Computationally-efficient linear scheme for overlap time-gating spatial frequency domain diffuse optical tomography using an analytical diffusion model.

Time-domain (TD) spatial frequency domain (SFD) diffuse optical tomography (DOT) potentially enables laminar tomography of both the absorption and scattering coefficients. Its full time-resolved-data scheme is expected to enhance performances of the image reconstruction but poses heavy computational costs and also susceptible signal-to-noise ratio (SNR) limits, as compared to the featured-data one. We herein propose a computationally-efficient linear scheme of TD-SFD-DOT, where an analytical solution to the TD phasor diffusion equation for semi-infinite geometry is derived and used to formulate the Jacobian matrices with regard to overlap time-gating data of the time-resolved measurement for improved SNR and reduced redundancy. For better contrasting the absorption and scattering and widely adapted to practically-available resources, we develop an algebraic-reconstruction-technique-based two-step linear inversion procedure with support of a balanced memory-speed strategy and multi-core parallel computation. Both simulations and phantom experiments are performed to validate the effectiveness of the proposed TD-SFD-DOT method and show an achieved tomographic reconstruction at a relative depth resolution of ∼4 mm.

Deep-learning approach to stratified reconstructions of tissue absorption and scattering in time-domain spatial frequency domain imaging.

Significance: The conventional optical properties (OPs) reconstruction in spatial frequency domain (SFD) imaging, like the lookup table (LUT) method, causes OPs aliasing and yields only average OPs without depth resolution. Integrating SFD imaging with time-resolved (TR) measurements enhances space-TR information, enabling improved reconstruction of absorption (µa) and reduced scattering (µs') coefficients at various depths. Aim: To achieve the stratified reconstruction of OPs and the separation between µa and µs', using deep learning workflow based on the temporal and spatial information provided by time-domain SFD imaging technique, while enhancing the reconstruction accuracy. Approach: Two data processing methods are employed for the OPs reconstruction with TR-SFD imaging, one is full TR data, and the other is the featured data extracted from the full TR data (E, continuous-wave component, ⟨t⟩, mean time of flight). We compared their performance using a series of simulation and phantom validations. Results: Compared to the LUT approach, utilizing full TR, E and ⟨t⟩ datasets yield high-resolution OPs reconstruction results. Among the three datasets employed, full TR demonstrates the optimal accuracy. Conclusions: Utilizing the data obtained from SFD and TR measurement techniques allows for achieving high-resolution separation reconstruction of µa and µs' at different depths within 5 mm.

Wide-field illumination diffuse optical tomography within a framework of single-pixel time-domain spatial frequency domain imaging.

We present a wide-field illumination time-domain (TD) diffusion optical tomography (DOT) for three-dimensional (3-D) reconstruction within a shallow region under the illuminated surface of the turbid medium. The methodological foundation is laid on the single-pixel spatial frequency domain (SFD) imaging that facilitates the adoption of the well-established time-correlated single-photon counting (TCSPC)-based TD detection and generalized pulse spectrum techniques (GPST)-based reconstruction. To ameliorate the defects of the conventional diffusion equation (DE) in the forward modeling of TD-SFD-DOT, mainly the low accuracy in the near-field region and in profiling early-photon migration, we propose a modified model employing the time-dependent δ-P1 approximation and verify its improved accuracy in comparison with both the Monte Carlo and DE-based ones. For a simplified inversion process, a modified GPST approach is extended to TD-SFD-DOT that enables the effective separation of the absorption and scattering coefficients using a steady-state equivalent strategy. Furthermore, we set up a single-pixel TD-SFD-DOT system that employs the TCSPC-based TD detection in the SFD imaging framework. For assessments of the reconstruction approach and the system performance, phantom experiments are performed for a series of scenarios. The results show the effectiveness of the proposed methodology for rapid 3-D reconstruction of the absorption and scattering coefficients within a depth range of about 5 mean free pathlengths.

Single pixel imaging via unsupervised deep compressive sensing with collaborative sparsity in discretized feature space.

Single-pixel imaging (SPI) enables the use of advanced detector technologies to provide a potentially low-cost solution for sensing beyond the visible spectrum and has received increasing attentions recently. However, when it comes to sub-Nyquist sampling, the spectrum truncation and spectrum discretization effects significantly challenge the traditional SPI pipeline due to the lack of sufficient sparsity. In this work, a deep compressive sensing (CS) framework is built to conduct image reconstructions in classical SPIs, where a novel compression network is proposed to enable collaborative sparsity in discretized feature space while remaining excellent coherence with the sensing basis as per CS conditions. To alleviate the underlying limitations in an end-to-end supervised training, for example, the network typically needs to be re-trained as the basis patterns, sampling ratios and so on. change, the network is trained in an unsupervised fashion with no sensing physics involved. Validation experiments are performed both numerically and physically by comparing with traditional and cutting-edge SPI reconstruction methods. Particularly, fluorescence imaging is pioneered to preliminarily examine the in vivo biodistributions. Results show that the proposed method maintains comparable image fidelity to a sCMOS camera even at a sampling ratio down to 4%, while remaining the advantages inherent in SPI. The proposed technique maintains the unsupervised and self-contained properties that highly facilitate the downstream applications in the field of compressive imaging.

Profile-based intensity and frequency corrections for single-snapshot spatial frequency domain imaging.

We have proposed the profile-based intensity and frequency corrections for single-snapshot spatial frequency domain (SFD) imaging to mitigate surface profile effects on the measured intensity and spatial frequency in extracting the optical properties. In the scheme, the spatially modulated frequency of the projected sinusoidal pattern is adaptively adjusted according to the sample surface profile, reducing distortions of the modulation amplitude in the single-snapshot demodulation and errors in the optical property extraction. The profile effects on both the measured intensities of light incident onto and reflected from the sample are then compensated using Minnaert's correction to obtain the true diffuse reflectance of the sample. We have validated the method by phantom experiments using a highly sensitive SFD imaging system based on the single-pixel photon-counting detection and assessed error reductions in extracting the absorption and reduced scattering coefficients by an average of 40% and 10%, respectively. Further, an in vivo topography experiment of the opisthenar vessels has demonstrated its clinical feasibility.