Penalized Maximum Likelihood Algorithm Research Articles

Three dimensional microspectroscopic tomography with synchrotron radiation infrared raster scanning method

A microspectroscopic tomography method is performed for a nondestructive three dimentional (3D) imaging. The synchrotron radiation infrared (SRIR) is used as a light source. A MiTeGen loop and a bird feather barb are taken as check samples. Their IR spectral informations are collected by raster scanning procedure with the incompleted projection mappings. Their 3D tomographic reconstructions are obtained by the penalized maximum likelihood algorithm with weighted linear and quadratic penalties (PML-Hybrid algorithm). The computed algorithm reconstructs the MiTeGen loop in the 1638–1572 cm−1 region, which corresponds to the NH bend vibration. Besides, the bird feather barb is measured in the mid-infrared spectral region, and the main characteristic absorption bands include amide A, the lipids, and amide I. Their 3D reconstruction images are obtained from three selected absorption bands. The results show that the 3D tomographic method presents a good signal-to-noise ratio (SNR). The 3D distributions of chemical compositions are obtained for the MiTeGen loop and the bird feather barb by SRIR microspectroscopic tomography.

Dual-echo Z-shimmed proton resonance frequency-shift magnetic resonance thermometry near metallic ablation probes: Technique and temperature precision.

To improve the precision of proton resonance frequency-shift magnetic resonance thermometry near ablation probes by recovering near-probe image signals that are typically lost due to magnetic susceptibility-induced field distortions. A dual-echo gradient-recalled echo sequence was implemented, in which the first echo was under- or over-refocused in the slice dimension to recover image signal and temperature precision near a probe, and the second echo was fully refocused to obtain image signal everywhere else in the slice. A penalized maximum likelihood algorithm was implemented to estimate a single temperature map from both echoes. Agar phantom and ex vivo experiments with and without microwave heating at 3 T evaluated how much temperature precision was improved near a microwave ablator compared to a conventional single-echo scan as a function of slice and needle orientation in the magnet. The number of near-probe voxels with temperature standard deviation σ>1°C was decreased by 51% in the phantom experiment, averaged across orientations, and by 31% in the pork. Temperature maps near the probe were more smoother and more complete in all orientations. Dual-echo z-shimmed temperature imaging can recover image signal for more precise temperature mapping near metallic ablation probes. Magn Reson Med 78:2299-2306, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Investigation of statistical iterative reconstruction for dedicated breast CT

Dedicated breast CT has great potential for improving the detection and diagnosis of breast cancer. Statistical iterative reconstruction (SIR) in dedicated breast CT is a promising alternative to traditional filtered backprojection (FBP). One of the difficulties in using SIR is the presence of free parameters in the algorithm that control the appearance of the resulting image. These parameters require tuning in order to achieve high quality reconstructions. In this study, the authors investigated the penalized maximum likelihood (PML) method with two commonly used types of roughness penalty functions: hyperbolic potential and anisotropic total variation (TV) norm. Reconstructed images were compared with images obtained using standard FBP. Optimal parameters for PML with the hyperbolic prior are reported for the task of detecting microcalcifications embedded in breast tissue. Computer simulations were used to acquire projections in a half-cone beam geometry. The modeled setup describes a realistic breast CT benchtop system, with an x-ray spectra produced by a point source and an a-Si, CsI:Tl flat-panel detector. A voxelized anthropomorphic breast phantom with 280 μm microcalcification spheres embedded in it was used to model attenuation properties of the uncompressed woman's breast in a pendant position. The reconstruction of 3D images was performed using the separable paraboloidal surrogates algorithm with ordered subsets. Task performance was assessed with the ideal observer detectability index to determine optimal PML parameters. The authors' findings suggest that there is a preferred range of values of the roughness penalty weight and the edge preservation threshold in the penalized objective function with the hyperbolic potential, which resulted in low noise images with high contrast microcalcifications preserved. In terms of numerical observer detectability index, the PML method with optimal parameters yielded substantially improved performance (by a factor of greater than 10) compared to FBP. The hyperbolic prior was also observed to be superior to the TV norm. A few of the best-performing parameter pairs for the PML method also demonstrated superior performance for various radiation doses. In fact, using PML with certain parameter values results in better images, acquired using 2 mGy dose, than FBP-reconstructed images acquired using 6 mGy dose. A range of optimal free parameters for the PML algorithm with hyperbolic and TV norm-based potentials is presented for the microcalcification detection task, in dedicated breast CT. The reported values can be used as starting values of the free parameters, when SIR techniques are used for image reconstruction. Significant improvement in image quality can be achieved by using PML with optimal combination of parameters, as compared to FBP. Importantly, these results suggest improved detection of microcalcifications can be obtained by using PML with lower radiation dose to the patient, than using FBP with higher dose.

PML Algorithm for Positron Emission Tomography Combined With Nonlocal Fuzzy Anisotropic Diffusion Filtering

Penalized iterative algorithm, which outperforms the maximum likelihood reconstruction by utilizing the image's prior, has became a standard reconstruction approach in PET (Positron Emission Tomography). Such an algorithm is usually called PML (Penalized Maximum likelihood) algorithm. However, this kind of method still suffers from noisy propagation and edge blurring. Recently, the MRP-like (Maximum Root Prior) reconstruction which combines with anisotropic diffusion filtering, taking PDEMedian (Partial Differential Equations Median) for example, was proposed for noise removing and it could obtain better results than traditional algorithms. However, due to the shortcoming of P-M diffusion model, step artifacts could still be observed in the reconstructed image. This work aims to improve the quality of PET images using a novel nonlocal fuzzy diffusion model. Compared to the PDEMedian method, the proposed approach can impose an effective edge-preserving and noise-removing diffusion model for PET image reconstruction. Experimental results showed that the proposed method is more effective in improving quality of reconstructed images comparing with other common methods.

An adaptive penalized maximum likelihood algorithm

The LMS algorithm is one of the most popular learning algorithms for identifying an unknown system. Many variants of the algorithm have been developed based on different problem formulations and principles. In this paper, we use the penalized maximum likelihood (PML) as a principled and unified approach for developing LMS-type algorithms. We study a general solution to the problem and develop algorithms to address the problems of robustness to impulsive noise and exploiting the sparseness of the system. We perform a statistical analysis of a special case of the proposed algorithm and propose a data-driven method to update the penalty parameter. We also reveal an invariant property of the algorithm. Connections with algorithms based on stochastic gradient descent are also studied. We demonstrate the competitive performance of the proposed algorithms by numerical examples and comparison with recently published algorithms.

An Accelerated Penalized Maximum Likelihood Algorithm for Positron Emission Tomography

We develop a fast algorithm for obtaining regularized estimates of emission means in positron emission tomography (PET). The algorithm, which iteratively minimizes a penalized maximum likelihood (PML) objective function (i.e., negative log likelihood function plus a scaled penalty function), is based on a pattern search and a previously developed PML algorithm. As desired, the proposed accelerated PML (APML) algorithm guarantees nonnegative estimates and monotonically decreases the PML objective function with increasing iterations. For the case where the PML objective function is strictly convex, which is true for the class of penalty functions under consideration, we prove that the APML algorithm converges to the unique minimizer of the PML objective function. To demonstrate the utility of the APML algorithm, we applied it to real thorax phantom data and compared it to two existing PML algorithms.