Phase estimation using phase gradients obtained through Hilbert transform

Frequency subspace amplitude flow for phase retrieval

A novel approach, termed frequency subspace amplitude flow (FSAF), is proposed to reconstruct complex-valued signal from "phaseless" measurements. The proposed FSAF consists of two stages: the first stage approximates low-frequency coefficients of an unknown signal by the spectral method, and the second stage refines the results by the truncated conjugate gradient of amplitude-based nonconvex formulation. FSAF is easy to implement and applicable to natural images, where no additional constraint is needed. Extensive experiments with 1D signals, 2D images, and natural images corroborate significant improvements by using the proposed FSAF method over the state of the art. Especially for sample complexity, FSAF pushes the state of the art for exactly reconstructing complex natural signals (with a size of n) from 3.2n to 2.2n under the Gaussian model, and from 5n to 3n under the coherent diffraction pattern (CDP) model without increasing computational complexity. More importantly, the proposed method is highly flexible and can be easily adapted to the existing algorithms under different noise models.

Determination of the complex refractive index segments of turbid sample with multispectral spatially modulated structured light and models approximation

Spectral data enabling the derivation of a biological tissue sample's complex refractive index (CRI) can provide a range of valuable information in the clinical and research contexts. Specifically, changes in the CRI reflect alterations in tissue morphology and chemical composition, enabling its use as an optical marker during diagnosis and treatment. In the present work, we report a method for estimating the real and imaginary parts of the CRI of a biological sample using Kramers-Kronig (KK) relations in the spatial frequency domain. In this method, phase-shifted sinusoidal patterns at single high spatial frequency are serially projected onto the sample surface at different near-infrared wavelengths while a camera mounted normal to the sample surface acquires the reflected diffuse light. In the offline analysis pipeline, recorded images at each wavelength are converted to spatial phase maps using KK analysis and are then calibrated against phase-models derived from diffusion approximation. The amplitude of the reflected light, together with phase data, is then introduced into Fresnel equations to resolve both real and imaginary segments of the CRI at each wavelength. The technique was validated in tissue-mimicking phantoms with known optical parameters and in mouse models of ischemic injury and heat stress. Experimental data obtained indicate variations in the CRI among brain tissue suffering from injury. CRI fluctuations correlated with alterations in the scattering and absorption coefficients of the injured tissue are demonstrated. This technique for deriving dynamic changes in the CRI of tissue may be further developed as a clinical diagnostic tool and for biomedical research applications. To the best of our knowledge, this is the first report of the estimation of the spectral CRI of a mouse head following injury obtained in the spatial frequency domain.

Conjugate gradient method for phase retrieval based on the Wirtinger derivative

A conjugate gradient Wirtinger flow (CG-WF) algorithm for phase retrieval is proposed in this paper. It is shown that, compared with recently reported Wirtinger flow and its modified methods, the proposed CG-WF algorithm is able to dramatically accelerate the convergence rate while keeping the dominant computational cost of each iteration unchanged. We numerically illustrate the effectiveness of our method in recovering 1D Gaussian signals and 2D natural color images under both Gaussian and coded diffraction pattern models.