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This paper introduces a novel lensless full colour diffractive computational imaging system with a planar Multilevel Phase Mask (MPM) as a diffractive optical element (DOE). The novelty concerns: a methodology of MPM design for improved depth of focus (DoF); design of PSFs for RGB imaging and an inverse imaging algorithm with sparse colour image modelling simultaneous for all RGB channels. MPMs are step-wise invariant. The cubic wavefront coding (WFC) is incorporated in MPMs with optimization of number of levels and width of invariant steps. This design of MPM makes the system robust with respect to defocus (improves DoF) and diminish chromatic aberrations typical for DOEs. Broadband multichannel test-images are exploited for design and testing of the lensless system. We consider two alternative optical setups: Wavelength Multiplexing (WM) and Wavelength Division (WD). In WM, the light beam is broadband multichannel with light sources radiating all wavelengths simultaneously and a CMOS sensor is equipped with a Bayer colour filter array (CFA) for registration of spectral measurements. In this setup, a single MPM is designed for the broadband multichannel light beams. In WD, separate exposures of RGB channels are registered by a broadband grey-scale CCD sensor. Different MPMs are designed for each of the RGB channels. Simulation experiments demonstrate the essentially extended DoF of the designed lensless systems and the advanced accuracy and quality of imaging with respect to the corresponding WM and WD systems with refractive lenses. Due to robustness of the designed lensless system to chromatic aberrations, this advantage has a place even with respect to the lens-system. [ABSTRACT FROM AUTHOR]

This paper contains an original development of the compressed sensing technique for restoring integral images from a number of observed 2D images. The proposed data acquisition uses a conventional camera equipped with a horizontal 1D mask placed in the pupil plane of the lens. The compressed sensing style algorithm developed is based on a sparsity hypothesis imposed on 2D cross sections of the light field. [ABSTRACT FROM PUBLISHER]

This paper addresses interferometric phase image estimation, i.e., the estimation of phase modulo-2π images from sinusoidal 2π-periodic and noisy observations. These degradation mechanisms make interferometric phase image estimation a quite challenging problem. We tackle this challenge by reformulating the true estimation problem as a sparse regression, often termed sparse coding, in the complex domain. Following the standard procedure in patch-based image restoration, the image is partitioned into small overlapping square patches, and the vector corresponding to each patch is modeled as a sparse linear combination of vectors, termed the atoms, taken from a set called dictionary. Aiming at optimal sparse representations, and thus at optimal noise removing capabilities, the dictionary is learned from the data that it represents viamatrix factorization with sparsity constraints on the code (i.e., the regression coefficients) enforced by the l1 norm. The effectiveness of the new sparse-coding-based approach to interferometric phase estimation, termed the SpInPHASE, is illustrated in a series of experiments with simulated and real data where it outperforms the state-of-the-art. [ABSTRACT FROM AUTHOR]

We present an extension of the BM3D filter to volumetric data. The proposed algorithm, BM4D, implements the grouping and collaborative filtering paradigm, where mutually similar d-dimensional patches are stacked together in a (d+1)-dimensional array and jointly filtered in transform domain. While in BM3D the basic data patches are blocks of pixels, in BM4D we utilize cubes of voxels, which are stacked into a 4-D “group.” The 4-D transform applied on the group simultaneously exploits the local correlation present among voxels in each cube and the nonlocal correlation between the corresponding voxels of different cubes. Thus, the spectrum of the group is highly sparse, leading to very effective separation of signal and noise through coefficient shrinkage. After inverse transformation, we obtain estimates of each grouped cube, which are then adaptively aggregated at their original locations. We evaluate the algorithm on denoising of volumetric data corrupted by Gaussian and Rician noise, as well as on reconstruction of volumetric phantom data with non-zero phase from noisy and incomplete Fourier-domain (k-space) measurements. Experimental results demonstrate the state-of-the-art denoising performance of BM4D, and its effectiveness when exploited as a regularizer in volumetric data reconstruction. [ABSTRACT FROM AUTHOR]

A family of the block matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patchwise image modeling refid="ref1"/, refid="ref2"/. In this paper, we construct analysis and synthesis frames, formalizing BM3D image modeling, and use these frames to develop novel iterative deblurring algorithms. We consider two different formulations of the deblurring problem, i.e., one given by the minimization of the single-objective function and another based on the generalized Nash equilibrium (GNE) balance of two objective functions. The latter results in the algorithm where deblurring and denoising operations are decoupled. The convergence of the developed algorithms is proved. Simulation experiments show that the decoupled algorithm derived from the GNE formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field, confirming a valuable potential of BM3D-frames as an advanced image modeling tool. [ABSTRACT FROM AUTHOR]

The local polynomial approximation (LPA) is a nonparametric regression technique with pointwise estimation in a sliding window. We apply the LPA of the argument of cos and sin in order to estimate the absolute phase from noisy wrapped phase data. Using the intersection of confidence interval (ICI) algorithm, the window size is selected as adaptive pointwise varying. This adaptation gives the phase estimate with the accuracy close to optimal in the mean squared sense. For calculations, we use a Gauss-Newton recursive procedure initiated by the phase estimates obtained for the neighboring points. It enables tracking properties of the algorithm and its ability to go beyond the principal interval [--π, π) and to reconstruct the absolute phase from wrapped phase observations even when the magnitude of the phase difference takes quite large values. The algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state-of-the-art algorithms developed for noisy phase unwrap. The theoretical analysis produced for the accuracy of the pointwise estimates is used for justification of the ICI adaptation algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is developed using the alternating projection framework and is aimed to obtain high performance for heavily noisy (Poissonian or Gaussian) observations. The estimation of the target images is reformulated as a sparse regression, often termed sparse coding, in the complex domain. This is accomplished by learning a complex domain dictionary from the data it represents via matrix factorization with sparsity constraints on the code (i.e., the regression coefficients). Our algorithm, termed dictionary learning phase retrieval (DLPR), jointly learns the referred to dictionary and reconstructs the unknown target image. The effectiveness of DLPR is illustrated through experiments conducted on complex images, simulated and real, where it shows noticeable advantages over the state-of-the-art competitors. [ABSTRACT FROM AUTHOR]