2Pb5-4
Compressed Sensing for Faster Optical-resolution
Photoacoustic Microscopy: A Simulation Framework
I Gede Eka Sulistyawan1‡, Daisuke Nishimae2, Takuro Ishii1,3, and Yoshifumi Saijo1(1Grad. School of Biomed Eng, Tohoku Univ.; 2School of Eng., Tohoku Univ.; 3FRIS,Tohoku Univ.)
1. Introduction
Optical resolution photoacoustic microscopy(OR-PAM) has been developed to visualize
microvascular with high spatial resolution. In
general, the OR-PAM system requires to scan thetarget point-by-point by moving the opt-acoustic
probe in two orthogonal directions. In the early
development of OR-PAM, the scanning was doneusing linear stages, but the linear scanning had alimited imaging speed. To improve the system, later
studies have investigated the utilization of microelectromechanical system (MEMS) mirrors thattranslates the linear movement into the rotational
movement and thus might increase the imaging
speed of OR-PAM. A study used a combination ofsingle direction MEMS and linear stage1), while
another group developed a dual-direction MEMS2).
In addition, a polygon mirror was employed as
substitute to the MEMS3). Those attempts have
proven the efficacy of the MEMS in improving thespeed of the OR-PAM, however the improved speed
is still in a range of 8 – 400 seconds for 1 × 1 cm2,
which is insufficient to visualize temporal changes
such as intra-cellular biochemical interactions andminute hemodynamics.
A potential solution is reducing the number ofsampling point, in addition to using the MEMSs’ fastscanning technique, and decreasing the acquisition
time. To do so, an emerging technique called
compressed sensing (CS) may be used to reconstruct
the full resolution image data from the undersampled scanning point. This study investigates theapplicability of CS in an OR-PAM system equippedwith a single-direction MEMS mirror and a singledirection linear stage by simulating an undersampling condition.
2. Material and Methods
2.1 Experiment setup and data acquisition
The OR-PAM system comprised of a singleaxis waterproof MEMS (1A-WP-MEMS) and alinear stage1). The object was illuminated withfocused laser (Wavelength: 532 nm, Pulse repetition
frequency (PRF): 10 kHz), and the yielded
photoacoustic signal was captured with an unfocusedultrasound (Center frequency: 50 MHz, Frequency
sampling: 500 MS/s).

A black-stained leaf skeleton phantom waschosen as the experiment object. The dimension of
the imaging was a patch of 2 mm × 2 mm and a depthof 0.75 mm. The speed of the linear stage wasdependent on the MEMS and pulse repetition
frequency (PRF). Following this setup1), the linear
stage speed was 62 μm/s and able to obtain full
resolution scanning in 32 seconds.
2.2 Signal processing
The acquired radio frequency data was bandpass filtered (5 – 100 MHz) then Hilbert transformed(HT). The OR-PAM system requires distortion
correction as the motion of the MEMS mirror
introduces linear and non-linear distortions in thepolar axis1). Once corrected, a Maximum Intensity
Projection (MIP) image was obtained bynormalizing and picking the maximum amplitude ofeach HT data. An illustration shown in Fig. 1 (a) andthe yielded MIP image for ground-truth was shownin Fig. 1 (b).
2.3 Sampling simulation
A CS framework was devised to generate afull-resolution MIP image from an under-sampleddataset. Although the CS framework requires anacquisition dataset randomly sampled over the 2D
imaging field, performing randomization wasconsidered in obstructing the advantage of resonant
movement of the MEMS. To achieve both minimum
sampling and retain the resonant movement ofMEMS, a simulation was done by increasing thespeed of the linear stage.
Considering the original linear stage speed
was 62.5 μm/s , the simulated samplings wereperformed on 188 μm/s, 250 μm/s and 383 μm/s
for 12.8 seconds. These speeds were approximately
3, 4 and 6 times faster than the original. The undersampled data obtained from simulation was shownin Fig. 1 (c – e). These data then transferred into theCS reconstruction that is described in the nextsection.
2.4 Reconstruction
Consider a reconstruction of a full resolution
MIP image 𝑀 ∈ ℝ𝑚×𝑛 from an obtained undersampled data 𝑌 ∈ ℝ𝑝×1 with 𝑝 ≪ 𝑚𝑛 . To matchthe dimension, a vectorized 𝑀 ∈ ℝ𝑚𝑛×1 was used(a)188 m/s

RF383 m/s

(d)

(e)

(f)

(g)

(h)

Sampling

MIP

250 m/s

(c)

RFT

(mm)

Reconstructed(b)(mm)

Fig. 1. (a) Acquisition in polar coordinate. (b) Ground-truth. (c-h) Under sampling simulation on various linear stage
speed for 12.8 seconds. (c, d, e) Sampling pattern. (f, g, h) reconstructed MIP after minimization and distortion correction.

instead. The process of a CS reconstruction was toiteratively estimate 𝑀 closer to 𝑌 with a priorknowledge on the sparsity of 𝑀. To achieve the goal,
𝑌 was modeled as sampling 𝑀 with pattern 𝐶 ∈ℤ𝑝×𝑚𝑛 , i.e., 𝑌 = 𝐶𝑀 . Then, an Inverse Discrete
Cosine Transform (IDCT) Ψ ∈ ℝ𝑚𝑛×𝑚𝑛 was used
to obtain 𝑀 from its sparse representation 𝑋 ∈ℝ𝑚𝑛×1 , i.e., 𝑀 = Ψ𝑋 . Finally, the reconstruction
algorithm can be represented in the followingequation,min‖𝐶Ψ𝑋 − 𝑌‖22 + ‖𝑋‖1(1)𝑋A Sub-gradient algorithm was utilized to solve
Equation 1. The obtained reconstructed MIP image
then distortion corrected before evaluation.
Evaluation was done using Structural Similarity(SSIM)4) and Mean Squared Error (MSE) against theground-truth.
3. Results and discussion
The reconstructed full resolution images wereshown in Fig. 1 (f – h). The yielded images weresimilar with the ground-truth, implying the successof the algorithm to reconstruct the data. Nevertheless,artifacts still existed in some parts of the images.
Structurally, the artifact was similar to the scanningpattern. This suggests that the artifact might beoriginated from the scanning pattern.
A quantitative evaluation was shown in
Table 1. The best and worst performance wasachieved by the speed 383 μm/s and 250 μm/s ,respectively. With simulation that allows backward
Table 1. SSIM and MSE for different stage speeds comparedto ground-truth.
188 μm/s
250 μm/s
383 μm/s
SSIM0.486
0.253
0.642
MSE
0.009
0.026
0.002

scanning for more scanning points, increasing speed
should be associated with increasing performance.
However, there exist speeds (e.g., 250 μm/s ) that
had the same path while scanning backward. This
causing in unimproved scanning points, thus limits
the reconstruction algorithm and should be avoided.
The current study utilized Sub-gradientalgorithm without considering the undifferentiable
properties of the Equation 1. This motivates further
investigation to different algorithm that able toovercome this limitation. In addition, an
identification of the origin of the artifact might help
in guiding to a better problem formulation, rather
than relying only on sparsity. In the future, it isinteresting to modify Equation 1 to suppress theartifact.
4. Conclusion
In this paper, the applicability of CS
framework on OR-PAM with 1-axis MEMS and alinear stage had investigated. Despite of undercontrolled simulation, the experiment results showed
positive potentials of the CS implementation in thereal system that will significantly increase theimaging acquisition time.
References
1. R. Shintate, T. Ishii, J. Ahn, J. Y. Kim, C. Kim,and Y. Saijo: Sci. Rep. 12 (2022) 9221.
2. J. Y. Kim, C. Lee, K. Park, G. Lim, and C. Kim:
Sci. Rep. 5 (2015) 7932.
3. B. Lan, W. Liu, Y. Wang, J. Shi, Y. Li, S. Xu, H.
Sheng, Q. Zhou, J. Zou, U. Hoffmann, W. Yang,
J. Yao: Biomed. Opt. Express 9 (2018) 4689.
4. Z. Wang, A. C. Bovik, H. R. Sheikh, E. P.
Simoncelli: IEEE Trans. Image Process. 13(2004) 600.