Transmission matrices (TMs) have become a powerful and widely used tool to describe and control wave propagation in complex media. In certain scenarios the TM is partially uncontrollable, complicating its identification and use. In standard optical wavefront shaping experiments, uncontrollable reflections or imperfect illumination may be the cause; in reverberating cavities, uncontrollable reflections off the walls have that effect. Here we employ phase retrieval techniques to identify such a partially uncontrollable TM solely based on random intensity-only reference measurements. We demonstrate the feasibility of our method by focusing both on a single target as well as on multiple targets in a microwave cavity, using a phase-binary Spatial-Microwave-Modulator.
In this paper, the problem of compressive imaging is addressed using natural randomization by means of a multiply scattering medium. To utilize the medium in this way, its corresponding transmission matrix must be estimated. For calibration purposes, we use a digital micromirror device (DMD) as a simple, cheap, and high-resolution binary intensity modulator. We propose a phase retrieval algorithm which is well adapted to intensity-only measurements on the camera, and to the input binary intensity patterns, both to estimate the complex transmission matrix as well as image reconstruction. We demonstrate promising experimental results for the proposed double phase retrieval algorithm using the MNIST dataset of handwritten digits as example images.
Modeling image properties using the Gaussian scale mixture (GSM) model in a multiresolution transform space is the basic idea of a denoising algorithm proposed by Portilla et al. [Image denoising using scale mixtures of Gaussians in the wavelet domain, IEEE Transactions on Image Processing, 12 (2003), pp. 1338-1351]. Under this model and using the correlations between pyramid coefficients, the Bayesian least squares (BLS) of each coefficient is used to estimate its original value. In this article, we analyze and discuss the BLS-GSM algorithm, its drawbacks and benefits in more detail. An analytical parameter study of this denoising approach is provided as well. Additionally, we propose a localized version of this algorithm and experimentally show that it outperforms the original method both numerically and visually. We also show that the resulting method is state-of-the-art in terms of PSNR.
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