Noise reduction in two-photon laser scanned microscopic images by singular value decomposition with copula threshold

Abstract

Multi-photon laser scanning microscopy is an advantageous technique for layered imaging in thick tissue samples. It enables reduced phototoxicity as the region of fluorescence excitation is limited. But, the small number and stochastic nature of detected photons require the multifold acquisition of each image so the photodamage may accumulate. This paper aims to reduce the number of repeated image acquisitions, proposing a denoising technique based on singular value decomposition with a novel two-stage copula threshold, thus the name SVD-COPULA. The first stage defines the referent noise level based on copula analysis. Following the comparative analysis of classical techniques and different copula families, Frank's copula is selected to determine the regions for noise estimation. The second threshold stage analyzes the stationarity of the singular values and adjusts the number of the eigenimages necessary for reconstruction, an issue important for images without the distinctive background regions. A problem of the mixed discrete-continual nature of pixel values is noticed and resolved. The procedure is fully automatic, with the built-in set of parameters and without the necessity for prior image analysis. The proposed method, together with twelve state-of-the-art denoising methods, are tested using the microscopic images from the proprietary and open databases, and the test images with simulated mixed Poisson-Gaussian noise. It is shown that the performance of SVD-COPULA is consistently good for all investigated images.