Compressive fluorescence microscopy for biological and hyperspectral imaging

Abstract

The mathematical theory of compressed sensing (CS) asserts that one can acquire signals from measurements whose rate is much lower than the total bandwidth. Whereas the CS theory is now well developed, challenges concerning hardware implementations of CS-based acquisition devices-especially in optics-have only started being addressed. This paper presents an implementation of compressive sensing in fluorescence microscopy and its applications to biomedical imaging. Our CS microscope combines a dynamic structured wide-field illumination and a fast and sensitive single-point fluorescence detection to enable reconstructions of images of fluorescent beads, cells, and tissues with undersampling ratios (between the number of pixels and number of measurements) up to 32. We further demonstrate a hyperspectral mode and record images with 128 spectral channels and undersampling ratios up to 64, illustrating the potential benefits of CS acquisition for higher-dimensional signals, which typically exhibits extreme redundancy. Altogether, our results emphasize the interest of CS schemes for acquisition at a significantly reduced rate and point to some remaining challenges for CS fluorescence microscopy.biological imaging | compressed sensing | computational imaging | sparse signals F luorescence microscopy is a fundamental tool in basic and applied biomedical research. Because of its optical sensitivity and molecular specificity, fluorescence imaging is employed in an increasing number of applications which, in turn, are continuously driving the development of advanced microscopy systems that provide imaging data with ever higher spatio-temporal resolution and multiplexing capabilities. In fluorescence microscopy, one can schematically distinguish two kinds of imaging approaches, differing by their excitation and detection modalities (1). In wide-field (WF) microscopy, a large sample area is illuminated and the emitted light is recorded on a multidetector array, such as a CCD camera. In contrast, in raster scan (RS) microscopy, a point excitation is scanned through the sample and a point detector is used to detect the fluorescence signal at each position.While very distinct in their implementation and applications, these imaging modalities have in common that the acquisition is independent of the information content of the image. Rather, the number of measurements, either serial in RS or parallel in WF, is imposed by the Nyquist-Shannon theorem. This theorem states that the sampling frequency (namely the inverse of the image pixel size) must be twice the bandwidth of the signal, which is determined by the diffraction limit of the microscope lens equal to λ∕2NA (λ is the optical wavelength and NA the objective numerical aperture). Yet, most images, including those of biological interest, can be described by a number of parameters much lower than the total number of pixels. In everyday's world, a striking consequence of this compressibility is the ability of consumer cameras with several megapixel detectors to routinely reduce t...

Probability of correct reconstruction in compressive spectral imaging

“…This new technique involves diverse mathematical areas such as numerical optimization, signal processing, random matrix analysis, and statistics. The enormous potential of CS has been recently applied in areas such as microscopy, holography, tomography and spectroscopy (Arce et al, 2014;Brady et al, 2009;Studer et al, 2012;Wagadarikar et al, 2008;Yu and Wang, 2009). CS allows sensing a signal with a fewer number of samples than that required by the Nyquist criterion.…”

Compressive Sampling Multispectral Imaging and Unmixing Method for Fluorescent Imaging

“…As mentioned in Ref. [16], a higher compression rate leads to a reconstructed CS image with a lower SNR. Taken the SNR into account, through a series of pre-simulation, the number of CS measurements, T , was chosen to be 4096 (4096 = 128 × 128 × 1/4, i.e., a compression rate of 4 : 1).…”

“…The numerical results presented in this paper clearly demonstrate the potential of this method to be able to extract essential spectral informationin a precise manner. Extending this technique to situations with low signal to noise ratio is theoretically achievable since NESTA and MVSA have the capability to operate at high accuracy [12,16], but the denoising procedure would require more sophistication. Compressive sampling unmixing, as a complement to standard unmixing techniques, has the potential to be applied in the real large-scale multispectral imaging applications in the future.…”

Compressive microscopic imaging with “positive–negative” light modulation

“…Ghost imaging with a classical thermal source was studied in a two-arm microscope imaging system but it was only a theoretical simulation with a simple double-slit object [36]. Recently, CS was also applied to microscopy [37,38]; in [38], Studer et al tested their system on a sample of fluorescent beads which were sparsely distributed. In addition, they used binary patterns of a shifted and rescaled form (1 + h)/2 where h is a Hadamard sequence, thus each entry of patterns is either 0 or 1, still not the best range of values.…”