Vladimir Katkovnik - Academia.edu (original) (raw)

Papers by Vladimir Katkovnik

Electronic Imaging, 2020

Fast track article for IS&T International Symposium on Electronic Imaging 2020: Image Processing:... more Fast track article for IS&T International Symposium on Electronic Imaging 2020: Image Processing: Algorithms and Systems proceedings.

arXiv (Cornell University), Mar 9, 2021

The power-balanced hybrid optical imaging system is a special design of a computational camera, i... more The power-balanced hybrid optical imaging system is a special design of a computational camera, introduced in this paper, with image formation by a refractive lens and Multilevel Phase Mask (MPM) as a diffractive optical element (DoE). This system provides a long focal depth and low chromatic aberrations thanks to MPM, and a high energy light concentration due to the refractive lens. This paper additionally introduces the concept of a optimal power balance between lens and MPM for achromatic extended-depth-of-field (EDoF) imaging. To optimize this power-balance as well as to optimize MPM using Neural Network techniques, we build a fully-differentiable image formation model for joint optimization of optical and imaging parameters for the designed computational camera. Additionally, we determine a Wiener-like inverse imaging optimal optical transfer function (OTF) to reconstruct a sharp image from the defocused observation. We numerically and experimentally compare the designed system with its counterparts, lensless and just-lens optical systems, for the visible wavelength interval (400-700) nm and the EDoF range (0.5-1000) m. The attained results demonstrate that the proposed system equipped with the optimal OTF overcomes its lensless and just-lens counterparts (even when they are used with optimized OTFs) in terms of reconstruction quality for off-focus distances.

Optical Engineering, Jan 29, 2021

SPIE eBooks, Sep 10, 2009

Adaptability is a crucial feature of filtering and differentiating methods. It was demonstrated i... more Adaptability is a crucial feature of filtering and differentiating methods. It was demonstrated in the previous chapters that the performance of LPA kernel estimates depends strongly on the selection of the scale parameter. In Fig. 2.6 we saw the Nadaraya-Watson estimates for different h. A small h gives the limit estimate A⋅ h (x) as a stepwise curve passing exactly through the observations. For large h the same estimator gives a constant value equal to the sample mean of the observations. For intermediate h between these small and large values, we may obtain a large variety of the estimate curves, which are different by their curvature and closeness to the observations. The idea of the Nadaraya-Watson estimator is natural and fruitful. However, the estimation curve is quite sensitive to h, and the selection of h is a key factor that is able to transform this reasonable idea into an effective working tool. A selection of a proper scale for estimation is a hot topic in both signal processing and nonparametric regression methods. The number of publications in this area is very large and growing quickly.

Proceedings of SPIE, May 8, 2015

The topic of sparse representations (SR) of images has attracted tremendous interest from the res... more The topic of sparse representations (SR) of images has attracted tremendous interest from the research community in the last ten years. This interest stems from the fundamental role that the low dimensional models play in many signal and image processing areas, i.e., real world images can be well approximated by a linear combination of a small number of atoms (i.e., patches of images) taken from a large frame, often termed dictionary. The principal point is that these large dictionaries as well as the elements of these dictionaries taken for approximation are not known in advance and should be taken from given noisy observations. The sparse phase and amplitude reconstruction (SPAR) algorithm has been developed for monochromatic coherent wave field reconstruction, for phase-shifting interferometry and holography. In this paper the SPAR technique is extended to off-axis holography. Pragmatically, SPAR representations are result in design of efficient data-adaptive filters. We develop and study the algorithm where these filters are applied for denoising of phase and amplitude in object and sensor planes. This algorithm is iterative and developed as a maximum likelihood optimal solution provided that the noise in intensity measurements is Gaussian. The multiple simulation and real data experiments demonstrate the advance performance of the new technique.

Optics Express, Oct 18, 2016

The topography of surface relief gratings patterned on As2S3–Se nanomultilayers was investigated ... more The topography of surface relief gratings patterned on As2S3–Se nanomultilayers was investigated by digital holographic microscopy. For the high-accuracy phase reconstruction of the topography we used the sparse wavefront modeling. Experimental results are presented.

$Research paper thumbnail of Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography$

Applied Optics, Jan 18, 2018

IEEE Signal Processing Magazine

arXiv (Cornell University), Mar 3, 2022

Frontiers in Remote Sensing

A fast and shallow convolutional neural network is proposed for hyperspectral image super-resolut... more A fast and shallow convolutional neural network is proposed for hyperspectral image super-resolution inspired by Spatial-Spectral Reconstruction Network (SSR-NET). The feature extraction ability is improved compared to SSR-NET and other state-of-the-art methods, while the proposed network is also shallow. Numerical experiments show both the visual and quantitative superiority of our method. Specifically, for the fusion setup with two inputs, obtained by 32× spatial downsampling for the low-resolution hyperspectral (LR HSI) input and 25× spectral downsampling for high-resolution multispectral (HR MSI) input, a significant improvement of the quality of super-resolved HR HSI over 4 dB is demonstrated as compared with SSR-NET. It is also shown that, in some cases, our method with a single input, HR MSI, can provide a comparable result with that achieved with two inputs, HR MSI and LR HSI.

$Research paper thumbnail of On design of hybrid diffractive optics for achromatic extended depth-of-ﬁeld (EDoF) RGB imaging$

Unconventional Optical Imaging III

2018 52nd Asilomar Conference on Signals, Systems, and Computers, 2018

This paper introduces novel binary and multilevel phase masks (BPMs) for improved depth of focus ... more This paper introduces novel binary and multilevel phase masks (BPMs) for improved depth of focus (DoF) in infrared imaging. The procedure developed for design of BPMs combines two ideas: cubic wavefront coding (WFC) of continuous absolute phase and original discretization of this phase profile. Both these ingredients of the design make the optical system robust with respect to defocus and uncontrolled variations in the optical system. The method allows us to design a flat and very thin BPM using piecewise invariant diffractive optical element (DOE) of simple geometry. The BPMs are used for wavefront modulation in two optical setups: a lensless system and a lens/BPM optical hybrid. Computational inverse imaging (deblurring) is applied in order to reconstruct a sharp image from respective blurred observations. The optical system is optimized end-to-end, including both the BPMs and the deblurring algorithm. Simulation experiments demonstrated for midwave infrared (MWIR) imaging, show high quality imaging even for very large amounts of defocus. Imaging systems incorporating this method show advantages over conventional optical systems with a refractive lens.

Digital Optical Technologies 2019, 2019

$Research paper thumbnail of Noise minimizing by harmonic phase diffraction gratings in off-axis lensless digital holography$

Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies IX, 2018

Off-axis lensless holography is considered with a sinusoidal phase modulation at the object plane... more Off-axis lensless holography is considered with a sinusoidal phase modulation at the object plane. The variational algorithm for phase and amplitude reconstruction is based on the algorithm proposed in the paper 1[V. Katkovnik, I. A. Shevkunov, N. V. Petrov, and K. Egiazarian, “Wavefront reconstruction in digital off-axis holography via sparse coding of amplitude and absolute phase”, Opt. Lett. 40, 2417-2420 (2015)]. The forward wavefront propagation is modelled using the Fourier transform with the angular spectrum transfer function. The multiple intensities (holograms) recorded by the sensor vary in dependence to the angle of the phase diffraction grating. The i.i.d. Gaussian noise is added to observations to make them closer to real experimental conditions. The root mean square error (RMSE) values of the phase reconstructions were compared in two scenarios: with and without the diffraction grating. Computational experiments showed that with sinusoidal phase modulation RMSE values are decreased about 20%. These results support the conclusion on advantage of the proposed phase modulation gratings in off-axis lensless digital holography.

Optics Express, 2021

We propose a novel approach for lensless single-shot phase retrieval, which provides pixel super-... more We propose a novel approach for lensless single-shot phase retrieval, which provides pixel super-resolution phase imaging. The approach is based on a computational separation of carrying and object wavefronts. The imaging task is to reconstruct the object wavefront, while the carrying wavefront corrects the discrepancies between the computational model and physical elements of an optical system. To reconstruct the carrying wavefront, we do two preliminary tests as system calibration without an object. Essential for phase retrieval noise is suppressed by a combination of sparse- and deep learning-based filters. Robustness to discrepancies in computational models and pixel super-resolution of the proposed approach are shown in simulations and physical experiments. We report an experimental computational super-resolution of 2μm, which is 3.45× smaller than the resolution following from the Nyquist-Shannon sampling theorem for the used camera pixel size of 3.45μm. For phase bio-imaging,...

Terahertz, RF, Millimeter, and Submillimeter-Wave Technology and Applications XIII, 2020

We propose a novel approach and algorithm based on two preliminary tests of the optical system el... more We propose a novel approach and algorithm based on two preliminary tests of the optical system elements to enhance the super-resolved complex-valued imaging. The approach is developed for inverse phase imaging in a single-shot lensless optical setup. Imaging is based on wavefront modulation by a single binary phase mask. The preliminary tests compensate errors in the optical system and correct a carrying wavefront, reducing the gap between real-life experiments and computational modeling, which improve imaging significantly both qualitatively and quantitatively. These two tests are performed for observation of the laser beam and phase mask along, and might be considered as a preliminary system calibration. The corrected carrying wavefront is embedded into the proposed iterative Single-shot Super-Resolution Phase Retrieval (SSR-PR) algorithm. Improved initial diffraction pattern upsampling, and a combination of sparse and deep learning based filters achieves the super-resolved recons...