High dynamic range coherent imaging using compressed sensing

Recovery of spatial frequencies in coherent diffraction imaging in the presence of a central obscuration

Coherent diffraction imaging (CDI) and its scanning version, ptychography, are lensless imaging approaches used to iteratively retrieve a sample's complex scattering amplitude from its measured diffraction patterns. These imaging methods are most useful in extreme ultraviolet (EUV) and X-ray regions of the electromagnetic spectrum, where efficient imaging optics are difficult to manufacture. CDI relies on high signal-to-noise ratio diffraction data to recover the phase, but increasing the flux can cause saturation effects on the detector. A conventional solution to this problem is to place a beam stop in front of the detector. The pixel masking method is a common solution to the problem of missing frequencies due to a beam stop. This paper describes the information redundancy in the recorded data set and expands on how the reconstruction algorithm can exploit this redundancy to estimate the missing frequencies. Thereafter, we modify the size of the beam stop in experimental and simulation data to assess the impact of the missing frequencies, investigate the extent to which the lost portion of the diffraction spectrum can be recovered, and quantify the effect of the beam stop on the image quality. The experimental findings and simulations conducted for EUV imaging demonstrate that when using a beam stop, the numerical aperture of the condenser is a crucial factor in the recovery of lost frequencies. Our thorough investigation of the reconstructed images provides information on the overall quality of reconstruction and highlights the vulnerable frequencies if the beam stop size is larger than the extent of the illumination NA. The outcome of this study can be applied to other sources of frequency loss, and it will contribute to the improvement of experiments and reconstruction algorithms in CDI.

Non-interferometric stand-alone single-shot holographic camera using reciprocal diffractive imaging

An ideal holographic camera measures the amplitude and phase of the light field so that the focus can be numerically adjusted after the acquisition, and depth information about an imaged object can be deduced. The performance of holographic cameras based on reference-assisted holography is significantly limited owing to their vulnerability to vibration and complex optical configurations. Non-interferometric holographic cameras can resolve these issues. However, existing methods require constraints on an object or measurement of multiple-intensity images. In this paper, we present a holographic image sensor that reconstructs the complex amplitude of scattered light from a single-intensity image using reciprocal diffractive imaging. We experimentally demonstrate holographic imaging of three-dimensional diffusive objects and suggest its potential applications by imaging a variety of samples under both static and dynamic conditions.

Towards practical holographic coherent diffraction imaging via maximum likelihood estimation

A new algorithmic framework is developed for holographic coherent diffraction imaging (HCDI) based on maximum likelihood estimation (MLE). This method provides superior image reconstruction results for various practical HCDI settings, such as when data is highly corrupted by Poisson shot noise and when low-frequency data is missing due to occlusion from a beamstop apparatus. This method is also highly robust in that it can be implemented using a variety of standard numerical optimization algorithms, and requires fewer constraints on the physical HCDI setup compared to current algorithms. The mathematical framework developed using MLE is also applicable beyond HCDI to any holographic imaging setup where data is corrupted by Poisson shot noise.

Robust contrast-transfer-function phase retrieval via flexible deep learning networks

By exploiting the total variation (TV) regularization scheme and the contrast transfer function (CTF), a phase map can be retrieved from single-distance coherent diffraction images via the sparsity of the investigated object. However, the CTF-TV phase retrieval algorithm often struggles in the presence of strong noise, since it is based on the traditional compressive sensing optimization problem. Here, convolutional neural networks, a powerful tool from machine learning, are used to regularize the CTF-based phase retrieval problems and improve the recovery performance. This proposed method, the CTF-Deep phase retrieval algorithm, was tested both via simulations and experiments. The results show that it is robust to noise and fast enough for high-resolution applications, such as in optical, x-ray, or terahertz imaging.

Phase retrieval with complexity guidance

Iterative phase retrieval methods based on the Gerchberg-Saxton (GS) or Fienup algorithm typically show stagnation artifacts even after a large number of iterations. We introduce a complexity parameter ζ that can be computed directly from the Fourier magnitude data and provides a measure of fluctuations in the desired phase retrieval solution. It is observed that when initiated with a constant or a uniformly random phase map, the complexity of the Fienup solution containing stagnation artifacts stabilizes at a numerical value that is higher than ζ. We propose a modified Fienup algorithm that uses a controlled sparsity-enhancing step such that in every iteration the complexity of the resulting guess solution is explicitly made close to ζ. This approach, which we refer to as complexity-guided phase retrieval, is seen to provide an artifact-free phase retrieval solution within a few hundred iterations. Numerical illustrations are provided for both amplitude as well as phase objects with and without Poisson noise introduced in the Fourier intensity data. The complexity-guidance concept may potentially be combined with a variety of phase retrieval algorithms and can enable several practical applications.

Compressive sampling based on frequency saliency for remote sensing imaging

In saliency-based compressive sampling (CS) for remote sensing image signals, the saliency information of images is used to allocate more sensing resources to salient regions than to non-salient regions. However, the pulsed cosine transform method can generate large errors in the calculation of saliency information because it uses only the signs of the coefficients of the discrete cosine transform for low-resolution images. In addition, the reconstructed images can exhibit blocking effects because blocks are used as the processing units in CS. In this work, we propose a post-transform frequency saliency CS method that utilizes transformed post-wavelet coefficients to calculate the frequency saliency information of images in the post-wavelet domain. Specifically, the wavelet coefficients are treated as the pixels of a block-wise megapixel sensor. Experiments indicate that the proposed method yields better-quality images and outperforms conventional saliency-based methods in three aspects: peak signal-to-noise ratio, mean structural similarity index, and visual information fidelity.

Lensless complex amplitude image retrieval through a visually opaque scattering medium

We propose and experimentally demonstrate lensless complex amplitude image retrieval through a visually opaque scattering medium from spatially fluctuating fields using intensity measurement and a phase-retrieval algorithm. The complex amplitude information of the hidden object is encoded in the form of a real and nonnegative amplitude function represented as an interference pattern. A single charge coupled device (CCD) image of the scattered light collected through a visually opaque optical diffuser contains enough information to digitally regenerate the interference pattern. Furthermore, a lensless configuration is implemented which eliminates any possible aberration effects associated with optical components, and this further has promising applications where the use of imaging optics is not feasible. Experimental results for the recovery of complex fields corresponding to optical vortices of two different topological charges are presented.

Contrast-transfer-function phase retrieval based on compressed sensing

We report on a new contrast-transfer-function (CTF) phase-retrieval method based on the alternating direction method of multipliers (ADMMs), which allows us to exploit any compressed sensing regularization scheme reflecting the sparsity of the investigated object. The proposed iterative algorithm retrieves accurate phase maps from highly noisy single-distance projection microscopy data and is characterized by a stable convergence, not bounded to the prior knowledge of the object support or to the initialization strategy. Experiments on simulated and real datasets show that ADMM-CTF yields reconstructions with a substantial lower amount of artifacts and enhanced signal-to-noise ratio compared to the standard analytical inversion.

Subsampled phase retrieval for temporal resolution enhancement in lensless on-chip holographic video

On-chip holographic video is a convenient way to monitor biological samples simultaneously at high spatial resolution and over a wide field-of-view. However, due to the limited readout rate of digital detector arrays, one often faces a tradeoff between the per-frame pixel count and frame rate of the captured video. In this report, we propose a subsampled phase retrieval (SPR) algorithm to overcome the spatial-temporal trade-off in holographic video. Compared to traditional phase retrieval approaches, our SPR algorithm uses over an order of magnitude less pixel measurements while maintaining suitable reconstruction quality. We use an on-chip holographic video setup with pixel sub-sampling to experimentally demonstrate a factor of 5.5 increase in sensor frame rate while monitoring the in vivo movement of Peranema microorganisms.

Efficient compressed imaging method for a microsatellite optical camera

Imaging integrated with compression is considered the holy grail of microsatellite photography because it improves the degree of integration of the camera system, removing the compression system, high capacity storage system, and high-speed image transmission system, which consume lots of resources of the satellite platform. In this paper, we propose an efficient compressed imaging method for remote sensing photography. We consider wavelet coefficients as pixels of a block-wise megapixel sensor (BMPS). We integrate the saliency information stage into the BMPS to perform compressed sampling (CS) in order to further improve imaging performance. In the compressed sensing process, we use transformed postwavelet coefficients to calculate saliency information of images in the postwavelet domain. According to different regions having different saliency information, the corresponding sensing resources are allocated to perform CS. CS can obtain the compressed discrete sparse samples of the original signal at a much lower sample rate than the Nyquist frequency. The discrete samples signal can be reconstructed by a nonlinear recovery algorithm in the ground. Experimental results show that the proposed compressed imaging method outperforms the traditional saliency-based methods in terms of multiple assessment approaches.