Time-resolved Hadamard fluorescence imaging

Compressed sensing in fluorescence microscopy

Compressed sensing (CS) is a signal processing approach that solves ill-posed inverse problems, from under-sampled data with respect to the Nyquist criterium. CS exploits sparsity constraints based on the knowledge of prior information, relative to the structure of the object in the spatial or other domains. It is commonly used in image and video compression as well as in scientific and medical applications, including computed tomography and magnetic resonance imaging. In the field of fluorescence microscopy, it has been demonstrated to be valuable for fast and high-resolution imaging, from single-molecule localization, super-resolution to light-sheet microscopy. Furthermore, CS has found remarkable applications in the field of mesoscopic imaging, facilitating the study of small animals' organs and entire organisms. This review article illustrates the working principles of CS, its implementations in optical imaging and discusses several relevant uses of CS in the field of fluorescence imaging from super-resolution microscopy to mesoscopy.

Hadamard-transform fluorescence-lifetime imaging

We discuss a Hadamard-transform-based fluorescence-lifetime-imaging (HT-FLI) technique for fluorescence-lifetime-imaging microscopy (FLIM). The HT-FLI uses a Fourier-transform phase-modulation fluorometer (FT-PMF) for fluorescence-lifetime measurements, where the modulation frequency of the excitation light is swept linearly in frequency from zero to a specific maximum during a fixed duration of time. Thereafter, fluorescence lifetimes are derived through Fourier transforms for the fluorescence and reference waveforms. The FT-PMF enables the analysis of multi-component samples simultaneously. HT imaging uses electronic exchange of HT illumination mask patterns, and a high-speed, high-sensitivity photomultiplier, to eliminate frame-rate issues that accompany two-dimensional image detectors.

Rapid identification of false peaks in the spectrum of Hadamard transform ion mobility spectrometry with inverse gating technique

With the introduction of inverse gating technique to Hadamard multiplexing ion mobility spectrometry, the false peaks in the spectrum of Hadamard transform could be rapidly identified.

Optical full Hadamard matrix multiplexing and noise effects

Hadamard multiplexing provides a considerable SNR boost over additive random noise but Poisson noise such as photon noise reduces the boost. We develop the theory for full H-matrix Hadamard transform imaging under additive and Poisson noise effects. We show that H-matrix encoding results in no effect on average on the noise level due to Poisson noise sources while preferentially reducing additive noise. We use this result to explain the wavelength-dependent varying SNR boost in a Hadamard hyperspectral imager and argue that such a preferential boost is useful when the main noise source is indeterminant or varying.