20.59

40.01

33.26

26.81

25.80

39.38

35.58

32.83

30.98

38.44

34.82

31.90

30.55

Lena

30.14

27.44

26.25

24.46

28.70

25.78

24.57

24.51

40.97

37.13

27.19

25.51

37.71

35.02

33.11

31.68

35.91

33.95

32.45

26.35

Fruits

26.50

22.48

20.92

20.24

26.97

22.35

21.03

20.53

36.21

32.33

24.82

23.34

37.29

33.36

30.03

28.35

36.02

32.43

30.13

28.83

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Mengwei Qin, Bo Chen, Bingliang Li, Jing Yang. Phase Retrieval Based on Fractional Order Total Variation Algorithm[J]. Laser & Optoelectronics Progress, 2025, 62(4): 0411003

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Paper Information

Category: Imaging Systems

Received: Jun. 12, 2024

Accepted: Aug. 1, 2024

Published Online: Mar. 5, 2025

The Author Email: Bo Chen (chenbo182001@163.com)

DOI:10.3788/LOP241465

CSTR:32186.14.LOP241465

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 0. [in Chinese]

Table 0. [in Chinese]

Table 1. Comparison of PSNR reconstruction results with different oversampling rates and orders

Table 1. Comparison of PSNR reconstruction results with different oversampling rates and orders

Table 2. Comparison of PSNR for noiseless reconstruction results of different algorithms

Table 2. Comparison of PSNR for noiseless reconstruction results of different algorithms

Table 3. Comparison of running times of different algorithms

Table 3. Comparison of running times of different algorithms

Table 4. Comparison of PSNR for noise reconstruction results of different algorithms

Table 4. Comparison of PSNR for noise reconstruction results of different algorithms