[Paper Review] Compressive Sampling Approach for Image Acquisition with Lensless Endoscope

Stéphanie Guérit, Siddharth Sivankutty+4 more|arXiv (Cornell University)|Oct 29, 2018

Sparse and Compressive Sensing Techniques13 references4 citations

TL;DR

This paper proposes a compressive sampling (CS) approach for lensless endoscope imaging that replaces traditional raster scanning with random illumination patterns from single-mode fibers, eliminating the need for beam calibration. The method achieves comparable or better image reconstruction quality than conventional raster scanning at reduced measurement rates, with CS using one random pattern outperforming raster scanning when compression exceeds 50% of the field of view.

ABSTRACT

The lensless endoscope is a promising device designed to image tissues in vivo at the cellular scale. The traditional acquisition setup consists in raster scanning during which the focused light beam from the optical fiber illuminates sequentially each pixel of the field of view (FOV). The calibration step to focus the beam and the sampling scheme both take time. In this preliminary work, we propose a scanning method based on compressive sampling theory. The method does not rely on a focused beam but rather on the random illumination patterns generated by the single-mode fibers. Experiments are performed on synthetic data for different compression rates (from 10 to 100% of the FOV).

Motivation & Objective

• To address the time-consuming calibration and scanning process in traditional lensless endoscopes that rely on focused beam raster scanning.
• To explore whether random illumination patterns via compressive sampling can replace calibrated focused illumination for in vivo cellular imaging.
• To evaluate the performance of compressive sampling in reconstructing high-quality images with fewer measurements compared to conventional raster scanning.
• To assess the impact of varying numbers of random illumination patterns (P = 1, 2, 4) and compression rates (M/N from 0.1 to 1.0) on image reconstruction quality.

Proposed method

• The method models image acquisition as a linear convolution between the image and a point spread function (PSF), with observations corrupted by i.i.d. Gaussian noise.
• For compressive sampling, the number of measurements M is reduced relative to the number of pixels N (M < N), and observations are acquired at the center of the field of view via a restriction operator R.
• Random illumination patterns (speckles) are generated without beam calibration, and the forward model uses a sum of masked convolutions with multiple PSFs (P = 1, 2, 4).
• Image reconstruction is performed using a total variation (TV) regularization term in a constrained optimization problem, solved via the alternating direction method of multipliers (ADMM).
• The regularization parameter ρ is iteratively adjusted based on residual whiteness to balance data fidelity and sparsity.
• The method avoids the need for wavefront shaping calibration by leveraging the inherent randomness of speckle patterns from uncalibrated single-mode fibers.

Experimental results

Research questions

• RQ1 Can compressive sampling with random illumination patterns achieve comparable or better image reconstruction quality than conventional raster scanning in lensless endoscopy?
• RQ2 How does the number of random illumination patterns (P = 1, 2, 4) affect reconstruction performance at different compression rates (M/N)?
• RQ3 At what compression rate (M/N) does the compressive sampling approach outperform raster scanning in terms of SNR?
• RQ4 Does the absence of beam calibration in the compressive sampling setup compromise image quality, and if so, to what extent?
• RQ5 How does the choice of total variation regularization influence reconstruction quality under low-measurement conditions?

Key findings

• When M/N = 1.0 (no compression), raster scanning yields better SNR than compressive sampling with one random pattern, confirming that calibration remains optimal under full sampling.
• For M/N < 0.5, the compressive sampling approach with a single random pattern outperforms raster scanning in terms of mean SNR, indicating improved performance under compression.
• At M/N = 0.5, using four random patterns increases the mean SNR compared to one or two patterns, showing that more diversity in illumination improves reconstruction.
• The compressive sampling method achieves a mean SNR of approximately 28 dB at M/N = 0.5 with four random patterns, while raster scanning achieves around 25 dB under the same conditions.
• The results demonstrate that compressive sampling can either reduce acquisition time by requiring fewer measurements or expand the field of view within the same time, without requiring beam calibration.