Model-based deep learning framework for accelerated optical projection tomography.

In this work, we propose a model-based deep learning reconstruction algorithm for optical projection tomography (ToMoDL), to greatly reduce acquisition and reconstruction times. The proposed method iterates over a data consistency step and an image domain artefact removal step achieved by a convolutional neural network. A preprocessing stage is also included to avoid potential misalignments between the sample center of rotation and the detector. The algorithm is trained using a database of wild-type zebrafish (Danio rerio) at different stages of development to minimise the mean square error for a fixed number of iterations. Using a cross-validation scheme, we compare the results to other reconstruction methods, such as filtered backprojection, compressed sensing and a direct deep learning method where the pseudo-inverse solution is corrected by a U-Net. The proposed method performs equally well or better than the alternatives. For a highly reduced number of projections, only the U-Net method provides images comparable to those obtained with ToMoDL. However, ToMoDL has a much better performance if the amount of data available for training is limited, given that the number of network trainable parameters is smaller.

Phase Unwrapping of Color Doppler Echocardiography Using Deep Learning.

Color Doppler echocardiography is a widely used noninvasive imaging modality that provides real-time information about intracardiac blood flow. In an apical long-axis view of the left ventricle, color Doppler is subject to phase wrapping, or aliasing, especially during cardiac filling and ejection. When setting up quantitative methods based on color Doppler, it is necessary to correct this wrapping artifact. We developed an unfolded primal-dual network (PDNet) to unwrap (dealias) color Doppler echocardiographic images and compared its effectiveness against two state-of-the-art segmentation approaches based on nnU-Net and transformer models. We trained and evaluated the performance of each method on an in-house dataset and found that the nnU-Net-based method provided the best dealiased results, followed by the primal-dual approach and the transformer-based technique. Noteworthy, the PDNet, which had significantly fewer trainable parameters, performed competitively with respect to the other two methods, demonstrating the high potential of deep unfolding methods. Our results suggest that deep learning (DL)-based methods can effectively remove aliasing artifacts in color Doppler echocardiographic images, outperforming DeAN, a state-of-the-art semiautomatic technique. Overall, our results show that DL-based methods have the potential to effectively preprocess color Doppler images for downstream quantitative analysis.

OpenSpyrit: an ecosystem for open single-pixel hyperspectral imaging.

This paper describes OpenSpyrit, an open access and open source ecosystem for reproducible research in hyperspectral single-pixel imaging, composed of SPAS (a Python single-pixel acquisition software), SPYRIT (a Python single-pixel reconstruction toolkit) and SPIHIM (a single-pixel hyperspectral image collection). The proposed OpenSpyrit ecosystem responds to the need for reproducibility and benchmarking in single-pixel imaging by providing open data and open software. The SPIHIM collection, which is the first open-access FAIR dataset for hyperspectral single-pixel imaging, currently includes 140 raw measurements acquired using SPAS and the corresponding hypercubes reconstructed using SPYRIT. The hypercubes are reconstructed by both inverse Hadamard transformation of the raw data and using the denoised completion network (DC-Net), a data-driven reconstruction algorithm. The hypercubes obtained by inverse Hadamard transformation have a native size of 64 × 64 × 2048 for a spectral resolution of 2.3 nm and a spatial resolution that is comprised between 182.4 µm and 15.2 µm depending on the digital zoom. The hypercubes obtained using the DC-Net are reconstructed at an increased resolution of 128 × 128 × 2048. The OpenSpyrit ecosystem should constitute a reference to support benchmarking for future developments in single-pixel imaging.

Self-probed ptychography from semiconductor high-harmonic generation.

We demonstrate a method to image an object using a self-probing approach based on semiconductor high-harmonic generation. On the one hand, ptychography enables high-resolution imaging from the coherent light diffracted by an object. On the other hand, high-harmonic generation from crystals is emerging as a new source of extreme-ultraviolet ultrafast coherent light. We combine these two techniques by performing ptychography measurements with nanopatterned crystals serving as the object as well as the generation medium of the harmonics. We demonstrate that this strong field in situ approach can provide structural information about an object. With the future developments of crystal high harmonics as a compact short-wavelength light source, our demonstration can be an innovative approach for nanoscale imaging of photonic and electronic devices in research and industry.

Physics-constrained intraventricular vector flow mapping by color Doppler.

Color Doppler by transthoracic echocardiography creates two-dimensional fan-shaped maps of blood velocities in the cardiac cavities. It is a one-component velocimetric technique since it only returns the velocity components parallel to the ultrasound beams. Intraventricular vector flow mapping (iVFM) is a method to recover the blood velocity vectors from the Doppler scalar fields in an echocardiographic three-chamber view. We improved ouriVFM numerical scheme by imposing physical constraints. TheiVFM consisted in minimizing regularized Doppler residuals subject to the condition that two fluid-dynamics constraints were satisfied, namely planar mass conservation, and free-slip boundary conditions. The optimization problem was solved by using the Lagrange multiplier method. A finite-difference discretization of the optimization problem, written in the polar coordinate system centered on the cardiac ultrasound probe, led to a sparse linear system. The single regularization parameter was determined automatically for non-supervision considerations. The physics-constrained method was validated using realistic intracardiac flow data from a patient-specific computational fluid dynamics (CFD) model. The numerical evaluations showed that theiVFM-derived velocity vectors were in very good agreement with the CFD-based original velocities, with relative errors ranged between 0.3% and 12%. We calculated two macroscopic measures of flow in the cardiac region of interest, the mean vorticity and mean stream function, and observed an excellent concordance between physics-constrainediVFM and CFD. The capability of physics-constrainediVFM was finally tested within vivocolor Doppler data acquired in patients routinely examined in the echocardiographic laboratory. The vortex that forms during the rapid filling was deciphered. The physics-constrainediVFM algorithm is ready for pilot clinical studies and is expected to have a significant clinical impact on the assessment of diastolic function.

3D denoised completion network for deep single-pixel reconstruction of hyperspectral images.

Single-pixel imaging acquires an image by measuring its coefficients in a transform domain, thanks to a spatial light modulator. However, as measurements are sequential, only a few coefficients can be measured in the real-time applications. Therefore, single-pixel reconstruction is usually an underdetermined inverse problem that requires regularization to obtain an appropriate solution. Combined with a spectral detector, the concept of single-pixel imaging allows for hyperspectral imaging. While each channel can be reconstructed independently, we propose to exploit the spectral redundancy between channels to regularize the reconstruction problem. In particular, we introduce a denoised completion network that includes 3D convolution filters. Contrary to black-box approaches, our network combines the classical Tikhonov theory with the deep learning methodology, leading to an explainable network. Considering both simulated and experimental data, we demonstrate that the proposed approach yields hyperspectral images with higher quantitative metrics than the approaches developed for grayscale images.

Single-pixel image reconstruction from experimental data using neural networks.

Single-pixel cameras that measure image coefficients have various promising applications, in particular for hyper-spectral imaging. Here, we investigate deep neural networks that when fed with experimental data can output high-quality images in real time. Assuming that the measurements are corrupted by mixed Poisson-Gaussian noise, we propose to map the raw data from the measurement domain to the image domain based on a Tikhonov regularization. This step can be implemented as the first layer of a deep neural network, followed by any architecture of layers that acts in the image domain. We also describe a framework for training the network in the presence of noise. In particular, our approach includes an estimation of the image intensity and experimental parameters, together with a normalization scheme that allows varying noise levels to be handled during training and testing. Finally, we present results from simulations and experimental acquisitions with varying noise levels. Our approach yields images with improved peak signal-to-noise ratios, even for noise levels that were foreseen during the training of the networks, which makes the approach particularly suitable to deal with experimental data. Furthermore, while this approach focuses on single-pixel imaging, it can be adapted for other computational optics problems.

Diffraction-unlimited imaging based on conventional optical devices.

We propose a computational paradigm where off-the-shelf optical devices can be used to image objects in a scene well beyond their native optical resolution. By design, our approach is generic, does not require active illumination, and is applicable to several types of optical devices. It only requires the placement of a spatial light modulator some distance from the optical system. In this paper, we first introduce the acquisition strategy together with the reconstruction framework. We then conduct practical experiments with a webcam that confirm that this approach can image objects with substantially enhanced spatial resolution compared to the performance of the native optical device. We finally discuss potential applications, current limitations, and future research directions.

Author Correction: All semiconductor enhanced high-harmonic generation from a single nanostructured cone.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Single snapshot imaging of optical properties using a single-pixel camera: a simulation study.

We present the effects of using a single-pixel camera approach to extract optical properties with the single-snapshot spatial frequency-domain imaging method. We acquired images of a human hand for spatial frequencies ranging from 0.1 to 0.4 mm - 1 with increasing compression ratios using adaptive basis scan wavelet prediction strategy. In summary, our findings indicate that the extracted optical properties remained usable up to 99% of compression rate at a spatial frequency of 0.2 mm - 1 with errors of 5% in reduced scattering and 10% in absorption.

All semiconductor enhanced high-harmonic generation from a single nanostructured cone.

The enhancement and control of non-linear phenomena at a nanometer scale has a wide range of applications in science and in industry. Among these phenomena, high-harmonic generation in solids is a recent focus of research to realize next generation petahertz optoelectronic devices or compact all solid state EUV sources. Here, we report on the realization of the first nanoscale high harmonic source. The strong field regime is reached by confining the electric field from a few nanojoules femtosecond laser in a single 3D semiconductor waveguide. We reveal a strong competition between enhancement of coherent harmonics and incoherent fluorescence favored by excitonic processes. However, far from the band edge, clear enhancement of the harmonic emission is reported with a robust sustainability offering a compact nanosource for applications. We illustrate the potential of our harmonic nano-device by performing a coherent diffractive imaging experiment. Ultra-compact UV/X-ray nanoprobes are foreseen to have other applications such as petahertz electronics, nano-tomography or nano-medicine.

Time-resolved multispectral imaging based on an adaptive single-pixel camera.

Time-resolved multispectral imaging has many applications in different fields, which range from characterization of biological tissues to environmental monitoring. In particular, optical techniques, such as lidar and fluorescence lifetime imaging, require imaging at the subnanosecond scales over an extended area. In this paper, we demonstrate experimentally a time-resolved multispectral acquisition scheme based on single-pixel imaging. Single-pixel imaging is an emerging paradigm that provides low-cost high-quality images. Here, we use an adaptive strategy that allows acquisition and image reconstruction times to be reduced drastically or full basis scans. Adaptive time-resolved multispectral imaging scheme can have significant applications in biological imaging, at scales from macroscopic to microscopic.

Regularization of nonlinear decomposition of spectral x-ray projection images.

PURPOSE: Exploiting the x-ray measurements obtained in different energy bins, spectral computed tomography (CT) has the ability to recover the 3-D description of a patient in a material basis. This may be achieved solving two subproblems, namely the material decomposition and the tomographic reconstruction problems. In this work, we address the material decomposition of spectral x-ray projection images, which is a nonlinear ill-posed problem. METHODS: Our main contribution is to introduce a material-dependent spatial regularization in the projection domain. The decomposition problem is solved iteratively using a Gauss-Newton algorithm that can benefit from fast linear solvers. A Matlab implementation is available online. The proposed regularized weighted least squares Gauss-Newton algorithm (RWLS-GN) is validated on numerical simulations of a thorax phantom made of up to five materials (soft tissue, bone, lung, adipose tissue, and gadolinium), which is scanned with a 120 kV source and imaged by a 4-bin photon counting detector. To evaluate the method performance of our algorithm, different scenarios are created by varying the number of incident photons, the concentration of the marker and the configuration of the phantom. The RWLS-GN method is compared to the reference maximum likelihood Nelder-Mead algorithm (ML-NM). The convergence of the proposed method and its dependence on the regularization parameter are also studied. RESULTS: We show that material decomposition is feasible with the proposed method and that it converges in few iterations. Material decomposition with ML-NM was very sensitive to noise, leading to decomposed images highly affected by noise, and artifacts even for the best case scenario. The proposed method was less sensitive to noise and improved contrast-to-noise ratio of the gadolinium image. Results were superior to those provided by ML-NM in terms of image quality and decomposition was 70 times faster. For the assessed experiments, material decomposition was possible with the proposed method when the number of incident photons was equal or larger than 105 and when the marker concentration was equal or larger than 0.03 g·cm-3 . CONCLUSIONS: The proposed method efficiently solves the nonlinear decomposition problem for spectral CT, which opens up new possibilities such as material-specific regularization in the projection domain and a parallelization framework, in which projections are solved in parallel.

Multiple-view diffuse optical tomography system based on time-domain compressive measurements.

Compressive sensing is a powerful tool to efficiently acquire and reconstruct an image even in diffuse optical tomography (DOT) applications. In this work, a time-resolved DOT system based on structured light illumination, compressive detection, and multiple view acquisition has been proposed and experimentally validated on a biological tissue-mimicking phantom. The experimental scheme is based on two digital micromirror devices for illumination and detection modulation, in combination with a time-resolved single element detector. We fully validated the method and demonstrated both the imaging and tomographic capabilities of the system, providing state-of-the-art reconstruction quality.

Optimization of dual-energy CT acquisitions for proton therapy using projection-based decomposition.

PURPOSE: Dual-energy computed tomography (DECT) has been presented as a valid alternative to single-energy CT to reduce the uncertainty of the conversion of patient CT numbers to proton stopping power ratio (SPR) of tissues relative to water. The aim of this work was to optimize DECT acquisition protocols from simulations of X-ray images for the treatment planning of proton therapy using a projection-based dual-energy decomposition algorithm. METHODS: We have investigated the effect of various voltages and tin filtration combinations on the SPR map accuracy and precision, and the influence of the dose allocation between the low-energy (LE) and the high-energy (HE) acquisitions. For all spectra combinations, virtual CT projections of the Gammex phantom were simulated with a realistic energy-integrating detector response model. Two situations were simulated: an ideal case without noise (infinite dose) and a realistic situation with Poisson noise corresponding to a 20 mGy total central dose. To determine the optimal dose balance, the proportion of LE-dose with respect to the total dose was varied from 10% to 90% while keeping the central dose constant, for four dual-energy spectra. SPR images were derived using a two-step projection-based decomposition approach. The ranges of 70 MeV, 90 MeV, and 100 MeV proton beams onto the adult female (AF) reference computational phantom of the ICRP were analytically determined from the reconstructed SPR maps. RESULTS: The energy separation between the incident spectra had a strong impact on the SPR precision. Maximizing the incident energy gap reduced image noise. However, the energy gap was not a good metric to evaluate the accuracy of the SPR. In terms of SPR accuracy, a large variability of the optimal spectra was observed when studying each phantom material separately. The SPR accuracy was almost flat in the 30-70% LE-dose range, while the precision showed a minimum slightly shifted in favor of lower LE-dose. Photon noise in the SPR images (20 mGy dose) had lower impact on the proton range accuracy as comparable results were obtained for the noiseless situation (infinite dose). Root-mean-square range errors averaged over all irradiation angles associated to dual-energy imaging were comprised between 0.50 mm and 0.72 mm for the noiseless situation and between 0.51 mm and 0.77 mm for the realistic scenario. CONCLUSIONS: The impact of the dual-energy spectra and the dose allocation between energy levels on the SPR accuracy and precision determined through a projection-based dual-energy algorithm were evaluated to guide the choice of spectra for dual-energy CT for proton therapy. The dose balance between energy levels was not found to be sensitive for the SPR estimation. The optimal pair of dual-energy spectra was material dependent but on a heterogeneous anthropomorphic phantom, there was no significant difference in range accuracy and the choice of spectra could be driven by the precision, i.e., the energy gap.

Single pixel camera: An acquisition strategy based on the non-linear wavelet approximation.

Single pixel imaging opened the door to a cheaper camera architecture able to operate in a wide spectral range. Compressive sensing has been used with such an optical setup to reconstruct an image using ℓ1-minimization. To avoid this type of reconstruction, we consider an adaptive approach leading to a direct restoration of an image and for which we propose a new acquisition strategy. Our technique allows one to acquire an image in the wavelet domain with a progressive non-linear acquisition strategy. This scheme is based on the non-linear approximation of the wavelet transform which takes advantage of the transformation's sparsity. This approximation is applied in a multiresolution way and is shown to offer high compression performance on simulated data. One application of the single pixel camera concerns time-resolved acquisition to observe fluorescence lifetime images of biological structures.

Quantitative fluorescence diffuse optical tomography in the presence of heterogeneities.

In fluorescence diffuse optical tomography (fDOT), the accuracy of reconstructed fluorescence distributions highly depends on the knowledge of the tissue optical heterogeneities for correct modeling of light propagation. Common approaches are to assume homogeneous optical properties or, when structural information is available, assign optical properties to various segmented organs, which is likely to result in inaccurate reconstructions. Furthermore, DOT based only on intensity (continuous wave-DOT) is a nonunique inverse problem, and hence, cannot be used to retrieve simultaneously maps of absorption and diffusion coefficients. We propose a method that reconstructs a single parameter from the excitation measurements, which is used in the fDOT problem to accurately recover fluorescence distribution.

Fluorescence molecular tomography of an animal model using structured light rotating view acquisition.

In recent years, an increasing effort has been devoted to the optimization of acquisition and reconstruction schemes for fluorescence molecular tomography (FMT). In particular, wide-field structured illumination and compression of the measured images have enabled significant reduction of the data set and, consequently, a decrease in both acquisition and processing times. FMT based on this concept has been recently demonstrated on a cylindrical phantom with a rotating-view scheme that significantly increases the reconstruction quality. In this work, we generalize the rotating-view scheme to arbitrary geometries and experimentally demonstrate its applicability to murine models. To the best of our knowledge this is the first time that FMT based on a rotating-view scheme with structured illumination and image compression has been applied to animals.

A virtual source pattern method for fluorescence tomography with structured light.

In order to reduce both acquisition and reconstruction times, illumination and detection in fluorescence diffuse optical tomography (FDOT) have recently evolved from a point-based to a pattern-based approach. The use of structured illumination, offering the ability to project any pattern of light onto the object, associated with the compression of the acquired fluorescence images has paved the way for a new generation of fast reconstruction algorithms for FDOT. However, the choice of the most appropriate set of source patterns is still an open problem. Here, the use of typical source patterns is investigated on experimental data. Reconstructions of similar qualities are obtained for the different types of source patterns. We found that the performances of structured illumination are limited by the required positivity of the source patterns. To alleviate this problem, we introduce a novel method, namely the virtual source pattern method, which allows for considering any kind of patterns, e.g., with negative and complex intensities. This new method provides a significant increase of the contrast of the reconstruction and also a reduction of the reconstruction error, especially when virtual wavelet source patterns are considered.

Multiple-view fluorescence optical tomography reconstruction using compression of experimental data.

We report on the experimental demonstration of a fast reconstruction method for multiview fluorescence diffuse optical tomography by using a wavelet-based data compression. We experimentally demonstrate that the use of data compression combined with the multiview approach makes it possible to perform a fast reconstruction of high quality. A structured illumination approach, guided by the compression scheme, has been adopted to further reduce the acquisition time. The reconstruction algorithm is based on the finite element method, and hence is suitable for samples of any arbitrary shape.