Kuan He

Compressive holographic video

Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device. In this paper we demonstrate 10× temporal super resolution with multiple depths recovery from a single image. Two examples are presented for the purpose of recording subtle vibrations and tracking small particles within 5 ms.

High dynamic range coherent imaging using compressed sensing.

In both lensless Fourier transform holography (FTH) and coherent diffraction imaging (CDI), a beamstop is used to block strong intensities which exceed the limited dynamic range of the sensor, causing a loss in low-frequency information, making high quality reconstructions difficult or even impossible. In this paper, we show that an image can be recovered from high-frequencies alone, thereby overcoming the beamstop problem in both FTH and CDI. The only requirement is that the object is sparse in a known basis, a common property of most natural and manmade signals. The reconstruction method relies on compressed sensing (CS) techniques, which ensure signal recovery from incomplete measurements. Specifically, in FTH, we perform compressed sensing (CS) reconstruction of captured holograms and show that this method is applicable not only to standard FTH, but also multiple or extended reference FTH. For CDI, we propose a new phase retrieval procedure, which combines Fienups hybrid input-output (HIO) method and CS. Both numerical simulations and proof-of-principle experiments are shown to demonstrate the effectiveness and robustness of the proposed CS-based reconstructions in dealing with missing data in both FTH and CDI.

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.

Rapid alignment of nanotomography data using joint iterative reconstruction and reprojection

As x-ray and electron tomography is pushed further into the nanoscale, the limitations of rotation stages become more apparent, leading to challenges in the alignment of the acquired projection images. Here we present an approach for rapid post-acquisition alignment of these projections to obtain high quality three-dimensional images. Our approach is based on a joint estimation of alignment errors, and the object, using an iterative refinement procedure. With simulated data where we know the alignment error of each projection image, our approach shows a residual alignment error that is a factor of a thousand smaller, and it reaches the same error level in the reconstructed image in less than half the number of iterations. We then show its application to experimental data in x-ray and electron nanotomography.

Video compressive sensing with on-chip programmable subsampling

The maximum achievable frame-rate for a video camera is limited by the sensors pixel readout rate. The same sensor may achieve either a slow frame-rate at full resolution (e.g., 60 fps at 4 Mpixel resolution) or a fast frame-rate at low resolution (e.g., 240 fps at 1 Mpixel resolution). Higher frame-rates are achieved using pixel readout modes (e.g., subsampling or binning) that sacrifice spatial for temporal resolution within a fixed bandwidth. A number of compressive video cameras have been introduced to overcome this fixed bandwidth constraint and achieve high frame-rates without sacrificing spatial resolution. These methods use electro-optic components (e.g., LCoS, DLPs, piezo actuators) to introduce high speed spatio-temporal multiplexing in captured images. Full resolution, high speed video is then restored by solving an undetermined system of equations using a sparse regularization framework. In this work, we introduce the first all-digital temporal compressive video camera that uses custom subsampling modes to achieve spatio-temporal multiplexing. Unlike previous compressive video cameras, ours requires no additional optical components, enabling it to be implemented in a compact package such as a mobile camera module. We demonstrate results using a TrueSense development kit with a 12 Mpixel sensor and programmable FPGA read out circuitry.

CS-ToF: High-resolution compressive time-of-flight imaging

Three-dimensional imaging using Time-of-flight (ToF) sensors is rapidly gaining widespread adoption in many applications due to their cost effectiveness, simplicity, and compact size. However, the current generation of ToF cameras suffers from low spatial resolution due to physical fabrication limitations. In this paper, we propose CS-ToF, an imaging architecture to achieve high spatial resolution ToF imaging via optical multiplexing and compressive sensing. Our approach is based on the observation that, while depth is non-linearly related to ToF pixel measurements, a phasor representation of captured images results in a linear image formation model. We utilize this property to develop a CS-based technique that is used to recover high resolution 3D images. Based on the proposed architecture, we developed a prototype 1-megapixel compressive ToF camera that achieves as much as 4× improvement in spatial resolution and 3× improvement for natural scenes. We believe that our proposed CS-ToF architecture provides a simple and low-cost solution to improve the spatial resolution of ToF and related sensors.

High-speed holographic imaging using compressed sensing and phase retrieval

Digital in-line holography serves as a useful encoder for spatial information. This allows three-dimensional reconstruction from a two-dimensional image. This is applicable to the tasks of fast motion capture, particle tracking etc. Sampling high resolution holograms yields a spatiotemporal tradeoff. We spatially subsample holograms to increase temporal resolution. We demonstrate this idea with two subsampling techniques, periodic and uniformly random sampling. The implementation includes an on-chip setup for periodic subsampling and a DMD (Digital Micromirror Device) -based setup for pixel-wise random subsampling. The on-chip setup enables direct increase of up to 20 in camera frame rate. Alternatively, the DMD-based setup encodes temporal information as high-speed mask patterns, and projects these masks within a single exposure (coded exposure). This way, the frame rate is improved to the level of the DMD with a temporal gain of 10. The reconstruction of subsampled data using the aforementioned setups is achieved in two ways. We examine and compare two iterative reconstruction methods. One is an error reduction phase retrieval and the other is sparsity-based compressed sensing algorithm. Both methods show strong capability of reconstructing complex object fields. We present both simulations and real experiments. In the lab, we image and reconstruct structure and movement of static polystyrene microspheres, microscopic moving peranema, macroscopic fast moving fur and glitters.

Compressive reconstruction for 3D incoherent holographic microscopy

Incoherent holography has recently attracted significant research interest due to its flexibility for a wide variety of light sources. In this paper, we use compressive sensing to reconstruct a three-dimensional volumetric object from its two-dimensional Fresnel incoherent correlation hologram. We show how compressed sensing enables reconstruction without out-of-focus artifacts, when compared to conventional back-propagation recovery. Finally, we analyze the reconstruction guarantees of the proposed approach both numerically and theoretically and compare that with coherent holography.

A Compressed Sensing Approach to Solving the Dynamic Range Problem in Fourier Transform Holography

We propose a reconstruction method using compressed sensing to accurately recover an image from a single hologram despite a large amount of unmeasured intensities, which allows us to overcome dynamic range limitations in the sensor.