Approximate Message Passing Reconstruction of Quantitative Acoustic Microscopy Images

Abstract

A novel framework for compressive sensing (CS) data acquisition and reconstruction in quantitative acoustic microscopy (QAM) is presented. Three different CS patterns, adapted to the specifics of QAM systems, were investigated as an alternative to the current raster-scanning approach. They consist of diagonal sampling, a row random, and a spiral scanning pattern and can all significantly reduce both the acquisition time and the amount of sampled data. For subsequent image reconstruction, we design and implement an innovative technique, whereby a recently proposed approximate message passing method is adapted to account for the underlying data statistics. A Cauchy maximum a posteriori image denoising algorithm is thus employed to account for the non-Gaussianity of QAM wavelet coefficients. The proposed methods were tested retrospectively on experimental data acquired with a 250- or 500-MHz QAM system. The experimental data were obtained from a human lymph node sample (250 MHz) and human cornea (500 MHz). Reconstruction results showed that the best performance is obtained using a spiral sensing pattern combined with the Cauchy denoiser in the wavelet domain. The spiral sensing matrix reduced the number of spatial samples by a factor of 2 and led to an excellent peak signal-to-noise ratio of 43.21 dB when reconstructing QAM speed-of-sound images of a human lymph node. These results demonstrate that the CS approach could significantly improve scanning time, while reducing costs of future QAM systems.

Compressed quantitative acoustic microscopy

“…Note that similar results can be obtained for other acoustic parameter maps including attenuation or impedance [3].…”

“…This study demonstrates that a discrete wavelet transform is an appropriate choice for SAM. The Cauchy distribution was used to construct the denoising function embedded in the proposed AMP algorithm [3]. The contribution of the proposed AMP-based QAM imaging framework is twofold: (i) to propose a spiral spatial sampling scheme that meets the practical constraints of QAM acquisition, (ii) to design a dedicated wavelet domain AMPbased reconstruction algorithm, which exploits underlying data statistics through the use of a Cauchy-based MAP algorithm.…”

Compressed quantitative acoustic microscopy

“…where s and t are values determined by v and σ 2 iteratively updated at each iteration together with a constant value γ; σ 2 is estimated as the variance of the z vector defined in (3). s and t are defined as:…”

Spatio-temporal compressed quantitative acoustic microscopy

“…In order to prevent changes to the sensitive thin sectioned tissue during scanning, reducing scanning time is an important practical issue. In this regard, our previous studies were devoted to demonstrating: i) spatially under sampled measurements, following a spiral pattern combined with image reconstruction based on approximate message passing (AMP), allow decreasing the number of acquired RF signals by 40% without degrading the QAM image quality [3], ii) because QAM RF signals at a given location follow a parametric form with a limited number of degrees of freedom, each RF signal can be sampled (and adequately processed) at a much lower rate (162.5 MHz) than the Nyquist rate (800 MHz for our QAM system) [4]. The aim of this study is to combine AMP and FRI for QAM data to yield far more parsimonious data acquisition and to demonstrate that the combined approach significantly reduces QAM data acquisition time and QAM data size at no detriment to image quality.…”