Incorporating low-resolution image into phase retrieval process
Incorporating low-resolution image into phase retrieval process
OUTPUT
1 Motivation
Coherent Diffraction Imaging (CDI), in which the sample’s diffraction intensity is measured, is a widely used technique for investigating non-periodic structures in biological systems such as viruses and cells [1]. While the resulting diffraction pattern provides the intensity of Fourier trans-form (FT) of the original image, the original image is generally inaccessible unless both its spectral amplitude (square root of the intensity) and phase components are available for performing inverse Fourier transform (IFT). Several phase retrieval algorithms have been developed to extract the phase component from the oversampled intensity component [2], the most well-known of which being the Hybrid Input-Output (HIO) algorithm [3]. HIO, an iterative algorithm, starts with a set of random phases as initial guess, then applies IFT and FT to the image to move it back and forth between re-
ciprocal and real spaces, where constraints such as finite support and Fourier amplitude are applied
to refine the calculated image, as shown in Figure 1(a).
In general HIO can give reasonable reconstruction result, but it usually takes few thousands
of cycles to converge, and sometimes it stagnates at a suboptimal result. In addition, phasing
algorithms like HIO are generally vulnerable to data defects such as quantum noise (due to limited
photon flux) and missing intensities (due to low frequency components being blocked). For the
reasons above, running phase retrieval algorithms like HIO for experimental data is generally costly
in terms of computation resources and time, as people would need to run HIO with large iteration
numbers multiple times to get optimal reconstruction result. While the calculated image is usually
validated by comparing it with a low-resolution (LR) image from other source such as an optical
microscope or scanning electron microscope (SEM), here we propose we can incorporate a low-
resolution image into the phase retrieval algorithm as a prior to guide the phasing process, thus
enhancing the reconstruction fidelity and convergence rate.
2 Project description
This project aims to improve upon the HIO algorithm by incorporating a low resolution image
as a stronger prior than the finite support constraint used by most algorithms, developing a phase
retrieval algorithm with a higher reconstruction fidelity and convergence rate. Figure 1(b) shows
the proposed pipeline we will be developing. We expect the modified algorithm to outperform the
original HIO, given a reasonably quality of the LR prior, as the LR image contains not only the
support boundary but also local intensities information.
For this project, LR images will be numerically generated by applying a Gaussian filter to the
original image with different bandwidth parameters; diffraction pattern will be simulated by using
fast Fourier transform (FFT). The reconstruction fidelity will be evaluated by a discrepancy function
ER(ρ0, ρcalc) which compares the calculated image ρcalc with the original one ρ0.
The main challenge of the project is to find a mathematically reasonable and computationally
practical way to constrain computed real space images based on the LR image. Previously we
have experimented with a na¨ıve technique where the on-the-flight real space image is dynamically
guided by the LR image with a simple linear combination [4]. For this project, We will research
into different methods for optimizing an image to be closer to the given LR image in a dynamic
fashion which can be tuned for convergence. One of the possible candidate method is to use the
deblurred LR image computed from Richard-Lucy deconvolution [5] or the ADMM algorithm [6]
to constrain the real space domain image.
3 Android devices
This project does not use Andorid devices.
References
[1] J. Miao et al., Nature 400, 342 (1999).
[2] J. Miao et al., Phys. Rev. Lett. 95, 085503 (2005).
[3] R. Fienup, Appl. Opt. 21, 2758 (1982).
[4] P.-N. Li et al. (under preparation).
[5] R. Hardley, JOSA 62, 55 (1972).
[6] M. Figueiredo and J. Bioucas-Dias, IEEE Trans. Image Process. 19, 3133 (2010).
FOR BASE PAPER PLEASE MAIL US AT ARNPRSTH@GMAIL.COM
DOWNLOAD SOURCE CODE CLICK HERE
OUTPUT
1 Motivation
Coherent Diffraction Imaging (CDI), in which the sample’s diffraction intensity is measured, is a widely used technique for investigating non-periodic structures in biological systems such as viruses and cells [1]. While the resulting diffraction pattern provides the intensity of Fourier trans-form (FT) of the original image, the original image is generally inaccessible unless both its spectral amplitude (square root of the intensity) and phase components are available for performing inverse Fourier transform (IFT). Several phase retrieval algorithms have been developed to extract the phase component from the oversampled intensity component [2], the most well-known of which being the Hybrid Input-Output (HIO) algorithm [3]. HIO, an iterative algorithm, starts with a set of random phases as initial guess, then applies IFT and FT to the image to move it back and forth between re-
ciprocal and real spaces, where constraints such as finite support and Fourier amplitude are applied
to refine the calculated image, as shown in Figure 1(a).
In general HIO can give reasonable reconstruction result, but it usually takes few thousands
of cycles to converge, and sometimes it stagnates at a suboptimal result. In addition, phasing
algorithms like HIO are generally vulnerable to data defects such as quantum noise (due to limited
photon flux) and missing intensities (due to low frequency components being blocked). For the
reasons above, running phase retrieval algorithms like HIO for experimental data is generally costly
in terms of computation resources and time, as people would need to run HIO with large iteration
numbers multiple times to get optimal reconstruction result. While the calculated image is usually
validated by comparing it with a low-resolution (LR) image from other source such as an optical
microscope or scanning electron microscope (SEM), here we propose we can incorporate a low-
resolution image into the phase retrieval algorithm as a prior to guide the phasing process, thus
enhancing the reconstruction fidelity and convergence rate.
2 Project description
This project aims to improve upon the HIO algorithm by incorporating a low resolution image
as a stronger prior than the finite support constraint used by most algorithms, developing a phase
retrieval algorithm with a higher reconstruction fidelity and convergence rate. Figure 1(b) shows
the proposed pipeline we will be developing. We expect the modified algorithm to outperform the
original HIO, given a reasonably quality of the LR prior, as the LR image contains not only the
support boundary but also local intensities information.
For this project, LR images will be numerically generated by applying a Gaussian filter to the
original image with different bandwidth parameters; diffraction pattern will be simulated by using
fast Fourier transform (FFT). The reconstruction fidelity will be evaluated by a discrepancy function
ER(ρ0, ρcalc) which compares the calculated image ρcalc with the original one ρ0.
The main challenge of the project is to find a mathematically reasonable and computationally
practical way to constrain computed real space images based on the LR image. Previously we
have experimented with a na¨ıve technique where the on-the-flight real space image is dynamically
guided by the LR image with a simple linear combination [4]. For this project, We will research
into different methods for optimizing an image to be closer to the given LR image in a dynamic
fashion which can be tuned for convergence. One of the possible candidate method is to use the
deblurred LR image computed from Richard-Lucy deconvolution [5] or the ADMM algorithm [6]
to constrain the real space domain image.
3 Android devices
This project does not use Andorid devices.
References
[1] J. Miao et al., Nature 400, 342 (1999).
[2] J. Miao et al., Phys. Rev. Lett. 95, 085503 (2005).
[3] R. Fienup, Appl. Opt. 21, 2758 (1982).
[4] P.-N. Li et al. (under preparation).
[5] R. Hardley, JOSA 62, 55 (1972).
[6] M. Figueiredo and J. Bioucas-Dias, IEEE Trans. Image Process. 19, 3133 (2010).
FOR BASE PAPER PLEASE MAIL US AT ARNPRSTH@GMAIL.COM
DOWNLOAD SOURCE CODE CLICK HERE
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