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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 , . 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.

We present a simple and usable noise model for the raw-data of digital imaging sensors. This signal-dependent noise model, which gives the pointwise standard-deviation of the noise as a function of the expectation of the pixel raw-data output, is composed of a Poissonian part, modeling the photon sensing, and Gaussian part, for the remaining stationary disturbances in the output data. We further explicitly take into account the clipping of the data (over- and under-exposure), faithfully reproducing the nonlinear response of the sensor. We propose an algorithm for the fully automatic estimation of the model parameters given a single noisy image. Experiments with synthetic images and with real raw-data from various sensors prove the practical applicability of the method and the accuracy of the proposed model.

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 (HCI) 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 [-pi, pi] 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 HCI adaptation algorithm.

We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2-D image fragments (e.g., blocks) into 3-D data arrays which we call "groups." Collaborative filtering is a special procedure developed to deal with these 3-D groups. We realize it using the three successive steps: 3-D transformation of a group, shrinkage of the transform spectrum, and inverse 3-D transformation. The result is a 3-D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

The shape-adaptive discrete cosine transform ISA-DCT) transform can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable block-DCT (B-DCT). Despite the near-optimal decorrelation and energy compaction properties, application of the SA-DCT has been rather limited, targeted nearly exclusively to video compression. In this paper, we present a novel approach to image filtering based on the SA-DCT. We use the SA-DCT in conjunction with the Anisotropic Local Polynomial Approximation-Intersection of Confidence Intervals technique, which defines the shape of the transform's support in a pointwise adaptive manner. The thresholded or attenuated SA-DCT coefficients are used to reconstruct a local estimate of the signal within the adaptive-shape support. Since supports corresponding to different points are in general overlapping, the local estimates are averaged together using adaptive weights that depend on the region's statistics. This approach can be used for various image-processing tasks. In this paper, we consider, in particular, image denoising and image deblocking and deringing from block-DCT compression. A special structural constraint in luminance-chrominance space is also proposed to enable an accurate filtering of color images. Simulation experiments show a state-of-the-art quality of the final estimate, both in terms of objective criteria and visual appearance. Thanks to the adaptive support, reconstructed edges are clean, and no unpleasant ringing artifacts are introduced by the fitted transform.

We propose a novel nonparametric regression metthod for deblurring noisy images. The method is based on the local polynomial approximation (LPA) of the image and the paradigm of intersecting confidence intervals (ICI) that is applied to define the adaptive varying scales (window sizes) of the LPA estimators. The LPA-ICI algorithm is nonlinear and spatially adaptive with respect to smoothness and irregularities of the image corrupted by additive noise. Multiresolution wavelet algorithms produce estimates which are combined from different scale projections. In contrast to them, the proposed ICI algorithm gives a varying scale adaptive estimate defining a single best scale for each pixel. In the new algorithm, the actual filtering is performed in signal domain while frequency domain Fourier transform operations are applied only for calculation of convolutions. The regularized inverse and Wiener inverse filters serve as deblurring operators used jointly with the LPA-design directional kernel filters. Experiments demonstrate the state-of-art performance of the new estimators which visually and quantitatively outperform some of the best existing methods.

Passive microwave remote sensing from satellites and ground stations has contributed uniquely, and substantially, to the study of atmospheric chemistry, meteorology, and environmental monitoring. As user requirements are raised, in terms of the accuracy and the spatial resolution, a mechanically scanning radiometer, with a real aperture, becomes impractical due to the requirement for a very large antenna size. However, an aperture synthesis interferometric radiometer presents a valuable alternative. The work presented in this paper was devoted to high spatial resolution imaging, using the 37 GHz band interferometric radiometer, developed by ourselves. The spatially adaptive Capon beamforming method was exploited for the imaging, which outperformed the conventional Fourier Transform method. We concluded that the high spatial resolution imaging of the brightness temperature of the atmosphere could be accomplished with an interferometric radiometer equipped with the developed Capon beamforming imaging algorithm.

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 review the evolution of the nonparametric regression modeling in imaging from the local Nadaraya-Watson kernel estimate to the nonlocal means and further to transform-domain filtering based on nonlocal block-matching. The considered methods are classified mainly according to two main features: local/nonlocal and pointwise/multipoint. Here nonlocal is an alternative to local, and multipoint is an alternative to pointwise. These alternatives, though obvious simplifications, allow to impose a fruitful and transparent classification of the basic ideas in the advanced techniques. Within this framework, we introduce a novel single- and multiple-model transform domain nonlocal approach. The Block Matching and 3-D Filtering (BM3D) algorithm, which is currently one of the best performing denoising algorithms, is treated as a special case of the latter approach. [ABSTRACT FROM AUTHOR]

Abstract: A new robust M-estimation technique is developed for combating impulsive noise and multiuser interference in code-division multiple-access (CDMA) communication channels with a phased array receiver. A special power function of the proposed robust estimator is derived from the Huber''s minimax robust estimation theory by minimizing a non-quadratic loss function of estimation residuals. Maximum peaks of this power function are used for estimation of communication signals as well as the direction-of-arrival (DOA). The produced theoretical analysis of the asymptotic accuracy of estimation is used for selection of the optimal minimax loss function. A strong advantage of the developed robust algorithm is a decreased sensitivity of the estimates with respect to actually unknown distributions of random noise and interferences. Simulation demonstrates that the proposed robust algorithms offer significant performance gain over the conventional least squares (LS) based estimator in terms of both BER and maximum user capacity. [Copyright &y& Elsevier]

This paper offers a new technique for spatially adaptive estimation. The local likeIihood is exploited for nonparametric modeling of observations and estimated signals. The approach is based on the assumption of a local homogeneity of the signal: for every point there exists a neighborhood in which the signal can be well approximated by a constant. The fitted local likelihood statistics are used for selectiotion of an adaptive size and shape of this neighborhood. The algorithm is developed for a quite general class of observations subject to the exponential distribution. The estimated signal can be uni- and multivariable. We demonstrate a good performance of the new algorithm for image denoising and compare the new method versus the intersection of confidence interval (ICI) technique that also exploits a selection of an adaptive neighborhood for estimation. [ABSTRACT FROM AUTHOR]

Recently, new efficient algorithms, based on Lepski's approach [7], have been proposed for spatially adaptive varying scale de-noising. Special statistical rules are exploited in order to select the estimate with the best point-wise varying scale h from a set of test-estimates yh(x), h ∈ H. In this paper, a novel multiresolution (MR) nonparametric regression technique is developed. The adaptive algorithm consists of two steps. The first step transforms the data into noisy spectrum coefficients (MR analysis). In the second step, these noisy spectrum is filtered by the thresholding procedure and exploited for estimation (MR synthesis). This nonlinear estimate is built using the test-estimates yh(x) of all scales. Simulation confirms the advanced performance of the new de-noising algorithms based on the MR nonparametric regression. [ABSTRACT FROM AUTHOR]

A system composed of a single transmitter, M receiving antennas, and a single receiving channel is studied. Echo radar signals are acquired in a number of the cycles and used for estimation of the angle, velocity, and range in a multiple moving target scenario. The receiving antennas are switched to the single receiving channel periodically once every cycle. The developed algorithms are based on minimum variance (Capon) beamforming. A new nonstationary version of Capon beamforming is developed for the time-varying steering vector model. It is shown in simulations done for an automotive scenario that the proposed algorithms yield very good performance in terms of both estimation accuracy and multiple-target resolution. The Capon-based estimation gives results close to the corresponding Cramér-Rao lower bounds (CRLBs). [ABSTRACT FROM AUTHOR]