### Citations

809 | A block sorting lossless data compression algorithm
- Burrows, Wheeler
- 1994
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Citation Context ...ple using Û�x, y� � round�U�x, y� � �2 m�1 � 1��U max�, (6) where U max � max�max�|Im�U�x, y��|�, max�|Re�U �x, y��|�). Following this, the quantized data are coded with a lossless algorithms such as =-=[21]-=- to further increase the compression rate. To obtain a reconstruction from the compressed data, lossless decoding is performed, and the decoded data are multiplied by U max to bring them back to their... |

465 |
efficient image codec based on set partitioning in hierarchical trees
- Said, Pearlman, et al.
- 1996
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Citation Context ...valued grayscale images so the usual image coding techniques can be used for their compression. Standard baseline JPEG [17] and JPEG2000 [18] as well as set partitioning in hierarchical trees (SPIHT) =-=[19]-=- coding have been used. These compression methods were designed for natural, real-world images and not for interference patterns. Nevertheless, it has been shown [11–13], and it is experimentally demo... |

379 | Splines: a perfect fit for signal and image processing
- Unser
- 1993
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Citation Context ...aphy applications [22]. They are a combination of b-spline wavelets and the Fresnel transform. One-dimensional b-splines of degree n are defined as the �n � 1�-fold convolution of a rectangular pulse =-=[23]-=- where � n �x� �� 0 � ... � � 0 �x�, (7) Ç n�1 times � 0 1, �1�2 � x � 1�2 �x� � 1�2, �x� � 1�2 0, otherwise. B-splines can be used to generate a multiresolution analysis of L2��� [24]. More specifica... |

106 |
Phase-shifting digital holography
- Yamaguchi, Zhang
- 1997
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Citation Context ...both parallax and depth effects can be illustrated. © 2007 Optical Society of America OCIS codes: 050.5080, 090.1760, 090.2880, 100.2000, 110.3000. 1. Introduction Phase-shifting interferometry (PSI) =-=[1]-=- digital holography is a 3D imaging technique where the complex light distribution at the plane of the recording camera can be calculated from several interference patterns corresponding to different ... |

63 |
Introduction to Fourier Optics (Roberts,
- Goodman
- 2005
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Citation Context ...lated at the plane of the camera. To reconstruct the wavefront at the plane of the object the PSI hologram has to be propagated to a distance d0. This can be done using the Fresnel–Kirchhoff integral =-=[16]-=- defined as Ud�x�, y�� � 1 � 2� �� �� � U�x, y�exp� �� �� i� � 2 ��x � x��2 � �y � y��2��dxdy � �U � G���x�, y��, (4) where G��x, y� � 1 i� 2 exp� � � 2 �x 2 � y 2 �� , (5) ����d, d is the propagation... |

61 |
Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt
- Schnars, Kreis, et al.
- 1996
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Citation Context ...erence light phases. Compared with other digital holography techniques this method has the advantage of increased reconstruction quality as the unwanted zero-order and twin image terms are eliminated =-=[2]-=-. This enables the use of an in-line recording setup reducing the recording sensor resolution requirements. As several interferograms have to be recorded, the use of the method is practically limited ... |

37 | Fresnelets: new multiresolution wavelet bases for digital holography
- Liebling, Blu, et al.
- 2003
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Citation Context ...D OPTICS 4581splane directly at the reconstruction plane [14] and the second uses Fresnelet decomposition [15]. Fresnelets are waveletlike bases specially designed for digital holography applications =-=[22]-=-. They are a combination of b-spline wavelets and the Fresnel transform. One-dimensional b-splines of degree n are defined as the �n � 1�-fold convolution of a rectangular pulse [23] where � n �x� �� ... |

27 | Compression of digital holograms for three-dimensional object reconstruction and recognition
- Naughton, Frauel, et al.
- 2002
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Citation Context ... PSI holographic data compression is of the significant importance. The speckle nature of the PSI holograms of macroscopic reflective objects places constraints on the possible compression efficiency =-=[4,5]-=-. Several techniques for PSI holographic data compression have been studied. Initially uniform scalar quantization of the PSI hologram values followed by lossless coding of the quantized data was sugg... |

19 | Compression of encrypted threedimensional objects using digital holography,” Opt
- Naughton, Javidi
- 2004
(Show Context)
Citation Context ...ation of b-spline wavelets and the Fresnel transform. One-dimensional b-splines of degree n are defined as the �n � 1�-fold convolution of a rectangular pulse [23] where � n �x� �� 0 � ... � � 0 �x�, =-=(7)-=- Ç n�1 times � 0 1, �1�2 � x � 1�2 �x� � 1�2, �x� � 1�2 0, otherwise. B-splines can be used to generate a multiresolution analysis of L2��� [24]. More specifically it has been shown that a two-scale r... |

16 |
Phase-shifting color digital holography
- Yamaguchi, Matsumura, et al.
- 2002
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Citation Context ...vefront consists of complex floating point numbers occupying a large amount of storage space. Recently introduced 0003-6935/07/214579-08$15.00/0 © 2007 Optical Society of America color PSI holography =-=[3]-=- requires that one wavefront for each of the primary colors (blue, green, and red) is used thus increasing the complexity. Practical applications of PSI holography, on the other hand, require that dat... |

9 | Efficient compression of Fresnel fields for internet transmission of three-dimensional images
- Naughton, McDonald, et al.
- 2003
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Citation Context ...nterestingly, with this blurring, the noise of the reconstructions is retained low after Fresnelet-based compression indicating that Fresnelets could be used to reduce speckle, as previously proposed =-=[6]-=-. 5. Conclusions A study of the visual effects of various PSI holographic data compression techniques on the reconstructions has been presented. The methods have been considered to fall within the fol... |

9 | Shift-orthogonal wavelet bases using splines
- Unser, Thévenaz, et al.
(Show Context)
Citation Context ...ctangular pulse [23] where � n �x� �� 0 � ... � � 0 �x�, (7) Ç n�1 times � 0 1, �1�2 � x � 1�2 �x� � 1�2, �x� � 1�2 0, otherwise. B-splines can be used to generate a multiresolution analysis of L2��� =-=[24]-=-. More specifically it has been shown that a two-scale relation of the form � n�x h�k�� n �x � k�, (9) 2� �� k where h�k� is the binomial filter h�k� � 1 n�1 2 n� k � holds. Also semiorthogonal b-spli... |

7 |
A companding approach for nonuniform quantization of digital holograms of three-dimensional objects
- Shortt, Naughton, et al.
- 2006
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Citation Context ...on followed by lossless coding of the quantized data [5–7], wavelet decomposition of U(x, y) and quantization of the wavelet coefficients [8], k-means quantization and lossless coding [9], companding =-=[20]-=-, and others. In this paper we will investigate only uniform scalar quantization at the camera plane and not other more advanced techniques such as k-mean quantization [9], which offer higher compress... |

6 |
Compression of interference patterns with application to phase-shifting digital holography
- Darakis, Soraghan
- 2006
(Show Context)
Citation Context ...e h�k� is the binomial filter h�k� � 1 n�1 2 n� k � holds. Also semiorthogonal b-spline wavelets of the form where (8) n ��j�2� n ��j,k � 2 � �2 �j x � k�� , (10) j,k�Z � n�x 2� �� k g�k�� n �x � k�, =-=(11)-=- with g�k� being the quadrature mirror filter of h�k� form Riesz bases of L2���. F-splines are Fresnel-transformed b-spline bases. By using the properties of the Fresnel transform (linearity, shift in... |

6 |
Use of Fresnelets for phase-shift digital hologram compression
- Darakis, Soraghan
- 2006
(Show Context)
Citation Context ...o not fulfill the two-scale relation condition. However the embeddedness of the decomposition is preserved as it has been shown [22]. B-splines can be extended to 2D as � n �x, y� �� n �x� · � n �y�, =-=(15)-=- where � corresponds to the tensor product. Similarly f-splines can be extended to 2D and hence 1D Fresnelet transform can be expanded to 2D. The Fresnelet coefficients of the wavefront U(x, y) at sca... |

5 |
Reconstruction domain compression of phaseshifting digital holograms
- Darakis, Soraghan
- 2007
(Show Context)
Citation Context ...fering promising results while using common image compression tech20 July 2007 � Vol. 46, No. 21 � APPLIED OPTICS 4579sniques. Finally, compression of PSI holographic data at the reconstruction plane =-=[13,14]-=- using Fresnelets [13,15] has been investigated as offering increased compression performance. In this paper we study the visual effects of the coding methods on the reconstructed images. Apart from a... |

3 |
Image compression in signal-dependent noise
- Shahnaz, Walkup, et al.
- 1999
(Show Context)
Citation Context ... PSI holographic data compression is of the significant importance. The speckle nature of the PSI holograms of macroscopic reflective objects places constraints on the possible compression efficiency =-=[4,5]-=-. Several techniques for PSI holographic data compression have been studied. Initially uniform scalar quantization of the PSI hologram values followed by lossless coding of the quantized data was sugg... |

3 |
Compression of digital holographic data using its electromagnetic field properties
- Kayser, Kreis, et al.
- 2005
(Show Context)
Citation Context ... 6 and 8 it can be seen that with high rate JPEG2000 coding of the interferograms the reconstruction suffers mainly from an increase in noise as well as ghosting effects, similar to those observed in =-=[25]-=-. These ghosting effects appear only in the case of JPEG2000 compression of the interferograms and not when other image compression techniques such as JPEG or SPIHT are applied. The main effect of qua... |

2 |
Effects of quantization in phase-shifting digital holography
- Mills, Yamaguchi
- 2005
(Show Context)
Citation Context ...rm � n�x h�k�� n �x � k�, (9) 2� �� k where h�k� is the binomial filter h�k� � 1 n�1 2 n� k � holds. Also semiorthogonal b-spline wavelets of the form where (8) n ��j�2� n ��j,k � 2 � �2 �j x � k�� , =-=(10)-=- j,k�Z � n�x 2� �� k g�k�� n �x � k�, (11) with g�k� being the quadrature mirror filter of h�k� form Riesz bases of L2���. F-splines are Fresnel-transformed b-spline bases. By using the properties of ... |

2 |
Measurement of compression defects in phase-shifting digital holographic data
- Darakis, Naughton, et al.
- 2006
(Show Context)
Citation Context ...fering promising results while using common image compression tech20 July 2007 � Vol. 46, No. 21 � APPLIED OPTICS 4579sniques. Finally, compression of PSI holographic data at the reconstruction plane =-=[13,14]-=- using Fresnelets [13,15] has been investigated as offering increased compression performance. In this paper we study the visual effects of the coding methods on the reconstructed images. Apart from a... |

1 |
are preparing a manuscript to be called “Nonuniform quantization compression of digital holograms
- Naughton
(Show Context)
Citation Context ...ested [5–7]. The method has also been applied following wavelet decomposition of the wavefront [8] and extended to use k-means instead of uniform quantization showing increased compression efficiency =-=[9]-=-. Each of these methods operates on the complex wavefront at the plane of the camera. Compression on the interference patterns has also been suggested [10–13] offering promising results while using co... |

1 |
Compression of phase-shifting digital holography interference patterns
- Darakis, Soraghan
- 2006
(Show Context)
Citation Context ...ce, and scaling) [22] the family of functions ���˜ n n j,k �� � G� * �j,k �j,k�Z can be derived. F-splines can be obtained by convolving G��x� with the b-spline � n �x� as �˜ n � �x� � �� n � G���x�. =-=(12)-=- The f-splines can then be used as appropriate bases to decompose the wavefront to different scales. More specifically the two-scale relation corresponding to Eq. (9) becomes �˜ n� ��2 x 2� �� k h�k��... |