Speckle imaging with blind source separation and total variation deconvolution

TL;DR

This work addresses imaging objects embedded in strongly diffusive environments where the ballistic wave is negligible. It proposes a two-stage strategy to achieve diffraction-limited resolution: first, blind source separation (ICA) to disentangle fields from different scatterers within a reflection matrix; second, total variation deconvolution that leverages the speckle memory effect to estimate scatterer separations. The method does not rely on a known propagation model and is robust to decorrelation properties as long as the incoming speckle has a finite correlation length and the backscattered field exhibits memory. Simulations in a realistic OCT-like setup demonstrate accurate imaging of both discrete scatterers and continuous objects, while highlighting the need for non-Gaussian separation (via SHG) and sufficiently many illuminations for reliable ICA-based separation. Overall, the approach yields diffraction-limited imaging in diffuse media and provides analytical characterizations of memory and correlation lengths relevant to practical implementations.

Abstract

This work is concerned with optical imaging in strongly diffusive environments. We consider a typical setting in optical coherence tomography where a sample is probed by a collection of wavefields produced by a laser and propagating through a microscope. We operate in a scenario where the illuminations are in a speckle regime, namely fully randomized. This occurs when the light propagates deep in highly heterogeneous media. State-of-the-art coherent techniques are based on the ballistic part of the wavefield, that is the fraction of the wave that propagates freely and decays exponentially fast. In a speckle regime, the ballistic field is negligible compared to the scattered field, which precludes the use of coherent methods and different approaches are needed. We propose a strategy based on blind source separation and total variation deconvolution to obtain images with diffraction-limited resolution. The source separation allows us to isolate the fields diffused by the different scatterers to be imaged, while the deconvolution exploits the speckle memory effect to estimate the distance between these scatterers. Our method is validated with numerical simulations and is shown to be effective not only for imaging discrete scatterers, but also continuous objects.

Figures (20)

• Figure 1: Measurement setting
• Figure 2: Forward (left) and SHG speckle (right). The SHG speckle has finer grains since its wavelength is half that of the forward field.
• Figure 3: Deconvolution with perfectly separated SHG speckles. Left: $d=2h$. Center $d=3h$. Right $d=5h$. The red dots show the exact locations of the scatterers. The deconvolution achieves the resolution of the camera pixel size.
• Figure 4: Reconstructions with 10 scatterers. Left: minimal distance $d$ is $3h$ with $N_r=1500$. Center: $d=4h$, $N_r=1000$. Right: $d=5h$, $N_r=1000$. The red dots show the exact locations of the scatterers.
• Figure 5: Numerical limit of the memory effect. Beyond about $18 \lambda \simeq 1.6 \ell_{\rm{me}}$, background noise increases and the scatterers may not be well located.