A nonlocal structure tensor-based approach for multicomponent image recovery problems

A No-Reference Edge-Preservation Assessment Index for SAR Image Filters under a Bayesian Framework Based on the Ratio Gradient

Denoising is an essential preprocessing step for most applications using synthetic aperture radar (SAR) images at different processing levels. Besides suppressing the noise, a good filter should also effectively preserve the image edge information. To quantitatively assess the edge-preservation performance of SAR filters, a number of indices have been investigated in the literature; however, most of them do not fully employ the statistical traits of the SAR image. In this paper, we review some of the typical edge-preservation assessment indices. A new referenceless index is then proposed. The ratio gradient is utilized to characterize the difference between two non-overlapping neighborhoods on opposite sides of each pixel in both the speckled and despeckled images. Based on these gradients and the statistical traits of the speckle, the proposed indicator is derived under a Bayesian framework. A series of experiments conducted with both simulated and real SAR datasets reveal that the proposed index shows good performances, in both robustness and consistency. For reproducibility, the source codes of the index and the testing datasets are provided.

A Novel Task-Based reconstruction approach for digital breast tomosynthesis

The reconstruction of a volumetric image from Digital Breast Tomosynthesis (DBT) measurements is an ill-posed inverse problem, for which existing iterative regularized approaches can provide a good solution. However, the clinical task is somehow omitted in the derivation of those techniques, although it plays a primary role in the radiologist diagnosis. In this work, we address this issue by introducing a novel variational formulation for DBT reconstruction, tailored for a specific clinical task, namely the detection of microcalcifications. Our method aims at simultaneously enhancing the detectability performance and enabling a high-quality restoration of the background breast tissues. Our contribution is threefold. First, we introduce an original task-based reconstruction framework through the proposition of a detectability function inspired from mathematical model observers. Second, we propose a novel total-variation regularizer where the gradient field accounts for the different morphological contents of the imaged breast. Third, we integrate the two developed measures into a cost function, minimized thanks to a new form of the Majorize Minimize Memory Gradient (3MG) algorithm. We conduct a numerical comparison of the convergence speed of the proposed method with those of standard convex optimization algorithms. Experimental results show the interest of our DBT reconstruction approach, qualitatively and quantitatively.

One-step deconvolution for multi-angle TIRF microscopy with enhanced resolution

Total internal reflection fluorescence microscopy (TIRF microscopy) uses a rapid decay of evanescent waves to excite fluorophores within several hundred nanometers (nm) beneath the plasma membrane, which can effectively suppress excitation of fluorescence signals in the deep layers. From image stacks obtained with a plurality of different incident angles, a three-dimensional spatial structure of the observed sample can be reconstructed by a Multi-Angle-TIRF (MA-TIRF) algorithm that provides an axial resolution of ~50 nm. Taking into account the point spread function (PSF) of the TIRF microscopes, we further increase its lateral resolution by introducing a fast deconvolution algorithm into the reconstruction of MA-TIRF data (DMA-TIRF), which is approached in just one step of minimizing the reconstruction function. We also introduce a TV regularization term in the deconvolution algorithm to suppress artifacts induced by the excessive noise. Therefore, based on the hardware of existing MA-TIRF microscopes, the proposed DMA-TIRF algorithm has achieved lateral and axial resolutions of ~200 and ~50 nm, respectively.

Nonsmooth Convex Optimization for Structured Illumination Microscopy Image Reconstruction

In this paper, we propose a new approach for structured illumination microscopy image reconstruction. We first introduce the principles of this imaging modality and describe the forward model. We then propose the minimization of nonsmooth convex objective functions for the recovery of the unknown image. In this context, we investigate two data-fitting terms for Poisson-Gaussian noise and introduce a new patch-based regularization method. This approach is tested against other regularization approaches on a realistic benchmark. Finally, we perform some test experiments on images acquired on two different microscopes.

Texture Reconstruction Guided by a High-Resolution Patch

In this paper, we aim at super-resolving a low-resolution texture under the assumption that a high-resolution patch of the texture is available. To do so, we propose a variational method that combines two approaches that are texture synthesis and image reconstruction. The resulting objective function holds a nonconvex energy that involves a quadratic distance to the low-resolution image, a histogram-based distance to the high-resolution patch, and a nonlocal regularization that links the missing pixels with the patch pixels. As for the histogram-based measure, we use a sum of Wasserstein distances between the histograms of some linear transformations of the textures. The resulting optimization problem is efficiently solved with a primal-dual proximal method. Experiments show that our method leads to a significant improvement, both visually and numerically, with respect to the state-of-the-art algorithms for solving similar problems.