Total variation based image restoration of three dimensional microscopic objects

The inverse problem involving the determination of a three-dimensional biological structure from images obtained by means of optical-sectioning microscopy is ill-posed. Regularization methods must often be used in order to obtain a reasonable solution. Recently, the total variation (TV) regularization, as proposed by Rudin, Osher and Fatemi (1992), has become very popular for this purpose. An iterative algorithm is used for minimizing a TV-penalized least squares problems. We also employ transform based methods for solving large linear subproblems arising from TV-penalized least squares problems. Preliminary numerical results show that the method performs quite well.published_or_final_versio

An efficient parallel algorithm for high resolution color image reconstruction

This paper studies the application of preconditioned conjugate gradient methods in high resolution color image reconstruction problems. The high resolution color images are reconstructed from multiple undersampled, shifted, degraded color frames with subpixel displacements. The resulting degradation matrices are spatially variant. The preconditioners are derived by taking the cosine transform approximation of the degradation matrices. The resulting preconditioning matrices allow the use of fast transform methods. We show how the methods can be implemented on parallel computers, and we demonstrate their parallel efficiency using experiments on a sixteen processor IBM SP-2.published_or_final_versio

Fast direct methods for Toeplitz least squares problems

Least squares estimations have been used extensively in many applications system identification and signal prediction. These applications, the least squares estimators can usually be found by solving Toeplitz least squares problems. We present fast algorithms for solving the Toeplitz least squares problems. The algorithm is derived by using the displacement representation of the normal equations matrix. Numerical experiments show that these algorithms are efficient.published_or_final_versio

Half-quadratic regularization, preconditioning and applications

The article addresses a wide class of image deconvolution or reconstruction situations where a sought image is recovered from degraded observed image. The sought solution is defined to be the minimizer of an objective function combining a data-fidelity term and an edge-preserving, convex regularization term. Our objective is to speed up the calculation of the solution in a wide range of situations. We propose a method applying pertinent preconditioning to an adapted half-quadratic equivalent form of the objective function. The optimal solution is then found using an alternating minimization (AM) scheme. We focus specifically on Huber regularization. We exhibit the possibility of getting very fast calculations while preserving the edges in the solution. Preliminary numerical results are reported to illustrate the effectiveness of our method.published_or_final_versio

Preconditioned Lanczos Methods for the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix

In this paper, we apply the preconditioned Lanczos (PL) method to compute the minimum eigenvalue of a symmetric positive definite Toeplitz matrix. The sine transform-based preconditioner is used to speed up the convergence rate of the PL method. The resulting method involves only Toeplitz and sine transform matrix-vector multiplications and hence can be computed efficiently by fast transform algorithms. We show that if the symmetric Toeplitz matrix is generated by a positive $2 \pi$-periodic even continuous function, then the PL method will converge sufficiently fast. Numerical results including Toeplitz and non-Toeplitz matrices are reported to illustrate the effectiveness of the method.published_or_final_versio

Fast image reconstruction algorithms combining half-quadratic regularization and preconditioning

We focus on image deconvolution and image reconstruction problems where a sought image is recovered from degraded observed data. The solution is defined to be the minimizer of an objective function combining a data-fidelity term and an edge-preserving, convex regularization term. Our objective is to speed up the calculation of the solution in a wide range of situations. To this end, we propose a method applying pertinent preconditioning to an adapted half-quadratic equivalent form of the objective function. The optimal solution is then found using an alternating minimization (AM) scheme. We focus specifically on Huber regularization. We exhibit the possibility of getting very fast calculations while preserving the edges in the solution. Preliminary numerical results are reported to illustrate the effectiveness of our method.published_or_final_versio

Preconditioned iterative methods for superresolution image reconstruction with multisensors

We study the problem of reconstructing a super-resolution image f from multiple undersampled, sifted, degraded frames with subpixel displacement errors. The corresponding operator H is a spatially- variant operator. In this paper, we apply the preconditioned conjugate gradient method with cosine transform preconditioners to solve the discrete problems. Preliminary results show that our method converges very fast and gives sound recovery of the super- resolution images.published_or_final_versio

Effective Assessment of Power Standing Device to Adults with Permanent Lower Limb Paralysis

Introduction: Standing routine is a known beneficial daily activity for both healthy and disabled persons, especially those with permanent lower limb paralysis. However, the prescription of standing device for adults with permanent paralysis was inadequate and non-standard in existing local practice because of lack of good design and evidence based funding support. Objective: In view of the availability of new advances in power standing device, we aim to perform an effective health technology assessment (HTA) from professional and users perspectives to develop the decision pathway in prescription for long term home use. Methodology: A functional test and social cost analysis was performed on one high cost new standing mobile devices in recent market. A practical workshop and surveys were performed to collect feedback from 24 healthcare professionals and 8 expert users on a spectrum of new standing mobile device. Results: From the survey results, there was consensus among all participants that ‘Standing’ as daily routine at home is essential and beneficial. 62.5% of healthcare professionals would provide training to users and their cares to facilitate users to perform standing at home. Eight factors were identified from factor analysis in affecting the choice of standing devices for home use by healthcare professionals and users. Users scored high (mean=9.25/10) in “compliance with the new power standing mobile device”. The cost analysis showed considerable savings in social costs in using even the high-cost power standing mobile device. Discussion: The group welcomed power standing device with or without mobile function to support their standing activity at home. A possible clinical decision for prescribing different standing devices with identified factors was summarized. Conclusion: More recent researches have reported the negative health issues associated with prolonged sitting. With more innovative product designs, the power standing devices with or without mobile function is a new concept welcomed by both healthcare professionals and users in promotion of their health, preventing complications as well as independent living in home environment. A larger scale of HTA with structured cost-effectiveness analysis is essential to inform the healthcare resources planners

Preconditioners for Wiener--Hopf Equations with High-Order Quadrature Rules

We consider solving the Wiener--Hopf equations with high-order quadrature rules by preconditioned conjugate gradient (PCG) methods. We propose using convolution operators as preconditioners for these equations. We will show that with the proper choice of kernel functions for the preconditioners, the resulting preconditioned equations will have clustered spectra and therefore can be solved by the PCG method with superlinear convergence rate. Moreover, the discretization of these equations by high-order quadrature rules leads to matrix systems that involve only Toeplitz or diagonal matrix--vector multiplications and hence can be computed efficiently by FFTs. Numerical results are given to illustrate the fast convergence of the method and the improvement on accuracy by using higher-order quadrature rule. We also compare the performance of our preconditioners with the circulant integral operators.published_or_final_versio

Recursive-Based PCG Methods for Toeplitz Systems with Nonnegative Generating Functions

In this paper, we consider the solutions of symmetric positive definite, but ill-conditioned, Toeplitz systems An x = b. Here we propose to solve the system by the recursive-based preconditioned conjugate gradient method. The idea is to use the inverse of Am (the principal submatrix of An with the Gohberg--Semencul formula as a preconditioner for An. The inverse of Am can be generated recursively by using the formula until m is small enough. The construction of the preconditioners requires only the entries of An and does not require the explicit knowledge of the generating function f of An. We show that if f is a nonnegative, bounded, and piecewise continuous even function with a finite number of zeros of even order, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers. Hence the conjugate gradient method, when applied to solving the preconditioned system, converges very quickly. Numerical results are included to illustrate the effectiveness of our approach.published_or_final_versio