Superresolving imaging is a term that encompasses optical techniques of image aquisition and transmission with better resolution than could be expected from the characteristics of the imaging set-up or in some cicumstances also better than predicted by the diffraction limit.
One of the methods of superresolving imaging is to use a medium with an increased refractive index. Going further, the same is possible with specially designed synthetic nanostructured materials such as metal-dielectric layered materials. Such structers are one of the points of interest of our group.

Computational ghost imaging includes indirect imaging techniques. With this approach, we measure a different physical quantity or kind of data than we are finaly interested in. At the same time, the optical signal is subject to modulation during its aquisition. Then the measurement has to be recovered through computationaly demanding digital processing by solving an inverse problem. Image reconstruction techniques based on the theory of compressive sensing often allow for solving an incomplete inverse problem with ambiguous solutions. These methods make use of an a priori unknown internal structure of the data together with the assumption of the compressibility of the measured data. Intensive research is going on to use computational imaging and single-pixel detection for hyperspectral imaging, polarimetric imaging, 3D imaging, imaging through scattering media, imaging in IR anfd THZ ranges, or behind-the-corner imaging.

Our current subject of interest related to the NCN-Opus project "Superresolution hidden in the far-field and spatial-spectral transformations" is to use an indirect measurement of the image spectrum in the far-field for recovering the information on near-field nanostructures in a situation when the direct microscopic measurement is not possible due to the diffraction limit. To make it realistic it is necesary to introduce a dispersive spatial-spectral mixing in the near-field into the measurement.

The following are our recent publications on single-pixel imaging:

• Pastuszczak A., Stojek R., Wróbel P. and Kotynski R., 2021: Differential real-time single-pixel imaging with Fourier domain regularization - applications to VIS-IR imaging and polarization imaging, Optics Express, vol. 29(17) , pp. 26685-26700 , 10.1364/OE.433199
• Bancerek M., Czajkowski K.M. and Kotyński R.: Far-field signature of sub-wavelength microscopic objects, Optics Express, vol. 28(24) , pp. 36206-36218 , 2020 10.1364/OE.410240
• Czajkowski K., Pastuszczak A., and Kotyński R., 2019, Single-pixel imaging with sampling distributed over simplex vertices, Optics Letters, vol. 44(5), pp. 1241-1244, 10.1364/OL.44.001241
• Czajkowski K.M., Pastuszczak A., Kotyński R., 2018:  Real-time single-pixel video imaging with Fourier domain regularization, Optics Express, vol. 26 , pp. 20009-20022 , 10.1364/OE.26.020009
• Czajkowski K., Pastuszczak A. and Kotyński R., 2018: Single-pixel imaging with Morlet wavelet correlated random patterns,  Scientific Reports, vol. 8, art. 466 , 10.1038/s41598-017-18968-6

We have introduced a Fourier domain regularization of the inverse problem occuring in single-pixel detection, with which the single-pixel camera may work in real-time. We have also demonstrated experimental results at the frequency of 11 Hz with 256x256 resolution. For those interested, we have released the FDRI Matlab/Octave package under the GNU license.

Published software (GNU license):

• https://github.com/rkotynski/D_FDRID-FDRI - an efficient, fast, single-step reconstruction method for single-pixel imaging(A. Pastuszczak, R. Stojek, P. Wróbel, R. Kotyński), 2021

• https://github.com/rkotynski/RDFTRestricted domain Fourier Transform for Matlab/Octave/Python (M. Bancerek, K. Czajkowski, R. Kotyński), 2020

• https://github.com/KMCzajkowski/FDRI-single-pixel-imaging oraz FDRI.Fourier Domain Regularized Inversion (K. M. Czajkowski, A. Pastuszczak, and R. Kotyński), 2019