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We consider the application of a recently developed hyperspectral broadband phase retrieval (HSPhR) technique for spectrally varying object and modulation phase masks at 100 spectral components. The HSPhR method utilizes advanced techniques such as Spectral Proximity Operators and ADMM to retrieve complex-domain spectral components from multiple spectral observations. These techniques filter out noisy observations and strike a balance between noisy intensity observations and their predicted counterparts, resulting in accurate retrieval of the broadband hyperspectral phase even for low signal-to-noise ratio components. Both simulation and physical experiments have confirmed the effectiveness of this approach. [ABSTRACT FROM AUTHOR]

We consider reconstruction of a wave field distribution in an input/object plane from data in an output/ diffraction (sensor) plane. We provide digital modeling both for the forward and backward wave field propagation. A novel algebraic matrix form of the discrete diffraction transform (DDT) originated in Katkovnik et al. [Appl. Opt. 47, 3481 (2008)] is proposed for the forward modeling that is aliasing free and precise for pixelwise invariant object and sensor plane distributions. This 'matrix DDT' is a base for formalization of the object wave field reconstruction (backward propagation) as an inverse problem. The transfer matrices of the matrix DDT are used for calculations as well as for the analysis of conditions when the perfect reconstruction of the object wave field distribution is possible. We show by simulation that the developed inverse propagation algorithm demonstrates an improved accuracy as compared with the standard convolutional and discrete Fresnel transform algorithms. OCIS codes: 070.2025, 100.3010, 100.3190.

The paper attacks absolute phase estimation with a two-step approach: the first step applies an adaptive local denoising scheme to the modulo-2[pi] noisy phase; the second step applies a robust phase unwrapping algorithm to the denoised modulo-2[pi] phase obtained in the first step. The adaptive local modulo-2[pi] phase denoising is a new algorithm based on local polynomial approximations. The zero-order and the first-order approximations of the phase are calculated in sliding windows of varying size. The zero-order approximation is used for pointwise adaptive window size selection, whereas the first-order approximation is used to filter the phase in the obtained windows. For phase unwrapping, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [IEEE Trans. Image Process. 16, 698 (2007)] to the denoised wrapped phase. Simulations give evidence that the proposed algorithm yields state-of-the-art performance, enabling strong noise attenuation while preserving image details. OCIS codes: 100.5088, 110.5086, 280.0280.

The article discusses a newly developed simple and usable noise model, which consists of a Poissonian part for the modeling of photon sensing and a Gaussian part for the remaining disturbances in the output. The model presents the pointwise standard-deviation of noise as a function of the pixel-raw-data output and is widely used in digital imaging sensors.

A discrete diffraction transform (DDT) is a novel discrete wavefield propagation model that is aliasing free for a pixelwise invariant object distribution. For this class of distribution, the model is precise and has no typical discretization effects because it corresponds to accurate calculation of the diffraction integral. A spatial light modulator (SLM) is a good example of a system where a pixelwise invariant distribution appears. Frequency domain regularized inverse algorithms are developed for reconstruction of the object wavefield distribution from the distribution given in the sensor plane. The efficiency of developed frequency domain algorithms is demonstrated by simulation. OCIS codes: 070.2025, 100.3010, 100.3190.

Local polynomial approximation (LPA) technique was used for estimating the absolute phase reconstruction from noisy wrapped phase data. Findings revealed a reasonable compromise between the noise smoothing and preservation of details in phase image due to window size adaptation.

A new method is described for spatially adaptive estimation and the local likelihood is used for nonparametric modeling of estimated signals. The new algorithm has performed well for image denoising and it is compared with the intersection of confidence interval (ICI) technique that has used a selection of an adaptive neighborhood for estimation.

Direction-of-arrival (DOA) estimation in a phased-array system is considered for a non-Gaussian noise environment. In this paper, a robust M-estimation scheme based on Huber's loss function with an adaptive threshold is proposed. The method is evaluated using experimental data from the University of California, Los Angeles, 60-GHz antennaarray system. It is shown that the proposed method enables a decreased sensitivity of the DOA estimates with respect to noise components having heavy-tailed distributions. Index Terms--Adaptive threshold, non-Gaussian noise, robust direction-of-arrival (DOA) estimation, 60-GHz antenna array.

A new image denoising strategy based on enhanced sparse representation in transform domain achieved an excellent denoising performance in both peak signal-to-noise ratio and subjective visual quality.

The shape-adaptive discrete cosine transform (SA-DCT) transform is found to be extremely useful for the denoising and deblocking of grayscale and color images, hence providing clean reconstructed edges without any unpleasant ringing artifacts due to the adaptive support provided by the structural constraints.

In this paper, new robust Al-estimation techniques are developed for combating impulsive noise and multiple-access interference in communication systems. Power functions of the proposed robust estimators are obtained by minimizing a non-quadratic residual function derived from the Huber's minimax robust estimation theory. Maximum peaks of these power functions are used for estimation of communication signals as well as direction of arrival. A strong advantage of the proposed robust M-estimation algorithms is a decreased sensitivity of the estimates with respect to an actual unknown distribution of random noises and interferences. Simulation results demonstrate that the proposed robust algorithms, the robust median, and robust Huber estimators, offer significant performance gain over the conventional and minimum-variance distortionless-response estimators, with the best results given by the robust Huber estimator. Index Terms--Antenna array, direction-of-arrival (DOA) estimation, impulsive noise, M-estimation, wireless communications.

A novel nonparametric regression method for deblurring noisy images is proposed. The regularized inverse and Wiener inverse filters serve as deblurring operator used jointly with the local polynomial approximation-design directional kernel filters.

Modern standard high-resolution array signal processing techniques are based on simultaneous sampling of the whole multiple-sensor array. A switch antenna array system is a promising substitute for the multiple-channel array due to its lower cost and a simpler front-end circuitry. A system composed of a single transmitter, M receiving antennas, and a single receiving channel is explained.

A windowed local polynomial approximation (LPA) of time-varying directions of arrival is used to develop an LPA-beamformer for localization of rapidly moving sources. Closed-form expressions are obtained for the bias and variance of the LPA-beamformer in the moving source case and the problem of the optimal window choice is discussed. Index Terms--Array processing, beamforming, moving sources.

The L-Wigner distributions are defined in order to improve the concentration of signal's time-frequency representation. For a finite distribution order and nonlinear instantaneous frequency (IF) it gives biased IF estimates. In the case of noisy signals the optimal window length and distribution order depend on the noise variance and unknown IF. In this correspondence an adaptive IF estimator with the time-varying and data-driven window length and distribution order is developed. Based on the analysis that has been done here, lower order time-frequency distributions are introduced. Index Terms:Estimation, instantaneous frequency, time-frequency analysis, Wigner distribution, window optimization.

A unique strategy for solving a problem of bandwidth selection for filtering a signal with additive noise is shown. The linear local polynomial approximation is employed to demonstrate the efficiency of the technique, while a development to nonlinear observations and robust M-estimates is possible. The algorithm is simple to implement and needs the computation of the estimates and their standard deviations for a set of bandwidth values.

Minimax Huber's robust statistics is an alternative to the maximum likelihood approach in the estimation of the distribution of random errors. A new periodogram is developed based on the nonlinear estimates of the amplitude C. The M-periodogram is robust in the estimation of the distribution of errors with unknown but heavy-tailed distributions. A key point of the robust M-periodogram is the choice of the nonquadratic residual function F.

A new form of the Fourier transform and the local polynomial periodogram is developed as an estimator of the instantaneous frequency (IF) of a harmonic complex-valued signal, using the local polynomial approximation of the time-varying phase. An examination of the variance and bias of the estimate for the short- and long-time asymptotic behavior of the IF estimates shows that the orders for the optimal asymptotic mean squared error of the estimates of omega(super k-1)(t) are 0(N-(super 2k+1)) and 0(N-2(m-k+1)/2m+3), respectively, for a polynomial omega(t) of the degree m-1 and arbitrary smooth omega(t) with a bounded mth derivative.

An adaptive estimator for calculating instantaneous frequency (IF) of a harmonic complex-valued signal with additive noise was created using the Wigner distribution. This estimation tool uses an algorithm with a time-varying and data-driven window length that was observed to generate IF calculations based on the formula for the variance of the estimate. Simulation testing also showed that this adaptive estimator has good accuracy and is capable of enhancing time-frequency representation of signal with a nonlinear IF.

The local polynomial approximation of time-varying phase is used in order to estimate the instantaneous frequency and its derivatives for a complex-valued harmonic signal given by discrete-time observations with a noise. The considered estimators are high-order nonparametric generalizations of the short-time Fourier transform and the Wigner-Ville distribution. The asymptotic variance and bias of the estimates are obtained. Index Terms - Fourier analysis, nonparametric estimation, spectral analysis, time-frequency distribution, time-varying frequency.

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]

We propose an algorithm for absolute phase retrieval from multiwavelength noisy phase coded diffraction patterns. A lensless optical system is considered with a set of successive single wavelength experiments (wavelength-division setup). The phase masks are applied for modulation of the multiwavelength object wavefronts. The algorithm uses the forward/backward propagation for coherent light beams and sparsely encoding wavefronts, which leads to the complex-domain block-matching three-dimensional filtering. The key-element of the algorithm is an original aggregation of the multiwavelength object wavefronts for high-dynamic-range absolute phase reconstruction. Simulation tests demonstrate that the developed approach leads to the effective solutions explicitly using the sparsity for noise suppression and high-accuracy object absolute phase reconstruction from noisy data. [ABSTRACT FROM AUTHOR]

We introduce a paradigm for nonlocal sparsity reinforced deep convolutional neural network denoising. It is a combination of a local multiscale denoising by a convolutional neural network (CNN) based denoiser and a nonlocal denoising based on a nonlocal filter (NLF), exploiting the mutual similarities between groups of patches. CNN models are leveraged with noise levels that progressively decrease at every iteration of our framework, while their output is regularized by a nonlocal prior implicit within the NLF. Unlike complicated neural networks that embed the nonlocality prior within the layers of the network, our framework is modular, and it uses standard pretrained CNNs together with standard nonlocal filters. An instance of the proposed framework, called NN3D, is evaluated over large grayscale image datasets showing state-of-the-art performance. [ABSTRACT FROM AUTHOR]

We study the problem of multiwavelength absolute phase retrieval from noisy diffraction patterns. The system is lensless with multiwavelength coherent input light beams and random phase masks applied for wavefront modulation. The light beams are formed by light sources radiating all wavelengths simultaneously. A sensor equipped by a Color Filter Array (CFA) is used for spectral measurement registration. The developed algorithm targeted on optimal phase retrieval from noisy observations is based on maximum likelihood technique. The algorithm is specified for Poissonian and Gaussian noise distributions. One of the key elements of the algorithm is an original sparse modeling of the multiwavelength complex-valued wavefronts based on the complex-domain block-matching 3D filtering. Presented numerical experiments are restricted to noisy Poissonian observations. They demonstrate that the developed algorithm leads to effective solutions explicitly using the sparsity for noise suppression and enabling accurate reconstruction of absolute phase of high-dynamic range. [ABSTRACT FROM AUTHOR]

We consider a computational superresolution inverse diffraction problem for phase retrieval from phase-coded intensity observations. The optical setup includes a thin lens and a spatial light modulator for phase coding. The designed algorithm is targeted on an optimal solution for Poissonian noisy observations. One of the essential instruments of this design is a complex-domain sparsity applied for complex-valued object (phase and amplitude) to be reconstructed. Simulation experiments demonstrate that good quality imaging can be achieved for high-level of the superresolution with a factor of 32, which means that the pixel of the reconstructed object is 32 times smaller than the sensor’s pixel. This superresolution corresponds to the object pixel as small as a quarter of the wavelength. [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]

A study was conducted to analyze the problem of estimating the instantaneous frequency (IF). The asymptotic minimax lower bound was determined for the mean squared error of estimation while the local polynomial periodogram was represented as a nonparametric estimator of the IF. Results indicated that the optimal choice of the window size in the local polynomial periodogram estimator of the IF and its derivatives correlated with mean squared errors that were different from the minimax lower bounds.

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]