Blind deconvolution using generalized cross-validation approach to regularization parameter estimation

Blind Remote Sensing Image Deblurring Based on Overlapped Patches' Non-Linear Prior

The remote sensing imaging environment is complex, in which many factors cause image blur. Thus, without prior knowledge, the restoration model established to obtain clear images can only rely on the observed blurry images. We still build the prior with extreme pixels but no longer traverse all pixels, such as the extreme channels. The features are extracted in units of patches, which are segmented from an image and partially overlap with each other. In this paper, we design a new prior, i.e., overlapped patches' non-linear (OPNL) prior, derived from the ratio of extreme pixels affected by blurring in patches. The analysis of more than 5000 remote sensing images confirms that OPNL prior prefers clear images rather than blurry images in the restoration process. The complexity of the optimization problem is increased due to the introduction of OPNL prior, which makes it impossible to solve it directly. A related solving algorithm is established based on the projected alternating minimization (PAM) algorithm combined with the half-quadratic splitting method, the fast iterative shrinkage-thresholding algorithm (FISTA), fast Fourier transform (FFT), etc. Numerous experiments prove that this algorithm has excellent stability and effectiveness and has obtained competitive processing results in restoring remote sensing images.

Blind Remote Sensing Image Deblurring Using Local Binary Pattern Prior

In this paper, an algorithm based on local binary pattern (LBP) is proposed to obtain clear remote sensing images under the premise of unknown causes of blurring. We find that LBP can completely record the texture features of the images, which will not change widely due to the generation of blur. Therefore, LBP prior is proposed, which can filter out the pixels containing important textures in the blurry image through the mapping relationship. The corresponding processing methods are adopted for different types of pixels to cope with the challenges brought by the rich texture and details of remote sensing images and prevent over-sharpening. However, the existence of LBP prior increases the difficulty of solving the model. To solve the model, we construct the projected alternating minimization (PAM) algorithm that involves the construction of the mapping matrix, the fast iterative shrinkage-thresholding algorithm (FISTA) and the half-quadratic splitting method. Experiments with the AID dataset show that the proposed method can achieve highly competitive processing results for remote sensing images.

L1-L2 norm regularization via forward-backward splitting for fluorescence molecular tomography

Fluorescent molecular tomography (FMT) is a highly sensitive and noninvasive imaging approach for providing three-dimensional distribution of fluorescent marker probes. However, owing to its light scattering effect and the ill-posedness of inverse problems, it is challenging to develop an efficient reconstruction algorithm that can achieve the exact location and morphology of the fluorescence source. In this study, therefore, in order to satisfy the need for early tumor detection and improve the sparsity of solution, we proposed a novel L ₁-L ₂ norm regularization via the forward-backward splitting method for enhancing the FMT reconstruction accuracy and the robustness. By fully considering the highly coherent nature of the system matrix of FMT, it operates by splitting the objective to be minimized into simpler functions, which are dealt with individually to obtain a sparser solution. An analytic solution of L ₁-L ₂ norm proximal operators and a forward-backward splitting algorithm were employed to efficiently solve the nonconvex L ₁-L ₂ norm minimization problem. Numerical simulations and an in-vivo glioma mouse model experiment were conducted to evaluate the performance of our algorithm. The comparative results of these experiments demonstrated that the proposed algorithm obtained superior reconstruction performance in terms of spatial location, dual-source resolution, and in-vivo practicability. It was believed that this study would promote the preclinical and clinical applications of FMT in early tumor detection.

Computational polarized Raman microscopy on sub-surface nanostructures with sub-diffraction-limit resolution

Raman microscopy with resolution below the diffraction limit is demonstrated on sub-surface nanostructures. Unlike most other modalities for nanoscale measurements, our approach is able to image nanostructures buried several microns below the sample surface while still extracting details about the chemistry, strain, and temperature of the nanostructures. In this work, we demonstrate that combining polarized Raman microscopy adjusted to optimize edge enhancement effects and nanostructure contrast with fast computational deconvolution methods can improve the spatial resolution while preserving the flexibility of Raman microscopy. The cosine transform method demonstrated here enables significant computational speed-up from O(N³) to O(Nlog N) - resulting in computation times that are significantly below the image acquisition time. CMOS poly-Si nanostructures buried below 0.3 - 6 µm of complex dielectrics are used to quantify the performance of the instrument and the algorithm. The relative errors of the feature sizes, the relative chemical concentrations and the fill factors of the deconvoluted images are all approximately 10% compared with the ground truth. For the smallest poly-Si feature of 230 nm, the absolute error is approximately 25 nm.

Blind Image Deblurring Using a Non-Linear Channel Prior Based on Dark and Bright Channels

Blind image deblurring aims at recovering a clean image from the given blurry image without knowing the blur kernel. Recently proposed dark and extreme channel priors have shown their effectiveness in deblurring various blurry scenarios. However, these two priors fail to help the blur kernel estimation under the particular circumstance that clean images contain neither enough darkest nor brightest pixels. In this paper, we propose a novel and robust non-linear channel (NLC) prior for the blur kernel estimation to fill this gap. It is motivated by a simple idea that the blurring operation will increase the ratio of dark channel to bright channel. This change has been proved to be true both theoretically and empirically. Nonetheless, the presence of the NLC prior introduces a thorny optimization model. To handle it, an efficient algorithm based on projected alternating minimization (PAM) has been established which innovatively combines an approximate strategy, the half-quadratic splitting method, and fast iterative shrinkage-thresholding algorithm (FISTA). Extensive experimental results show that the proposed method achieves state-of-the-art results no matter when it has been applied in synthetic uniform and non-uniform benchmark datasets or in real blurry images.

Effective Blind Image Deblurring Using Matrix-Variable Optimization

Blind image deblurring has been a challenging issue due to the unknown blur and computation problem. Recently, the matrix-variable optimization method successfully demonstrates its potential advantages in computation. This paper proposes an effective matrix-variable optimization method for blind image deblurring. Blur kernel matrix is exactly decomposed by a direct SVD technique. The blur kernel and original image are well estimated by minimizing a matrix-variable optimization problem with blur kernel constraints. A matrix-type alternative iterative algorithm is proposed to solve the matrix-variable optimization problem. Finally, experimental results show that the proposed blind image deblurring method is much superior to the state-of-the-art blind image deblurring algorithms in terms of image quality and computation time.

A Novel Adaptive Parameter Search Elastic Net Method for Fluorescent Molecular Tomography

Fluorescence molecular tomography (FMT) is a new type of medical imaging technology that can quantitatively reconstruct the three-dimensional distribution of fluorescent probes in vivo. Traditional Lp norm regularization techniques used in FMT reconstruction often face problems such as over-sparseness, over-smoothness, spatial discontinuity, and poor robustness. To address these problems, this paper proposes an adaptive parameter search elastic net (APSEN) method that is based on elastic net regularization, using weight parameters to combine the L1 and L2 norms. For the selection of elastic net weight parameters, this approach introduces the L0 norm of valid reconstruction results and the L2 norm of the residual vector, which are used to adjust the weight parameters adaptively. To verify the proposed method, a series of numerical simulation experiments were performed using digital mice with tumors as experimental subjects, and in vivo experiments of liver tumors were also conducted. The results showed that, compared with the state-of-the-art methods with different light source sizes or distances, Gaussian noise of 5%-25%, and the brute-force parameter search method, the APSEN method has better location accuracy, spatial resolution, fluorescence yield recovery ability, morphological characteristics, and robustness. Furthermore, the in vivo experiments demonstrated the applicability of APSEN for FMT.

Surface Mass Variations from GPS and GRACE/GFO: A Case Study in Southwest China

Surface mass variations inferred from the Global Positioning System (GPS), and observed by the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO) complement each other in terms of spatial and temporal coverage. This paper presents an analysis of regional surface mass variations inverted from GPS vertical displacements under different density distributions of GPS stations, and compares the GPS-derived mass variations with GRACE/GFO inversion results in spatial and temporal domains. To this end, GPS vertical displacement data from a total of 85 permanent GPS stations of the Crustal Movement Observation Network of China (CMONOC), the latest GRACE/GFO RL06 spherical harmonic (SH) solutions and GRACE RL06 mascon solutions are used to investigate surface mass variations in four regions or basins, including the Yunnan Province (YNP), Min River Basin (MRB), Jialing River Basin (JLRB), and Wu River Basin (WRB) in Southwest China. Our results showed that the spatial distributions and seasonal characteristics of GPS-derived mass change time series agree well with those from GRACE/GFO observations, especially in regions with relatively dense distributions of GPS stations (e.g., in the YNP and MRB), but there are still obvious discrepancies between the GPS and GRACE/GFO results. Scale factor methods (both basin-scaled and pixel-scaled) were employed to reduce the amplitude discrepancies between GPS and GRACE/GFO results. The results also showed that the one-year gap between the GRACE and GFO missions can be bridged by scaled GPS-derived mass change time series in the four studied regions, especially in the YNP and MRB regions (with relatively dense distributions of GPS stations).

Nonlocal low-rank-based blind deconvolution of Raman spectroscopy for automatic target recognition

Raman spectroscopy often suffers from the problems of band overlap and random noise. In this work, we develop a nonlocal low-rank regularization (NLR) approach toward exploiting structured sparsity and explore its applications in Raman spectral deconvolution. Motivated by the observation that the rank of a ground-truth spectrum matrix is lower than that of the observed spectrum, a Raman spectral deconvolution model is formulated in our method to regularize the rank of the observed spectrum by total variation regularization. Then, an effective optimization algorithm is described to solve this model, which alternates between the instrument broadening function and latent spectrum until convergence. In addition to conceptual simplicity, the proposed method has achieved highly competent objective performance compared to several state-of-the-art methods in Raman spectrum deconvolution tasks. The restored Raman spectra are more suitable for extracting spectral features and recognizing the unknown materials or targets.

Studies on the Clustering Algorithm for Analyzing Gene Expression Data with a Bidirectional Penalty

This article reports a new clustering method based on the k-means algorithm to high-dimensional gene expression data. The proposed approach makes use of bidirectional penalties to constrain the number of clusters and centroids of clusters to simultaneously determine the unknown number of clusters and handle large amounts of noise in gene expression data. Numeric studies indicate that this algorithm not only performs better in clustering but is also comparable to other approaches in its ability to obtain the correct number of clusters and correct signal features. Finally, we apply the proposed approach to analyze two benchmark gene expression datasets. These analyses again indicate that the proposed algorithm performs well in clustering high-dimensional gene expression data with an unknown number of clusters.

Automatic regularization parameter selection by generalized cross-validation for total variational Poisson noise removal

In this paper, we propose an alternating minimization algorithm with an automatic selection of the regularization parameter for image reconstruction of photon-counted images. By using the generalized cross-validation technique, the regularization parameter can be updated in the iterations of the alternating minimization algorithm. Experimental results show that our proposed algorithm outperforms the two existing methods, the maximum likelihood expectation maximization estimator with total variation regularization and the primal dual method, where the parameters must be set in advance.

Joint baseline-correction and denoising for Raman spectra

Laser instruments often suffer from the problem of baseline drift and random noise, which greatly degrade spectral quality. In this article, we propose a variation model that combines baseline correction and denoising. First, to guide the baseline estimation, morphological operations are adopted to extract the characteristics of the degraded spectrum. Second, to suppress noise in both the spectrum and baseline, Tikhonov regularization is introduced. Moreover, we describe an efficient optimization scheme that alternates between the latent spectrum estimation and the baseline correction until convergence. The major novel aspect of the proposed algorithms is the estimation of a smooth spectrum and removal of the baseline simultaneously. Results of a comparison with state-of-the-art methods demonstrate that the proposed method outperforms them in both qualitative and quantitative assessments.

A novel SURE-based criterion for parametric PSF estimation

We propose an unbiased estimate of a filtered version of the mean squared error--the blur-SURE (Stein's unbiased risk estimate)--as a novel criterion for estimating an unknown point spread function (PSF) from the degraded image only. The PSF is obtained by minimizing this new objective functional over a family of Wiener processings. Based on this estimated blur kernel, we then perform nonblind deconvolution using our recently developed algorithm. The SURE-based framework is exemplified with a number of parametric PSF, involving a scaling factor that controls the blur size. A typical example of such parametrization is the Gaussian kernel. The experimental results demonstrate that minimizing the blur-SURE yields highly accurate estimates of the PSF parameters, which also result in a restoration quality that is very similar to the one obtained with the exact PSF, when plugged into our recent multi-Wiener SURE-LET deconvolution algorithm. The highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on SURE-like estimates.

Robust destriping method with unidirectional total variation and framelet regularization

Multidetector imaging systems often suffer from the problem of stripe noise and random noise, which greatly degrade the imaging quality. In this paper, we propose a variational destriping method that combines unidirectional total variation and framelet regularization. Total-variation-based regularizations are considered effective in removing different kinds of stripe noise, and framelet regularization can efficiently preserve the detail information. In essence, these two regularizations are complementary to each other. Moreover, the proposed method can also efficiently suppress random noise. The split Bregman iteration method is employed to solve the resulting minimization problem. Comparative results demonstrate that the proposed method significantly outperforms state-of-the-art destriping methods on both qualitative and quantitative assessments.

Semi-blind spectral deconvolution with adaptive Tikhonov regularization

Deconvolution has become one of the most used methods for improving spectral resolution. Deconvolution is an ill-posed problem, especially when the point spread function (PSF) is unknown. Non-blind deconvolution methods use a predefined PSF, but in practice the PSF is not known exactly. Blind deconvolution methods estimate the PSF and spectrum simultaneously from the observed spectra, which become even more difficult in the presence of strong noise. In this paper, we present a semi-blind deconvolution method to improve the spectral resolution that does not assume a known PSF but models it as a parametric function in combination with the a priori knowledge about the characteristics of the instrumental response. First, we construct the energy functional, including Tikhonov regularization terms for both the spectrum and the parametric PSF. Moreover, an adaptive weighting term is devised in terms of the magnitude of the first derivative of spectral data to adjust the Tikhonov regularization for the spectrum. Then we minimize the energy functional to obtain the spectrum and the parameters of the PSF. We also discuss how to select the regularization parameters. Comparative results with other deconvolution methods on simulated degraded spectra, as well as on experimental infrared spectra, are presented.

Regularization parameter selection for nonlinear iterative image restoration and MRI reconstruction using GCV and SURE-based methods

Regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values. We focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive (possibly complex) Gaussian noise. Generalized cross-validation (GCV) and (weighted) mean-squared error (MSE) approaches (based on Steinfs Unbiased Risk Estimate. SURE) need the Jacobian matrix of the nonlinear reconstruction operator (representative of the iterative algorithm) with respect to the data. We derive the desired Jacobian matrix for two types of nonlinear iterative algorithms: a fast variant of the standard iterative reweighted least-squares method and the contemporary split-Bregman algorithm, both of which can accommodate a wide variety of analysis- and synthesis-type regularizers. The proposed approach iteratively computes two weighted SURE-type measures: Predicted-SURE and Projected-SURE (that require knowledge of noise variance Ð2), and GCV (that does not need Ð2) for these algorithms. We apply the methods to image restoration and to magnetic resonance image (MRI) reconstruction using total variation (TV) and an analysis-type .1-regularization. We demonstrate through simulations and experiments with real data that minimizing Predicted-SURE and Projected-SURE consistently lead to near-MSE-optimal reconstructions. We also observed that minimizing GCV yields reconstruction results that are near-MSE-optimal for image restoration and slightly suboptimal for MRI. Theoretical derivations in this work related to Jacobian matrix evaluations can be extended, in principle, to other types of regularizers and reconstruction algorithms.

Framelet-based blind motion deblurring from a single image

How to recover a clear image from a single motion-blurred image has long been a challenging open problem in digital imaging. In this paper, we focus on how to recover a motion-blurred image due to camera shake. A regularization-based approach is proposed to remove motion blurring from the image by regularizing the sparsity of both the original image and the motion-blur kernel under tight wavelet frame systems. Furthermore, an adapted version of the split Bregman method is proposed to efficiently solve the resulting minimization problem. The experiments on both synthesized images and real images show that our algorithm can effectively remove complex motion blurring from natural images without requiring any prior information of the motion-blur kernel.