Multispectral imaging plays an important role in many applications from astronomical imaging, earth observation to biomedical imaging. However, the current technologies are complex with multiple alignment-sensitive components, predetermined spatial and spectral parameters by manufactures. Here, we demonstrate a single-shot multispectral imaging technique that gives flexibility to end-users with a very simple optical setup, thank to spatial correlation and spectral decorrelation of speckle patterns. These seemingly random speckle patterns are point spreading functions (PSFs) generated by light from point sources propagating through a strongly scattering medium. The spatial correlation of PSFs allows image recovery with deconvolution techniques, while the spectral decorrelation allows them to play the role of tune-able spectral filters in the deconvolution process. Our demonstrations utilizing optical physics of strongly scattering media and computational imaging present the most cost-effective approach for multispectral imaging with great advantages

Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) are two well-known recovery algorithms in compressed sensing. To recover a d-dimensional m-sparse signal with high probability, OMP needs O (m ln d) number of measurements, whereas BP needs only O m ln d m number of measurements. In contrary, OMP is a practically more appealing algorithm due to its superior execution speed. In this piece of work, we have proposed a scheme that brings the required number of measurements for OMP closer to BP. We have termed this scheme as OMPα, which runs OMP for (m + αm )-iterations instead of m-iterations, by choosing a value of α ∈ [0, 1]. It is shown that OMPα guarantees a high probability signal recovery with O m ln d αm +1number of measurements. Another limitation of OMP unlike BP is that it requires the knowledge of m. In order to overcome this limitation, we have extended the idea of OMPα to illustrate another recovery scheme called OMP∞, which runs OMP until the signal residue vanishes. It is shown that OMP∞ can achieve a close to 0-norm recovery without any knowledge of m like BP.

Recent dictionary training algorithms for sparse representation like -SVD, MOD, and their variation are reminiscent of -means clustering, and this letter investigates such algorithms from that viewpoint. It shows: though -SVD is sequential like -means, it fails to simplify to -means by destroying the structure in the sparse coefficients. In contrast, MOD can be viewed as a parallel generalization of -means, which simplifies to -means without perturbing the sparse coefficients. Keeping memory usage in mind, we propose an alternative to MOD; a sequential generalization of -means (SGK). While experiments suggest a comparable training performances across the algorithms, complexity analysis shows MOD and SGK to be faster under a dimensionality condition.

Super-resolution imaging has been revolutionizing technical analysis in various fields from biological to physical sciences. However, many objects are hidden by strongly scattering media such as biological tissues that scramble light paths, create speckle patterns and hinder object’s visualization, let alone super-resolution imaging. Here, we demonstrate non-invasive super-resolution imaging through scattering media based on a stochastic optical scattering localization imaging (SOSLI) technique. After capturing multiple speckle patterns of photo-switchable point sources, our computational approach utilizes the speckle correlation property of scattering media to retrieve an image with a 100-nm resolution, an eight-fold enhancement compared to the diffraction limit. More importantly, we demonstrate our SOSLI to do non-invasive super-resolution imaging through not only static scattering media, but also dynamic scattering media with strong decorrelation such as biological tissues. Our approach paves the way to non-invasively visualize various samples behind scattering media at nanometer levels of detail.