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Computed tomography is a widely used imaging modality with applications ranging from medical imaging to material analysis. One major challenge arises from the lack of scanning information at certain angles, leading to distorted CT images with artifacts. This results in an ill-posed problem known as the Limited Angle Computed Tomography (LACT) reconstruction problem. To address this problem, we propose Residual Null-Space Diffusion Stochastic Differential Equations (RN-SDEs), which are a variant of diffusion models that characterize the diffusion process with mean-reverting (MR) stochastic differential equations. To demonstrate the generalizability of RN-SDEs, our experiments are conducted on two different LACT datasets, i.e., ChromSTEM and C4KC-KiTS. Through extensive experiments, we show that by leveraging learned Mean-Reverting SDEs as a prior and emphasizing data consistency using Range-Null Space Decomposition (RNSD) based rectification, RN-SDEs can restore high-quality images from severe degradation and achieve state-of-the-art performance in most LACT tasks. Additionally, we present a quantitative comparison of computational complexity and runtime efficiency, highlighting the superior effectiveness of our proposed approach.

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally-defined domains observed by single cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as Rad21 degradation.

Reflection statistics have not been well studied for optical random media whose mean refractive indices do not match with the refractive indices of their surrounding media. Here, we theoretically study how this refractive index mismatch between a one dimensional (1D) optical sample and its surrounding medium affects the reflection statistics in the weak disorder limit, when the fluctuation part of the refractive index (dn) is much smaller than the mismatch as well as the mean refractive index of the sample (dn << ). In the theoretical derivation, we perform a detailed calculation that results in the analytical forms of mean and standard deviation (STD) of the reflectance in terms of disorder parameters (dn and lc) in an index mismatched backscattering system. Particularly, the orders of disorder parameters in STD of the reflectance for index mismatched systems is shown to be lower ( ( lc )^1/2 ) than that of the matched systems ( lc). By comparing STDs of the reflection coefficient of index matched and mismatched systems, we show that reflectance at the sample boundaries in index mismatched systems can enhance the signal of the STD to the disorder parameters of the reflectance. In terms of biophotonics applications, this result can lead to potential techniques that effectively extract the sample disorder parameters by manipulating the index mismatch conditions. Potential applications of the technique for enhancement in sensitivity of cancer detection at single cell level are also discussed., Comment: 14 pages,4 figures

Based on the difference between mean background of an optical sample refractive index n_0 and an outside medium, n_out, different than n_0, we study the reflection statistics of a one-dimensional weakly disordered optical medium with refractive index n(x)=n_0+dn(x). Considering dn(x) as color noise with the exponential spatial correlation decay length l_c and k as the incident wave vector, our results show that for the small correlation length limit, i.e. k*l_c<1, the average value of reflectance, r, follows a form that is similar to that of the matched refractive-index case n_0=n_out, i.e., proportional to l_c. However, the standard deviation of r is proven to be std(r(dn,l_c)) proportional to sqrt(l_c), which is different from the matched case. Applications to light scattering from layered media and biological cells are discussed, Comment: 9 pages, 2 figures

Possible origins of the experimentally observed beat-like signal in elastic light backscattering from an epithelial biological cell are identified. The source of the beat-like signal is most likely the cellular nucleus, which is a spheroidal particle with an optically sharp edge, low relative index of refraction, and a size parameter in the resonant range; another possible source is an agglomeration of cell organelles of a similar size. Using Mie theory computer simulations for a dielectric sphere with biological nucleus-like parameters, we have shown that backscattering as a function of size parameter has a beat-like pattern. The high frequency periodic oscillation is the single scattering contribution, while multiple scattering events give slowly varying oscillatory contributions. With increasing contrast, the backscattering signal changes from a pure sinusoid to that of a beat signal. The beat-like pattern in scattering from a low contrast particle does not depend on any particular features of the sphere; a similar pattern is observable in scattering from star-like non-spherical objects with a sharp optical contrast and smooth shape; in this case, the high frequency of oscillations depends on the object orientation relative to incident light, Comment: 14 pages, 4 figures

We experimentally study the propagation of circularly polarized light in the sub-diffusion regime by exploiting enhanced backscattering (EBS, also known as coherent backscattering) of light under low spatial coherence illumination. We demonstrate for the first time that circular polarization memory effect exists in EBS over a large range of scatterers' sizes in this regime. We show that EBS measurements under low spatial coherence illumination from the helicity preserving and orthogonal helicity channels cross over as the mean free pathlength of light in media varies, and that the cross point indicates the transition from multiple to double scattering in EBS of light., Comment: 3 pages and 3 figures. It is in press for publication in Optics Letters

The mechanisms of photon propagation in random media in the diffusive multiple scattering regime have been previously studied using diffusion approximation. However, similar understanding in the low-order (sub-diffusion) scattering regime is not complete due to difficulties in tracking photons that undergo very few scatterings events. Recent developments in low-coherence enhanced backscattering (LEBS) overcome these difficulties and enable probing photons that travel very short distances and undergo only a few scattering events. In LEBS, enhanced backscattering is observed under illumination with spatial coherence length L_sc less than the scattering mean free path l_s. In order to understand the mechanisms of photon propagation in LEBS in the subdiffusion regime, it is imperative to develop analytical and numerical models that describe the statistical properties of photon trajectories. Here we derive the probability distribution of penetration depth of LEBS photons and report Monte Carlo numerical simulations to support our analytical results. Our results demonstrate that, surprisingly, the transport of photons that undergo low-order scattering events has only weak dependence on the optical properties of the medium (l_s and anisotropy factor g) and strong dependence on the spatial coherence length of illumination, L_sc, relative to those in the diffusion regime. More importantly, these low order scattering photons typically penetrate less than l_s into the medium due to low spatial coherence length of illumination and their penetration depth is proportional to the one-third power of the coherence volume (i.e. [l_s \pi L_sc^2 ]^1/3)., Comment: 32 pages(including 7 figures), modified version to appear in Phys. Rev. E

We exploit low spatial coherence illumination to dephase time-reversed partial waves outside its finite coherence area, which virtually creates a controllable coherence volume and isolates the minimal number of scattering events from higher order scattering in enhanced backscattering (EBS, also known as coherent backscattering) of light. We report the first experimental evidence that the minimum number of scattering events in EBS is double scattering in discrete random media, which has been hypothesized since the first observation of EBS of light. We discuss several unique characteristics and potential applications of low-coherence EBS in weakly scattering random media., Comment: 4 pages and 5 figures

Constructive interference among coherent waves traveling time-reversed paths in a random medium gives rise to the enhancement of light scattering observed in directions close to backscattering. This phenomenon is known as enhanced backscattering (EBS). According to diffusion theory, the angular width of an EBS cone is proportional to the ratio of the wavelength of light $\lambda$ to the transport mean free path length ls* of a random medium. In biological media, large ls* ~ 0.5-2 mm >> $\lambda$ results in an extremely small (~0.001 $^\degree$) angular width of the EBS cone making the experimental observation of such narrow peaks difficult. Recently, the feasibility of observing EBS under low spatial coherence illumination (spatial coherence length Lsc<