Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement

Stimulation Montage Achieves Balanced Focality and Intensity

Transcranial direct current stimulation (tDCS) is a non-invasive neuromodulation technique to treat brain disorders by using a constant, low current to stimulate targeted cortex regions. Compared to the conventional tDCS that uses two large pad electrodes, multiple electrode tDCS has recently received more attention. It is able to achieve better stimulation performance in terms of stimulation intensity and focality. In this paper, we first establish a computational model of tDCS, and then propose a novel optimization algorithm using a regularization matrix λ to explore the balance between stimulation intensity and focality. The simulation study is designed such that the performance of state-of-the-art algorithms and the proposed algorithm can be compared via quantitative evaluation. The results show that the proposed algorithm not only achieves desired intensity, but also smaller target error and better focality. Robustness analysis indicates that the results are stable within the ranges of scalp and cerebrospinal fluid (CSF) conductivities, while the skull conductivity is most sensitive and should be carefully considered in real clinical applications.

Towards a super-resolution based approach for improved face recognition in low resolution environment

The video surveillance activity generates a vast amount of data, which can be processed to detect miscreants. The task of identifying and recognizing an object in surveillance data is intriguing yet difficult due to the low resolution of captured images or video. The super-resolution approach aims to enhance the resolution of an image to generate a desirable high-resolution one. This paper develops a robust real-time face recognition approach that uses super-resolution to improve images and detect faces in the video. Many previously developed face detection systems are constrained by the severe distortion in the captured images. Further, many systems failed to handle the effect of motion, blur, and noise on the images registered on a camera. The presented approach improves descriptor count of the image based on the super-resolved faces and mitigates the effect of noise. Furthermore, it uses a parallel architecture to implement a super-resolution algorithm and overcomes the efficiency drawback increasing face recognition performance. Experimental analysis on the ORL, Caltech, and Chokepoint datasets has been carried out to evaluate the performance of the presented approach. The PSNR (Peak Signal-to-Noise-Ratio) and face recognition rate are used as the performance measures. The results showed significant improvement in the recognition rates for images where the face didn't contain pose expressions and scale variations. Further, for the complicated cases involving scale, pose, and lighting variations, the presented approach resulted in an improvement of 5%-6% in each case.

Sparse-graph manifold learning method for bioluminescence tomography

In preclinical researches, bioluminescence tomography (BLT) has widely been used for tumor imaging and monitoring, imaged-guided tumor therapy, and so forth. For these biological applications, both tumor spatial location and morphology analysis are the leading problems needed to be taken into account. However, most existing BLT reconstruction methods were proposed for some specific applications with a focus on sparse representation or morphology recovery, respectively. How to design a versatile algorithm that can simultaneously deal with both aspects remains an impending problem. In this study, a Sparse-Graph Manifold Learning (SGML) method was proposed to balance the source sparseness and morphology, by integrating non-convex sparsity constraint and dynamic Laplacian graph model. Furthermore, based on the nonconvex optimization theory and some iterative approximation, we proposed a novel iteratively reweighted soft thresholding algorithm (IRSTA) to solve the SGML model. Numerical simulations and in vivo experiments result demonstrated that the proposed SGML method performed much superior to the comparative methods in spatial localization and tumor morphology recovery for various source settings. It is believed that the SGML method can be applied to the related optical tomography and facilitate the development of optical molecular tomography.

Adaptive Regularization of Some Inverse Problems in Image Analysis

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized at convergence. We also introduce a Huber loss function in both data fidelity and regularization terms, and present an efficient convex optimization algorithm based on the alternating direction method of multipliers (ADMM) using the equivalent relation between the Huber function and the proximal operator of the one-norm. We illustrate and validate our adaptive Huber-Huber model on synthetic and real images in segmentation, motion estimation, and denoising problems.

Efficient Bandwidth Estimation in 2D Filtered Backprojection Reconstruction

A generalized cross-validation approach to estimate the reconstruction filter bandwidth in 2D filtered backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form, derives results on eigendecomposition of symmetric 2D circulant matrices, and applies them to make bandwidth estimation a computationally efficient operation within the context of standard backprojected filtering reconstruction. Performance evaluations on a range of simulated emission tomography experiments give promising results. The superior performance holds at both low and high total expected counts, pointing to the method's applicability even in weak signal-to-noise-ratio situations. The approach also applies to the more general class of elliptically symmetric filters, with the reconstructed estimate's performance often better than even that obtained with the true optimal radially symmetric filter.

Non-Additive Imprecise Image Super-Resolution in a Semi-Blind Context

The most effective superresolution methods proposed in the literature require precise knowledge of the so-called point spread function of the imager, while in practice its accurate estimation is nearly impossible. This paper presents a new superresolution method, whose main feature is its ability to account for the scant knowledge of the imager point spread function. This ability is based on representing this imprecise knowledge via a non-additive neighborhood function. The superresolution reconstruction algorithm transfers this imprecise knowledge to output by producing an imprecise (interval-valued) high-resolution image. We propose some experiments illustrating the robustness of the proposed method with respect to the imager point spread function. These experiments also highlight its high performance compared with very competitive earlier approaches. Finally, we show that the imprecision of the high-resolution interval-valued reconstructed image is a reconstruction error marker.

Multi-sensor super-resolution for hybrid range imaging with application to 3-D endoscopy and open surgery

In this paper, we propose a multi-sensor super-resolution framework for hybrid imaging to super-resolve data from one modality by taking advantage of additional guidance images of a complementary modality. This concept is applied to hybrid 3-D range imaging in image-guided surgery, where high-quality photometric data is exploited to enhance range images of low spatial resolution. We formulate super-resolution based on the maximum a-posteriori (MAP) principle and reconstruct high-resolution range data from multiple low-resolution frames and complementary photometric information. Robust motion estimation as required for super-resolution is performed on photometric data to derive displacement fields of subpixel accuracy for the associated range images. For improved reconstruction of depth discontinuities, a novel adaptive regularizer exploiting correlations between both modalities is embedded to MAP estimation. We evaluated our method on synthetic data as well as ex-vivo images in open surgery and endoscopy. The proposed multi-sensor framework improves the peak signal-to-noise ratio by 2 dB and structural similarity by 0.03 on average compared to conventional single-sensor approaches. In ex-vivo experiments on porcine organs, our method achieves substantial improvements in terms of depth discontinuity reconstruction.

Depth-variant deconvolution of 3D widefield fluorescence microscopy using the penalized maximum likelihood estimation method

We investigated the deconvolution of 3D widefield fluorescence microscopy using the penalized maximum likelihood estimation method and the depth-variant point spread function (DV-PSF). We build the DV-PSF by fitting a parameterized theoretical PSF model to an experimental microbead image. On the basis of the constructed DV-PSF, we restore the 3D widefield microscopy by minimizing an objective function consisting of a negative Poisson likelihood function and a total variation regularization function. In simulations and experiments, the proposed method showed better performance than existing methods.

Unified blind method for multi-image super-resolution and single/multi-image blur deconvolution

This paper presents, for the first time, a unified blind method for multi-image super-resolution (MISR or SR), single-image blur deconvolution (SIBD), and multi-image blur deconvolution (MIBD) of low-resolution (LR) images degraded by linear space-invariant (LSI) blur, aliasing, and additive white Gaussian noise (AWGN). The proposed approach is based on alternating minimization (AM) of a new cost function with respect to the unknown high-resolution (HR) image and blurs. The regularization term for the HR image is based upon the Huber-Markov random field (HMRF) model, which is a type of variational integral that exploits the piecewise smooth nature of the HR image. The blur estimation process is supported by an edge-emphasizing smoothing operation, which improves the quality of blur estimates by enhancing strong soft edges toward step edges, while filtering out weak structures. The parameters are updated gradually so that the number of salient edges used for blur estimation increases at each iteration. For better performance, the blur estimation is done in the filter domain rather than the pixel domain, i.e., using the gradients of the LR and HR images. The regularization term for the blur is Gaussian (L2 norm), which allows for fast noniterative optimization in the frequency domain. We accelerate the processing time of SR reconstruction by separating the upsampling and registration processes from the optimization procedure. Simulation results on both synthetic and real-life images (from a novel computational imager) confirm the robustness and effectiveness of the proposed method.

Frame fundamental high-resolution image fusion from inhomogeneous measurements

Frame and fusion frame high-resolution image fusion formulations are presented. These techniques use the physical point spread function (PSF) of cameras as the building block of the mathematical frames in the fusion process. Cameras producing the low-resolution images are allowed to be different, and thereby possess different PSFs. Fused image reconstructions are carried out by a dimension invariance principle and by a set of iterative reconstruction algorithms. These frame fundamental approaches are also seen to be robust to realistic fusion problems from inhomogeneous image measurements (taken at different space or time or by different cameras), which is one of the main focuses of this paper. The effectiveness of this approach is demonstrated through both simulated and realistic examples. The results are quite encouraging.

Supervised restoration of degraded medical images using multiple-point geostatistics

Reducing noise in medical images has been an important issue of research and development for medical diagnosis, patient treatment, and validation of biomedical hypotheses. Noise inherently exists in medical and biological images due to the acquisition and transmission in any imaging devices. Being different from image enhancement, the purpose of image restoration is the process of removing noise from a degraded image in order to recover as much as possible its original version. This paper presents a statistically supervised approach for medical image restoration using the concept of multiple-point geostatistics. Experimental results have shown the effectiveness of the proposed technique which has potential as a new methodology for medical and biological image processing.

Commutability of blur and affine warping in super-resolution with application to joint estimation of triple-coupled variables

This paper proposes a new approach to the image blind super-resolution (BSR) problem in the case of affine interframe motion. Although the tasks of image registration, blur identification, and high-resolution (HR) image reconstruction are coupled in the imaging process, when dealing with nonisometric interframe motion or without the exact knowledge of the blurring process, classic SR techniques generally have to tackle them (maybe in some combinations) separately. The main difficulty is that state-of-the-art deconvolution methods cannot be straightforwardly generalized to cope with the space-variant motion. We prove that the operators of affine warping and blur commute with some additional transforms and derive an equivalent form of the BSR observation model. Using this equivalent form, we develop an iterative algorithm to jointly estimate the triple-coupled variables, i.e., the motion parameters, blur kernels, and HR image. Experiments on synthetic and real-life images illustrate the performance of the proposed technique in modeling the space-variant degradation process and restoring local textures.

Preconditioning for edge-preserving image super resolution

We propose a simple preconditioning method for accelerating the solution of edge-preserving image super-resolution (SR) problems in which a linear shift-invariant point spread function is employed. Our technique involves reordering the high-resolution (HR) pixels in a similar manner to what is done in preconditioning methods for quadratic SR formulations. However, due to the edge preserving requirements, the Hessian matrix of the cost function varies during the minimization process. We develop an efficient update scheme for the preconditioner in order to cope with this situation. Unlike some other acceleration strategies that round the displacement values between the low-resolution (LR) images on the HR grid, the proposed method does not sacrifice the optimality of the observation model. In addition, we describe a technique for preconditioning SR problems involving rational magnification factors. The use of such factors is motivated in part by the fact that, under certain circumstances, optimal SR zooms are nonintegers. We show that, by reordering the pixels of the LR images, the structure of the problem to solve is modified in such a way that preconditioners based on circulant operators can be used.

Super-resolution without explicit subpixel motion estimation

The need for precise (subpixel accuracy) motion estimates in conventional super-resolution has limited its applicability to only video sequences with relatively simple motions such as global translational or affine displacements. In this paper, we introduce a novel framework for adaptive enhancement and spatiotemporal upscaling of videos containing complex activities without explicit need for accurate motion estimation. Our approach is based on multidimensional kernel regression, where each pixel in the video sequence is approximated with a 3-D local (Taylor) series, capturing the essential local behavior of its spatiotemporal neighborhood. The coefficients of this series are estimated by solving a local weighted least-squares problem, where the weights are a function of the 3-D space-time orientation in the neighborhood. As this framework is fundamentally based upon the comparison of neighboring pixels in both space and time, it implicitly contains information about the local motion of the pixels across time, therefore rendering unnecessary an explicit computation of motions of modest size. The proposed approach not only significantly widens the applicability of super-resolution methods to a broad variety of video sequences containing complex motions, but also yields improved overall performance. Using several examples, we illustrate that the developed algorithm has super-resolution capabilities that provide improved optical resolution in the output, while being able to work on general input video with essentially arbitrary motion.

Space-variant restoration of images degraded by camera motion blur

We examine the problem of restoration from multiple images degraded by camera motion blur. We consider scenes with significant depth variations resulting in space-variant blur. The proposed algorithm can be applied if the camera moves along an arbitrary curve parallel to the image plane, without any rotations. The knowledge of camera trajectory and camera parameters is not necessary. At the input, the user selects a region where depth variations are negligible. The algorithm belongs to the group of variational methods that estimate simultaneously a sharp image and a depth map, based on the minimization of a cost functional. To initialize the minimization, it uses an auxiliary window-based depth estimation algorithm. Feasibility of the algorithm is demonstrated by three experiments with real images.

Model study of imaging myocardial infarction by intracardiac electrical impedance tomography

Electrical impedance tomography (EIT) detects tissue composition inside a medium by determining its resistive properties, and uses various electrode configurations to pass a small electric current and measure corresponding potential. We investigated the feasibility of reconstructing scarred tissue inside the heart wall by employing EIT on the basis of a catheter carrying a plurality of electrodes and placed inside the blood-filled heart cavity. We built a computer model of the biological medium, and reconstructed the resistivity distribution using the finite element method and Tikhonov regularization. The results established the successful implementation of the numeric methods and the possibility of localizing and quantifying scarred myocardium. Novel application of EIT from inside the heart cavity could be useful during catheterization and may complement other diagnostic modalities. Further research is necessary to assess the impact of several factors on the accuracy of the reconstruction and include number of electrodes, catheter location, and scar size.

A unified approach to superresolution and multichannel blind deconvolution

This paper presents a new approach to the blind deconvolution and superresolution problem of multiple degraded low-resolution frames of the original scene. We do not assume any prior information about the shape of degradation blurs. The proposed approach consists of building a regularized energy function and minimizing it with respect to the original image and blurs, where regularization is carried out in both the image and blur domains. The image regularization based on variational principles maintains stable performance under severe noise corruption. The blur regularization guarantees consistency of the solution by exploiting differences among the acquired low-resolution images. Several experiments on synthetic and real data illustrate the robustness and utilization of the proposed technique in real applications.

Multiresolution imaging of MEG cortical sources using an explicit piecewise model

Imaging neural generators from MEG magnetic fields is often considered as a compromise between computationally-reasonable methodology that usually yields poor spatial resolution on the one hand, and more sophisticated approaches on the other hand, potentially leading to intractable computational costs. We approach the problem of obtaining well-resolved source images with unexcessive computation load with a multiresolution image model selection (MiMS) technique. The building blocks of the MiMS source model are parcels of the cortical surface which can be designed at multiple spatial resolutions with the combination of anatomical and functional priors. Computation charge is reduced owing to 1) compact parametric models of the activation of extended brain parcels using current multipole expansions and 2) the optimization of the generalized cross-validation error on image models, which is closed-form for the broad class of linear estimators of neural currents. Model selection can be complemented by any conventional imaging approach of neural currents restricted to the optimal image support obtained from MiMS. The estimation of the location and spatial extent of brain activations is discussed and evaluated using extensive Monte-Carlo simulations. An experimental evaluation was conducted with MEG data from a somatotopic paradigm. Results show that MiMS is an efficient image model selection technique with robust performances at realistic noise levels.

MNR Method with Self-Determined Regularization Parameters for Solving Inverse Resistivity Problem

The modified Newton-Raphson (MNR) method is used to solve the inverse resistivity problem in this paper. Using Tikhonov regularization method, comparisons among the L-curve method, the zero-crossing (ZC) method and the generalized cross validation (GCV) method are carried out for determining the regularization parameters of MNR method. By these criterions the appropriate regularization parameters are self-determined and adjusted with the reconstruction iterations. Our simulation experiments on 2D circle model showed that the GCV method can provide the best reconstruction quality with the fastest speed in inverse resistivity problem using MNR method.

Three EIT approaches for static imaging of head

Three EIT approaches for static imaging of head are investigated in this paper. The modified Newton-Raphson (MNR) method and the differential evolution (DE) algorithm are applied to the impedance reconstruction of 2D section of head based on real head model. Comparisons are carried out on the results obtained using simulated data, and a DE-MNR combination method is proposed, which demonstrated high impedance reconstruction quality with fast convergence in the 2D EIT simulation for static imaging of head.

A MAP approach for joint motion estimation, segmentation, and super resolution

Super resolution image reconstruction allows the recovery of a high-resolution (HR) image from several low-resolution images that are noisy, blurred, and down sampled. In this paper, we present a joint formulation for a complex super-resolution problem in which the scenes contain multiple independently moving objects. This formulation is built upon the maximum a posteriori (MAP) framework, which judiciously combines motion estimation, segmentation, and super resolution together. A cyclic coordinate descent optimization procedure is used to solve the MAP formulation, in which the motion fields, segmentation fields, and HR images are found in an alternate manner given the two others, respectively. Specifically, the gradient-based methods are employed to solve the HR image and motion fields, and an iterated conditional mode optimization method to obtain the segmentation fields. The proposed algorithm has been tested using a synthetic image sequence, the "Mobile and Calendar" sequence, and the original "Motorcycle and Car" sequence. The experiment results and error analyses verify the efficacy of this algorithm.

Small-kernel superresolution methods for microscanning imaging systems

Two computationally efficient methods for superresolution reconstruction and restoration of microscanning imaging systems are presented. Microscanning creates multiple low-resolution images with slightly different sample-scene phase shifts. The digital processing methods developed here combine the low-resolution images to produce an image with higher pixel resolution (i.e., superresolution) and higher fidelity. The methods implement reconstruction to increase resolution and restoration to improve fidelity in one-pass convolution with a small kernel. One method uses a small-kernel Wiener filter and the other method uses a parametric cubic convolution filter. Both methods are based on an end-to-end, continuous-discrete-continuous microscanning imaging system model. Because the filters are constrained to small spatial kernels they can be efficiently applied by convolution and are amenable to adaptive processing and to parallel processing. Experimental results with simulated imaging and with real microscanned images indicate that the small-kernel methods efficiently and effectively increase resolution and fidelity.

Multiframe demosaicing and super-resolution of color images

In the last two decades, two related categories of problems have been studied independently in image restoration literature: super-resolution and demosaicing. A closer look at these problems reveals the relation between them, and, as conventional color digital cameras suffer from both low-spatial resolution and color-filtering, it is reasonable to address them in a unified context. In this paper, we propose a fast and robust hybrid method of super-resolution and demosaicing, based on a maximum a posteron estimation technique by minimizing a multiterm cost function. The L1 norm is used for measuring the difference between the projected estimate of the high-resolution image and each low-resolution image, removing outliers in the data and errors due to possibly inaccurate motion estimation. Bilateral regularization is used for spatially regularizing the luminance component, resulting in sharp edges and forcing interpolation along the edges and not across them. Simultaneously, Tikhonov regularization is used to smooth the chrominance components. Finally, an additional regularization term is used to force similar edge location and orientation in different color channels. We show that the minimization of the total cost function is relatively easy and fast. Experimental results on synthetic and real data sets confirm the effectiveness of our method.

Blind image restoration with eigen-face subspace

Performance of conventional image restoration methods is sensitive to signal-to-noise ratios. For heavily blurred and noisy human facial images, information contained in the eigen-face subspace can be used to compensate for the lost details. The blurred image is decomposed into the eigen-face subspace and then restored with a regularized total constrained least square method. With Generalized cross-validation, a cost function is deduced to include two unknown parameters: the regularization factor and one parameter relevant to point spread function. It is shown that, in minimizing the cost function, the cost function dependence of any one unknown parameter can be separated from the other one, which means the cost function can be considered roughly, depending on single variable in an iterative algorithm. With realistic constraints on the regularized factor, a global minimum for the cost function is achieved to determine the unknown parameters. Experiments are presented to demonstrate the effectiveness and robustness of the new method.

Reconstruction of nonuniformly sampled images in spline spaces

This paper presents a novel approach to the reconstruction of images from nonuniformly spaced samples. This problem is often encountered in digital image processing applications. Nonrecursive video coding with motion compensation, spatiotemporal interpolation of video sequences, and generation of new views in multicamera systems are three possible applications. We propose a new reconstruction algorithm based on a spline model for images. We use regularization, since this is an ill-posed inverse problem. We minimize a cost function composed of two terms: one related to the approximation error and the other related to the smoothness of the modeling function. All the processing is carried out in the space of spline coefficients; this space is discrete, although the problem itself is of a continuous nature. The coefficients of regularization and approximation filters are computed exactly by using the explicit expressions of B-spline functions in the time domain. The regularization is carried out locally, while the computation of the regularization factor accounts for the structure of the nonuniform sampling grid. The linear system of equations obtained is solved iteratively. Our results show a very good performance in motion-compensated interpolation applications.

Fast and robust multiframe super resolution

Super-resolution reconstruction produces one or a set of high-resolution images from a set of low-resolution images. In the last two decades, a variety of super-resolution methods have been proposed. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses their short-comings. We propose an alternate approach using L1 norm minimization and robust regularization based on a bilateral prior to deal with different data and noise models. This computationally inexpensive method is robust to errors in motion and blur estimation and results in images with sharp edges. Simulation results confirm the effectiveness of our method and demonstrate its superiority to other super-resolution methods.

Parameter estimation in Bayesian high-resolution image reconstruction with multisensors

In this paper, we consider the estimation of the unknown parameters for the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. We derive mathematical expressions for the iterative calculation of the maximum likelihood estimate of the unknown parameters given the low resolution observed images. These iterative procedures require the manipulation of block-semi circulant (BSC) matrices, that is, block matrices with circulant blocks. We show how these BSC matrices can be easily manipulated in order to calculate the unknown parameters. Finally the proposed method is tested on real and synthetic images.

High resolution image formation from low resolution frames using Delaunay triangulation

An algorithm based on spatial tessellation and approximation of each triangle patch in the Delaunay (1934) triangulation (with smoothness constraints) by a bivariate polynomial is advanced to construct a high resolution (HR) high quality image from a set of low resolution (LR) frames. The high resolution algorithm is accompanied by a site-insertion algorithm for update of the initial HR image with the availability of more LR frames till the desired image quality is attained. This algorithm, followed by post filtering, is suitable for real-time image sequence processing because of the fast expected (average) time construction of Delaunay triangulation and the local update feature.