Compressive Fluorescence Microscopy for Biological and Hyperspectral Imaging
Maxime Dahan
2012
Imaging and Applied Optics Technical Papers
unpublished
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
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... namic 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 the number of bits in a raw data file by an order of magnitude or two without substantial information loss. To quote from David Brady: "if it is possible to compress measured data, one might argue that too many measurements were taken" (2). The recent mathematical theory of compressed or compressive sensing (CS-see refs. 3, 4) has addressed this challenge and shown how the sensing modality could be modified to reduce the sampling rate of objects which are sparse in the sense that their information content is lower than the total bandwidth or the number of pixels suggest. The fact that one can sample such signals nonadaptively and without much information loss-if any at all-at a rate close to the image information content (instead of the total bandwidth) has important consequences, especially in applications where sensing modalities are slow or costly. To be sure, the applications of CS theory to data acquisition are rapidly growing in fields as diverse as medical resonance imaging (5, 6), analog-to-digital conversion (7), or astronomy (8). In optics, the interest in CS has been originally spurred by the demonstration of the so-called "single-pixel camera" (9). Since then, reports have explored the potential of CS for visible and infrared imaging (10, 11), holography (12), or ghost imaging (13). In microscopy, the feasibility of CS measurements has recently been demonstrated (14). Altogether, these results open exciting prospects, notably for the important case of biomedical imaging. Yet, there are very few results about the performance of CS hardware devices on relevant biological samples. As such samples often have low fluorescence, it is especially important to understand how the associated noise will affect the acquisition and reconstruction schemes. In this paper, we describe Compressive Fluorescence Microscopy (CFM), a unique modality for fluorescence biological and hyperspectral imaging based on the concepts of CS theory. In CFM, the sample is excited with a patterned illumination and its fluorescence is collected on a point detector. Images are computationally reconstructed from measurements corresponding to a set of appropriately chosen patterns. Therefore, CFM benefits from many advantages associated with RS techniques, namely, high dynamic range, facilitated multiplexing, and wide spectral range (from the UV to the IR). In truth, the benefits of CS are particularly appealing in biology where fast, high-resolution, and multicolor imaging is highly sought after. The paper is organized as follows. We begin by recalling the principles of CS theory for optical imaging. We then turn to the description of the practical implementation of CFM and of Author contributions
doi:10.1364/isa.2012.im4c.5
fatcat:ntuuqideknaebb5lkz257yygkq