Spectroscopic photoacoustic denoising framework using hybrid analytical and data-free learning method

Abstract

Spectroscopic photoacoustic (sPA) imaging uses multiple wavelengths to differentiate and quantify chromophores based on their unique optical absorption spectra. This technique has been widely applied in areas such as vascular mapping, tumor detection, and therapeutic monitoring. However, PA imaging is highly susceptible to noise, leading to a low signal-to-noise ratio (SNR) and compromised image quality. Furthermore, low SNR in spectral data adversely affects spectral unmixing outcomes, hindering accurate quantitative PA imaging. Traditional denoising techniques like frame averaging, though effective in improving SNR, can be impractical for dynamic imaging scenarios due to reduced frame rates. Advanced methods, including learning-based approaches and analytical algorithms, have demonstrated promise but often require extensive training data and parameter tuning. Moreover, spectral information preservation is unclear, limiting their adaptability for clinical usage. Additionally, training data is not always accessible for learning-based methods. In this work, we propose a Spectroscopic Photoacoustic Denoising (SPADE) framework using hybrid analytical and data-free learning method. This framework integrates a data-free learning-based method with an efficient BM3D-based analytical approach while preserving spectral integrity, providing noise reduction, and ensuring that functional information is maintained. The SPADE framework was validated through simulation, phantom, in vivo, and ex vivo studies. These studies demonstrated that SPADE improved image SNR by over 15 $\mathrm{dB}$ in high noise cases and preserved spectral information (R > 0.8), outperforming conventional methods, especially in low SNR conditions. SPADE presents a promising solution for preserving the accuracy of quantitative PA imaging in clinical applications where noise reduction and spectral preservation are critical.

Keywords: Data-free; Denoising; In vivo demonstration; Multiwavelength; Photoacoustic imaging; Quantitative Imaging.

Graphical abstract

Fig. 1

(a) Spectroscopic Photoacoustic Denoising (SPADE) Framework. Data processing pipeline of the proposed SPADE method: The noisy spectroscopic photoacoustic (sPA) image is first reassembled using Spectral Domain Data Re-assembly (SDDR) before being denoised as a 2D image using Zero-Shot Hybrid (ZS-Hybrid). After denoising, the reverse SDDR is applied to restore the original dimensions of the sPA image. (b) Illustration of sPA image pixel reassembly during the SDDR process. Box color denotes the pixel wavelength, and brightness indicates the axial location.

Fig. 2

The denoising process starts with feeding the raw noisy image into SDDR, followed by the analytical component of vanilla BM3D: in the first step, the image is grouped by block matching, then a 3D transform is applied for hard thresholding, followed by an inverse 3D transform and aggregation of block-wise estimates; this is then repeated in a similar second step with further aggregation for the final Wiener estimate. After the analytical component, the image is downsampled by two fixed filters into two downsampled images, which are then processed through a two-layer image-to-image network for further denoising. Finally, the denoised image is recovered using reverse SDDR.

Fig. 3

In vivo tumor scanning: (a) Animal setup sketch, (b) Photograph of prepared animal with tumor region zoomed in.

Fig. 4

Simulated spectroscopic photoacoustic (sPA) image at 720 $\mathit{mm}$. (a) PA images (left to right): noisy single-frame PA image, vanilla BM3D denoised image, and image denoised by the proposed SPADE method. Quantitative evaluation of the SPADE method compared to vanilla BM3D and the noisy single-frame PA image: (b) Output signal-to-noise ratio (SNR) at different noise levels and SNR improvement. (c) Spectral correlation coefficient of vanilla BM3D and SPADE at various noise levels. (d) Structural similarity (SSIM) index and Peak signal-to-noise ratio (PSNR), computed with respect to the ground truth simulation image without noise, along with paired wise P value from T test. (e) Denoising performance across varying numbers of input wavelengths.

Fig. 5

(a) Photoacoustic (PA) imaging denoising results of the point phantom at 810 $\mathit{nm}$. From left to right: Raw noisy data, 64-frame averaging filter, vanilla BM3D, and the proposed SPADE algorithm. (b) Signal lateral profile across one of the targets with zoomed noise region. The white dash line in (a) indicates where we plot the lateral profile. (c) SNR statistics of point targets for each method, along with paired wise P value from T test. (d) Output SNR from the three denoising methods at various noise levels. (e) Spectral correlation coefficient of each method compared to the ground truth spectrum, along with paired wise P value from T test. (f) Structural similarity (SSIM) index and (g) Peak signal-to-noise ratio (PSNR) computed relative to the averaging filter image, along with paired wise P value from T test.

Fig. 6

Ex vivo evaluation of spectroscopic PA (sPA) analysis for cardiac ablation mapping. (a) PA image at 780 $\mathit{nm}$ and PA-mapped lesion boundary using different denoising methods, alongside the corresponding US image and post-scan gross-pathology highlighting the lesion. Quantitative analysis statistics: (b) Signal-to-noise ratio (SNR), along with paired wise P value from T test. (c) Peak signal-to-noise ratio (PSNR), along with paired wise P value from T test. (d) Structural similarity (SSIM) index, and (e) spectral correlation coefficient relative to the averaging filter, along with paired wise P value from T test. Denoising performance: SNR improvement (f), SSIM (g), PSNR (h) across varying numbers of input wavelengths based on ex vivo evaluation.

Fig. 7

In vivo mice tumor scanning: (a) before and (b) 24 hours after contrast agent injection. From left to right: single frames, PA image averaged with 64 frames (Reference), vanilla-BM3D, and SPADE (proposed), overlaid with the US image. The same color range is applied within each method before and after injection. Quantitative analysis statistics: (c) Signal-to-noise ratio (SNR), along with paired wise P value from T test. (d) Peak signal-to-noise ratio (PSNR), along with paired wise P value from T test. (e) Structural similarity (SSIM) index, and (f) spectral correlation coefficient relative to the averaging filter, along with paired wise P value from T test.

Fig. 8

Spectral angle mapper (SAM). (a) SAM of simulation data. (b) SAM of point phantom data.

Fig. 9

Simulated spectroscopic photoacoustic (sPA) image with single loss only. (a) PA images (left to right): noisy single-frame PA image, and image denoised by the proposed SPADE method. Quantitative evaluation of the SPADE method compared to two single losses (residual loss, consistency loss): (b) Output signal-to-noise ratio (SNR) at different noise levels. Spectral correlation coefficient of residual loss only and SPADE at various noise levels. (c) Output signal-to-noise ratio (SNR) at different noise levels. Spectral correlation coefficient of consistency loss only and SPADE at various noise levels.

Fig. 10

Simulated spectroscopic photoacoustic (sPA) image with different network architectures. (a) PA images (left to right): noisy single-frame PA image, and image denoised by the proposed SPADE method. Quantitative evaluation of the SPADE method compared to different network architectures: (b) Output signal-to-noise ratio (SNR) at different noise levels. Spectral correlation coefficient of BM3D + ZSN2N and SPADE at various noise levels. (c) Output signal-to-noise ratio (SNR) at different noise levels. Spectral correlation coefficient of SDDR + BM3D and SPADE at various noise levels. (d) Output signal-to-noise ratio (SNR) at different noise levels. Spectral correlation coefficient of SDDR + ZSN2N and SPADE at various noise levels. (e) Output signal-to-noise ratio (SNR) at different noise levels. Spectral correlation coefficient of ZSN2N and SPADE at various noise levels.