Abstract:The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate. However, most implementations developed to take advantage of this framework revolve around controlling the measurements with carefully engineered material or acquisition sequences. Instead, we use the natural randomness of wave propagation through multiply scattering media as a… Show more
“…One way to address such an issue resides in placing a scattering or heterogeneous medium in front of the US probe. This principle has been recently developed in optics and gives promising results [51]. However, such a new design raises many questions regarding the choice and the modelling of the heterogeneous medium.…”
Abstract-Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution of the image reconstruction problem. An alternative to DAS consists in using iterative techniques which require both an accurate measurement model and a strong prior on the image under scrutiny. Towards this goal, much effort has been deployed in formulating models for US imaging which usually require a large amount of memory to store the matrix coefficients. We present two different techniques which take advantage of fast and matrix-free formulations derived for the measurement model and its adjoint, and rely on sparsity of US images in well-chosen models. Sparse regularization is used for enhanced image reconstruction. Compressed beamforming exploits the compressed sensing framework to restore high quality images from fewer raw-data than state-of-the-art approaches. Using simulated data and in vivo experimental acquisitions, we show that the proposed approach is three orders of magnitude faster than non-DAS state-of-the-art methods, with comparable or better image quality.
“…One way to address such an issue resides in placing a scattering or heterogeneous medium in front of the US probe. This principle has been recently developed in optics and gives promising results [51]. However, such a new design raises many questions regarding the choice and the modelling of the heterogeneous medium.…”
Abstract-Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution of the image reconstruction problem. An alternative to DAS consists in using iterative techniques which require both an accurate measurement model and a strong prior on the image under scrutiny. Towards this goal, much effort has been deployed in formulating models for US imaging which usually require a large amount of memory to store the matrix coefficients. We present two different techniques which take advantage of fast and matrix-free formulations derived for the measurement model and its adjoint, and rely on sparsity of US images in well-chosen models. Sparse regularization is used for enhanced image reconstruction. Compressed beamforming exploits the compressed sensing framework to restore high quality images from fewer raw-data than state-of-the-art approaches. Using simulated data and in vivo experimental acquisitions, we show that the proposed approach is three orders of magnitude faster than non-DAS state-of-the-art methods, with comparable or better image quality.
“…On a different scale, optical microscopy demands the ability to reach large depths, in particular when dealing with intra-vital microscopy 17 . Similarly, the physics of optics in random media 3,18,19 , and the attempts to improve focusing through scattering media need to model the depth profile of re-emitted photons [20][21][22][23] . The penetration depth of photons migrating in random media has been studied by several research groups [24][25][26][27][28][29][30][31][32][33][34][35][36][37] .…”
We propose a comprehensive statistical approach describing the penetration depth of light in random media. The presented theory exploits the concept of probability density function f(z|ρ, t) for the maximum depth reached by the photons that are eventually re-emitted from the surface of the medium at distance ρ and time t. Analytical formulas for f, for the mean maximum depth 〈z max 〉 and for the mean average depth z reached by the detected photons at the surface of a diffusive slab are derived within the framework of the diffusion approximation to the radiative transfer equation, both in the time domain and the continuous wave domain. Validation of the theory by means of comparisons with Monte Carlo simulations is also presented. The results are of interest for many research fields such as biomedical optics, advanced microscopy and disordered photonics.
“…In this paper, we circumvent one major limitation of the previous proof-of-concept system [12]. Since optical sensors (here, a CCD camera) only measure the field intensity |y| 2 , in [12] the input image is phase-modulated using a phase-only SLM, with relative phases 0, π/4, π/2, and 3π/4.…”
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.
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