Spatial weight matrix in dimensionality reduction reconstruction for micro-electromechanical system-based photoacoustic microscopy

Abstract

A micro-electromechanical system (MEMS) scanning mirror accelerates the raster scanning of optical-resolution photoacoustic microscopy (OR-PAM). However, the nonlinear tilt angular-voltage characteristic of a MEMS mirror introduces distortion into the maximum back-projection image. Moreover, the size of the airy disk, ultrasonic sensor properties, and thermal effects decrease the resolution. Thus, in this study, we proposed a spatial weight matrix (SWM) with a dimensionality reduction for image reconstruction. The three-layer SWM contains the invariable information of the system, which includes a spatial dependent distortion correction and 3D deconvolution. We employed an ordinal-valued Markov random field and the Harris Stephen algorithm, as well as a modified delay-and-sum method during a time reversal. The results from the experiments and a quantitative analysis demonstrate that images can be effectively reconstructed using an SWM; this is also true for severely distorted images. The index of the mutual information between the reference images and registered images was 70.33 times higher than the initial index, on average. Moreover, the peak signal-to-noise ratio was increased by 17.08% after 3D deconvolution. This accomplishment offers a practical approach to image reconstruction and a promising method to achieve a real-time distortion correction for MEMS-based OR-PAM.

Fig. 1

An overview of MEMS-based photoacoustic microscopy system. a: Schematic of the MOR-PAM; b: Zoomed-in views of the ultrasonic sensor; c: B-Scan images associated with the acquired PA matrix, the PA signals in the red dashed line, and PA signals in the purple dashed line are utilized for reconstruction; d: Projection of the laser spot in MAP image. FPGA: Field programmable gate array; DAQ: Data acquisition unit; MEMS: Micro-electromechanical systems; PD: Photodiode; ECU: Electronic control unit; G: Glass; RP: Reflection prism; s: Scoustic path; PAS: Photoacoustic source; CA: The estimated convolution area; PA A.: Photoacoustic amplitude.

Fig. 2

Overall design of SWM. a: Flowchart of constructing SWM; b: Image processing flow through an SWM hierarchical structure. AWF: Adaptive Wiener filtering; NMI: Normalized mutual information; PSNR: Peak signal-noise-ratio; W_{i, j}: The element in an adaptive Wiener filter; R_{i, j}: The element in a registration matrix; $W_{i,j}^{\prime }$: The element in a deconvolution kernel

Fig. 3

Stage results of SWM construction with a resolution chart. a: The process of extracting feature points by utilizing OV-MRF and H&SA; b: The mapping relationship between the feature points-1 (the feature points in the input image) and the feature points-2 (the feature points in reference image); c: The process of image registration based on the feature point pairs; stage results after the first red dashed line are obtained by adding manually selected feature points for registration, and stage results after the second red dashed line are 3D deconvolution results. Norm.: Normalized; PA A.: Photoacoustic amplitude

Fig. 4

Analysis of using SWM to process a resolution chart. a: Original 3D image; b: The result of denoising and registration of Fig. a; c: 3D deconvolution result of Fig. b; d-f: A-lines stack of white dashed line in Figs. a-c, respectively; g-i: The profiles of MAP images of Figs. a-c marked with the white dashed line. Norm.: Normalized; A., Amplitude; I.: Intensity

Fig. 5

Experimental results of image reconstruction with SWM. a: Original MAP image of a ring texture resolution chart; b: The processed MAP image of Fig. a; c: Horizontal profile along colored dashed-lines in a and b rendered with different colors; d: Vertical profile along colored dashed-lines in Figs. a and b; e: Image of vessels in the abdomen of a laboratory rat; f: Joint histogram comparison of different images; g-i: The above images of g-i are distorted images; the middle images are the corrected depth-coded images (processed images); the lower images of g-i are superimposed images between the original images and the processed images; white-arrows and rulers are utilized to mark obvious correction. Norm.: Normalized; ToF: Time of flight; Pro.: Processed; Ref.: Reference; Reg.: Registered; units: μm