Multi-Wiener SURE-LET deconvolution

Accurate 3D morphological computational model reconstruction of suspended cells imaged through stratified media by the precise depth-varying point spread function method

Accurate three-dimensional (3D) morphological computational models of cells are important in a number of biological studies. This study proposes a precise depth-varying point spread function (PDV-PSF) method for reconstructing 3D computational models of suspended cells from two-dimensional (2D) confocal image stacks. Our approach deblurs the 2D images in horizontal plane and corrects the deformation in vertical direction to overcome the refractive index mismatch problem caused by suspended cells imaging through stratified media. Standard fluorescent polystyrene spheres and Jurkat T-lymphocytes are selected to evaluate the validity and accuracy of this PDV-PSF method. Qualitative and quantitative results demonstrate that our approach has superior performance in 3D morphological computational models reconstruction of suspended cells.

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.

The Fourier-Argand Representation: An Optimal Basis of Steerable Patterns

Computing the convolution between a 2D signal and a corresponding filter with variable orientations is a basic problem that arises in various tasks ranging from low level image processing (e.g. ridge/edge detection) to high level computer vision (e.g. pattern recognition). Through decades of research, there still lacks an efficient method for solving this problem. In this paper, we investigate this problem from the perspective of approximation by considering the following problem: what is the optimal basis for approximating all rotated versions of a given bivariate function? Surprisingly, solely minimising the L2-approximation-error leads to a rotation-covariant linear expansion, which we name Fourier-Argand representation. This representation presents two major advantages: 1) rotation-covariance of the basis, which implies a "strong steerability" - rotating by an angle α corresponds to multiplying each basis function by a complex scalar e-ikα; 2) optimality of the Fourier-Argand basis, which ensures a few number of basis functions suffice to accurately approximate complicated patterns and highly direction-selective filters. We show the relation between the Fourier-Argand representation and the Radon transform, leading to an efficient implementation of the decomposition for digital filters. We also show how to retrieve accurate orientation of local structures/patterns using a fast frequency estimation algorithm.

Simultaneous recovery of both bright and dim structures from noisy fluorescence microscopy images using a modified TV constraint

The quality and information content of biological images can be significantly enhanced by postacquisition processing using deconvolution and denoising. However, when imaging complex biological samples, such as neurons, stained with fluorescence labels, the signal level of different structures can differ by several orders of magnitude. This poses a challenge as current image reconstruction algorithms are focused on recovering low signals and generally have sample-dependent performance, requiring tedious manual tuning. This is one of the main hurdles for their wide adoption by nonspecialists. In this work, we modify the general constrained reconstruction method (in our case utilizing a total variation constraint) so that both bright and dim structures can drive the deconvolution with equal force. In this way, we can simultaneously obtain high-quality reconstruction across a wide range of signals within a single image or image sequence. The algorithm is tested on both simulated and experimental data. When compared with current state-of-art algorithms, our algorithm outperforms others in terms of maintaining the resolution in the high-signal areas and reducing artefacts in the low-signal areas. The algorithm was also tested on image sequences where one set of parameters are used to reconstruct all images, with blind evaluation by a group of biologists demonstrating a marked preference for the images produced by our method. This means that our method is suitable for batch processing of image sequences obtained from either spatial or temporal scanning. LAY DESCRIPTION: Fluorescence microscopy images of complex biological samples contain a wide range of signal levels. This signal variation leads current reconstruction algorithms, which aim to enhance the quality of the raw images, to have sample-dependent performance. In this work, we design a new optimization that allows the reconstruction to "pay equal eqattention to" both bright and dim structures. In this way, we can simultaneously recover both bright and dim structures within a single image or image sequence, as validated when the algorithm was quantitatively tested on both simulated and experimental data. When our method was evaluated alongside current state of art algorithms by a group of biologists, our algorithm was considered qualitatively superior.

PURE-LET Image Deconvolution

We propose a non-iterative image deconvolution algorithm for data corrupted by Poisson or mixed Poisson-Gaussian noise. Many applications involve such a problem, ranging from astronomical to biological imaging. We parameterize the deconvolution process as a linear combination of elementary functions, termed as linear expansion of thresholds. This parameterization is then optimized by minimizing a robust estimate of the true mean squared error, the Poisson unbiased risk estimate. Each elementary function consists of a Wiener filtering followed by a pointwise thresholding of undecimated Haar wavelet coefficients. In contrast to existing approaches, the proposed algorithm merely amounts to solving a linear system of equations, which has a fast and exact solution. Simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state-of-the-art techniques, in terms of both restoration quality and computational complexity. Finally, we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images.We propose a non-iterative image deconvolution algorithm for data corrupted by Poisson or mixed Poisson-Gaussian noise. Many applications involve such a problem, ranging from astronomical to biological imaging. We parameterize the deconvolution process as a linear combination of elementary functions, termed as linear expansion of thresholds. This parameterization is then optimized by minimizing a robust estimate of the true mean squared error, the Poisson unbiased risk estimate. Each elementary function consists of a Wiener filtering followed by a pointwise thresholding of undecimated Haar wavelet coefficients. In contrast to existing approaches, the proposed algorithm merely amounts to solving a linear system of equations, which has a fast and exact solution. Simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state-of-the-art techniques, in terms of both restoration quality and computational complexity. Finally, we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images.

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.

Dictionary learning approach for image deconvolution with variance estimation

In this paper, we propose a new dictionary learning approach for image deconvolution, which effectively integrates the Fourier regularization and dictionary learning technique into the deconvolution framework. Specifically, we propose an iterative algorithm with the decoupling of the deblurring and denoising steps in the restoration process. In the deblurring step, we involve a regularized inversion of the blur in the Fourier domain. Then we remove the colored noise using a dictionary learning method in the denoising step. In the denoising step, we propose an approach to update the estimation of noise variance for dictionary learning. We will show that this approach outperforms several state-of-the-art image deconvolution methods in terms of improvement in signal-to-noise ratio and visual quality.

Noise-aware image deconvolution with multidirectional filters

In this paper we propose an approach for handling noise in deconvolution algorithm based on multidirectional filters. Most image deconvolution techniques are sensitive to the noise. Even a small amount of noise will degrade the quality of image estimation dramatically. We found that by applying a directional low-pass filter to the blurred image, we can reduce the noise level while preserving the blur information in the orthogonal direction to the filter. So we apply a series of directional filters at different orientations to the blurred image, and a guided filter based edge-preserving image deconvolution is used to estimate an accurate Radon transform of the clear image from each filtered image. Finally, we reconstruct the original image using the inverse Radon transform. We compare our deconvolution algorithm with many competitive deconvolution techniques in terms of the improvement in signal-to-noise ratio and visual quality.

Parameter estimation for blind and non-blind deblurring using residual whiteness measures

Image deblurring (ID) is an ill-posed problem typically addressed by using regularization, or prior knowledge, on the unknown image (and also on the blur operator, in the blind case). ID is often formulated as an optimization problem, where the objective function includes a data term encouraging the estimated image (and blur, in blind ID) to explain the observed data well (typically, the squared norm of a residual) plus a regularizer that penalizes solutions deemed undesirable. The performance of this approach depends critically (among other things) on the relative weight of the regularizer (the regularization parameter) and on the number of iterations of the algorithm used to address the optimization problem. In this paper, we propose new criteria for adjusting the regularization parameter and/or the number of iterations of ID algorithms. The rationale is that if the recovered image (and blur, in blind ID) is well estimated, the residual image is spectrally white; contrarily, a poorly deblurred image typically exhibits structured artifacts (e.g., ringing, oversmoothness), yielding residuals that are not spectrally white. The proposed criterion is particularly well suited to a recent blind ID algorithm that uses continuation, i.e., slowly decreases the regularization parameter along the iterations; in this case, choosing this parameter and deciding when to stop are one and the same thing. Our experiments show that the proposed whiteness-based criteria yield improvements in SNR, on average, only 0.15 dB below those obtained by (clairvoyantly) stopping the algorithm at the best SNR. We also illustrate the proposed criteria on non-blind ID, reporting results that are competitive with state-of-the-art criteria (such as Monte Carlo-based GSURE and projected SURE), which, however, are not applicable for blind ID.