Light microscopy is a tool of paramount importance for biologists and has been constantly improved for the past four centuries. Despite many recent developments, microscopy techniques still require improvement, especially to reach better temporal and spectral resolutions. In particular, many high-end microscopes favor mostly spatial resolution, at the expense of the latter two types of resolution. In this thesis, we present methods based on the use of active illumination and computational algorithms to increase temporal and spectral resolutions of microscopes. Our methods aim to provide users with the flexibility to chose, within a single instrument, which type of resolution is to be favored based on the application at hand. More generally, our approach has fundamental implications on the signal sensing procedure, allowing, for example, to mitigate temporal aliasing in sequences of images.

Our first method performs temporal super-resolution imaging of monochrome scenes using a hue-encoded shutter. By making use of an active multi-spectral illumination, temporal information is encoded in the hue of the acquisitions. We characterize the method showing a resolution improvement of 2.8 and an increase of frame-rate of a factor 3. We demonstrate the applicability of our method to bright-field transmission microscopy by applying the method to the beating heart of a zebrafish.We then extend this method to fluorescence microscopy. We add a temporal regularization term to make the method robust to fluorescent labelings inhomogeneities. We present an application of the method to the beating heart of a zebrafish that emits fluorescent light of two different colors. Implementing our method within a light-sheet microscope allows us to reconstruct 3D+time videos of the beating heart at twice the acquisition frame-rate.

Our second method offers a way to perform temporal generalized sampling by computing simultaneous inner products with the sampled signal. Similarly to the first method, we take advantage of working with multiple illumination hues to compute as many simultaneous inner products, which we retrieve via an unmixing procedure. We use equivalent basic and dual B-splines representations to ensure having finite-length and positive pre-filters, as well as finite-support reconstruction functions. We show applications of our method to a fast rotating target, as well as to the beating heart of a zebrafish, both in transmission and fluorescence microscopy.

Finally, we introduce a method to perform spectral imaging of repeating processes, such as the beating heart. The method sequentially acquires multiple movies with various filters, performs temporal registration of all movies and reconstructs a spectral movie through solving of a spectral unmixing problem, pixel by pixel, at each time point. We characterize the method and show a median error of approximately 10%, by comparing reconstructions on a static sample from our method with measurements obtained with a spectrometer. We then perform validation by comparing static reconstructions with dynamic ones of the same sample. We demonstrate the potential of the method to microscopy by performing spectral imaging of the beating heart of a zebrafish.

Taken together, these methods offer a versatile toolbox to improve the temporal or spectral resolution in both bright field and fluorescence microscopy, which we foresee could be directly implemented in a number of specialized instruments.