Optimal Image Reconstruction Research Articles

Assessing Transducer Parameters for Accurate Medium Sound Speed Estimation and Image Reconstruction.

The influence of the transducer lens on image reconstruction is often overlooked. Lenses usually exhibit a lower sound speed than soft biological tissues. In academic research, the exact lens sound speed and thickness are typically unknown. Here, we present a simple and nondestructive method to characterize the lens sound speed and thickness as well as the time to peak of the round-trip ultrasound waveform, another key parameter for optimal image reconstruction. We applied our method to three transducers with center frequencies of 2.5, 7.5, and 15 MHz. We estimated the three parameters with an element-by-element transmission sequence that records internal reflections within the lens. We validated the retrieved parameters using an autofocusing approach that estimates sound speed in water. We show that the combination of our parameters estimation method with two-layer ray tracing outperforms standard image reconstruction. For all transducers, we successfully improved the accuracy of medium sound speed estimation, spatial resolution, and contrast. The proposed method is simple and robust and provides an accurate estimation of the transducer lens parameters and the time to peak of the ultrasound waveform, which leads to improved ultrasound image quality.

Optimal Image Reconstruction and Anomaly Detection in Diffuse Optical Tomography with Hybrid CNN-LSTM

Optimal Image Reconstruction and Anomaly Detection in Diffuse Optical Tomography with Hybrid CNN-LSTM

Stability of radiomic features from positron emission tomography images: a phantom study comparing advanced reconstruction algorithms and ordered subset expectation maximization.

In this study, we compared the repeatability and reproducibility of radiomic features obtained from positron emission tomography (PET) images according to the reconstruction algorithm used-advanced reconstruction algorithms, such as HYPER iterative (IT), HYPER deep learning reconstruction (DLR), and HYPER deep progressive reconstruction (DPR), or traditional Ordered Subset Expectation Maximization (OSEM)-to understand the potential variations and implications of using advanced reconstruction techniques in PET-based radiomics. We used a heterogeneous phantom with acrylic spherical beads (4- or 8-mm diameter) filled with 18F. PET images were acquired and reconstructed using OSEM, IT, DLR, and DPR. Original and wavelet radiomic features were calculated using SlicerRadiomics. Radiomic feature repeatability was assessed using the Coefficient of Variance (COV) and intraclass correlation coefficient (ICC), and inter-acquisition time reproducibility was assessed using the concordance correlation coefficient (CCC). For the 4- and 8-mm diameter beads phantom, the proportion of radiomic features with a COV < 10% was equivocal or higher for the advanced reconstruction algorithm than for OSEM. ICC indicated that advanced methods generally outperformed OSEM in repeatability, except for the original features of the 8-mm beads phantom. In the inter-acquisition time reproducibility analysis, the combinations of 3 and 5min exhibited the highest reproducibility in both phantoms, with IT and DPR showing the highest proportion of radiomic features with CCC > 0.8. Advanced reconstruction methods provided enhanced stability of radiomic features compared with OSEM, suggesting their potential for optimal image reconstruction in PET-based radiomics, offering potential benefits in clinical diagnostics and prognostics.

NEMA NU 2-2018 evaluation and image quality optimization of a new generation digital 32-cm axial field-of-view Omni Legend PET-CT using a genetic evolutionary algorithm

A performance evaluation was conducted on the new General Electric (GE) digital Omni Legend PET-CT system with 32 cm extended field of view. The first commercially available clinical digital bismuth germanate system. The system does not use time of flight (ToF). Testing was performed in accordance with the NEMA NU2–2018 standard. A comparison was made between two other commercial GE scanners with extended fields of view; the Discovery MI − 6 ring (ToF enabled) and the Discovery IQ (non-ToF). A genetic evolutionary algorithm was developed to optimize image reconstruction parameters from image quality assessments. The Omni demonstrated average spatial resolutions at 1 cm radial offset as 3.9 mm FWHM. The total system sensitivity at the center was 44.36 cps/kBq. The peak NECR was measured as 501 kcps at 17.8 kBq ml−1 with a 35.48% scatter fraction. The maximum count-rate error below NECR peak was 5.5%. Using standard iterative reconstructions, sphere contrast recovery coefficients were from 52.7 ± 3.2% (10 mm) to 92.5 ± 2.4% (37 mm). The PET-CT co-registration accuracy was 2.4 mm. In place of ToF, the Omni employs software corrections through a pre-trained neural network (PDL) (trained on non-ToF to ToF) that takes Bayesian penalized likelihood reconstruction (Q.Clear) images as input. The optimum parameters for image reconstruction, determined using the genetic algorithm were a Q.Clear parameter, β, of 350 and a ‘medium’ PDL setting. Using standard iterative reconstructions, the Omni initially showed increased background variability compared to the Discovery MI. With optimized PDL reconstruction parameters selected using the genetic algorithm the performance of the Omni surpassed that of the Discovery MI on all NEMA tests. The genetic algorithm’s demonstrated ability to enhance image quality in PET-CT imaging underscores the importance of algorithm driven optimization and underscores the requirement to validate its use in the clinical setting.

Dynamic Computed Tomography Angiography for capturing vessel wall motion: A phantom study for optimal image reconstruction.

Reliably capturing sub-millimeter vessel wall motion over time, using dynamic Computed Tomography Angiography (4D CTA), might provide insight in biomechanical properties of these vessels. This may improve diagnosis, prognosis, and treatment decision making in vascular pathologies. The aim of this study is to determine the most suitable image reconstruction method for 4D CTA to accurately assess harmonic diameter changes of vessels. An elastic tube (inner diameter 6 mm, wall thickness 2 mm) was exposed to sinusoidal pressure waves with a frequency of 70 beats-per-minute. Five flow amplitudes were set, resulting in increasing sinusoidal diameter changes of the elastic tube, measured during three simulated pulsation cycles, using ECG-gated 4D CTA on a 320-detector row CT system. Tomographic images were reconstructed using one of the following three reconstruction methods: hybrid iterative (Hybrid-IR), model-based iterative (MBIR) and deep-learning based (DLR) reconstruction. The three reconstruction methods where based on 180 degrees (half reconstruction mode) and 360 degrees (full reconstruction mode) raw data. The diameter change, captured by 4D CTA, was computed based on image registration. As a reference metric for diameter change measurement, a 9 MHz linear ultrasound transducer was used. The sum of relative absolute differences (SRAD) between the ultrasound and 4D CTA measurements was calculated for each reconstruction method. The standard deviation was computed across the three pulsation cycles. MBIR and DLR resulted in a decreased SRAD and standard deviation compared to Hybrid-IR. Full reconstruction mode resulted in a decreased SRAD and standard deviations, compared to half reconstruction mode. 4D CTA can capture a diameter change pattern comparable to the pattern captured by US. DLR and MBIR algorithms show more accurate results than Hybrid-IR. Reconstruction with DLR is >3 times faster, compared to reconstruction with MBIR. Full reconstruction mode is more accurate than half reconstruction mode.

A depth-of-interaction rebinning method based on both geometric and activity weights

Background and objectiveFor positron emission tomography (PET) scanners with depth-of-interaction (DOI) measurement, the DOI rebinning method that utilizes DOI information to process the projection data is critical to image quality. Current DOI rebinning methods map coincidence events onto the rebinned sinogram based on the correlation of lines of response (LOR). This study aims to incorporate prior radioactivity distribution of the imaging object into DOI rebinning to obtain better image quality. MethodsA DOI rebinning method based on both geometric and activity weights was proposed to assign coincidence events to the rebinned sinogram defined by a virtual ring. The geometric weights, representing the correlation between LORs, were calculated based on the areas of intersection. The activity weights, reflecting the activity distribution of the imaging object, were derived from the previous reconstructed image. ResultsMonte Carlo simulation data from four phantoms, including the image quality phantom, Derenzo phantom, and two rat-like ROBY phantoms, was used to evaluate the proposed method. The recovery coefficient (RC), contrast recovery coefficient (CRC), structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR) were used as image quality metrics. Compared to other DOI rebinning methods, the proposed method achieved the highest RC (maximum improvement of 32%) and CRC at the same noise level and was also optimal in terms of the SSIM and PSNR. Meanwhile, incorporating the prior activity distribution into DOI rebinning also improved the image reconstruction speed. ConclusionsThis work developed a new DOI rebinning method combining the correlation of LORs with the prior activity distribution, achieving relatively optimal image quality and reconstruction speed. Furthermore, it still needs to be evaluated on the actual equipment.

Joint Spatial-Spectral Pattern Optimization and Hyperspectral Image Reconstruction

Employing multispectral filter array (MSFA) and several spectral sensitivity functions (SSFs) as hardware encoder and spatial demosaicing (SpaDM) and spectral super-resolution (SpeSR) methods as software decoder to capture hyperspectral image (HSI) is a common method of computational spectral snapshot imaging. Previous works treat SpaDM and SpeSR as two separative processes, and the effect of MSFA and SSF patterns are rarely investigated. In this paper, we propose a deep-learning based method for high quality hyperspectral imaging by joint spatial-spectral optimization, including joint MSFA and SSF optimization, joint SpaDM and SpeSR, and joint pattern optimization and HSI reconstruction. To capture optimal mosaic image in hardware encoder, we design several spatial-spectral pattern optimization layers to automatically optimize the MSFA and SSF. To recover HSI with SpaDM and SpeSR in software decoder, we unfold an optimization algorithm into a convolutional neural network to explicitly consider the observation model and improve the interpretability of the network. Moreover, to boost the quality of hyperspectral imaging, we optimize spatial-spectral pattern and reconstruct HSI in a joint manner. Extensive evaluations and comparisons on HSI spatial and spectral reconstruction demonstrate our joint optimization method outperforms state-of-the-art methods, in terms of both restoration accuracy and visual quality.

Performance Prediction, Sensitivity Analysis and Parametric Optimization of Electrical Impedance Tomography Using A Bioelectrical Tissue Simulation Platform.

There is an urgent need to bring forth portable, low-cost, point-of-care diagnostic instruments to monitor patient health and wellbeing. This is elevated by the COVID-19 global pandemic in which the availability of proper lung imaging equipment has proven to be pivotal in the timely treatment of patients. Electrical impedance tomography (EIT) has long been studied and utilized as such a critical imaging device in hospitals especially for lung ventilation. Despite decades of research and development, many challenges remain with EIT in terms of 1) optimal image reconstruction algorithms, 2) simulation and measurement protocols, 3) hardware imperfections, and 4) uncompensated tissue bioelectrical physiology. Due to the inter-connectivity of these challenges, singular solutions to improve EIT performance continue to fall short of the desired sensitivity and accuracy. Motivated to gain a better understanding and optimization of the EIT system, we report the development of a bioelectric facsimile simulator demonstrating the dynamic operations, sensitivity analysis, and reconstruction outcome prediction of the EIT sensor with stepwise visualization. By building a sandbox platform to incorporate full anatomical and bioelectrical properties of the tissue under study into the simulation, we created a tissue-mimicking phantom with adjustable EIT parameters to interpret bioelectrical interactions and to optimize image reconstruction accuracy through improved hardware setup and sensing protocol selections.

Highly coherent illumination for imaging through opacity

Imaging through opacity has captured extensive attention in recent years for its promising applications in bioimaging systems and information extraction from scrambled light. Many optimized image reconstruction algorithms and advanced imaging scenarios are introduced and intensively studied in previous researches. However, intensity-based image reconstruction under the highly coherent light illumination is still a major challenge due to the strong interference effect. Here, we demonstrate that imaging through opacity can be implemented efficiently even under the highly coherent illumination with the aid of an intensity-based/incoherent deconvolution algorithm. Based on the experimental and theoretical analysis, we find the small phase correlation length of the diffuser plays a pivotal role in enabling the incoherent deconvolution operation for highly coherent illumination. Furthermore, the deconvolution algorithm shows insensitivity to the light coherence since the spatial frequencies of the object are well preserved in the spatial frequency spectrum of the speckle pattern. Our results provide a phase-information-free scheme for imaging through opacity under the highly coherent illumination. We anticipate our work would motivate the deep understanding of imaging using highly coherent illumination, increase the structural robustness of imaging systems and facilitate wavelength-sensitive imaging applications.

Development and Evaluation of the Fourier Spectral Distortion Metric.

A spatial resolution metric is presented for tomosynthesis. The Fourier spectral distortion metric (FSD) was developed to evaluate specific resolution properties of different imaging techniques for digital tomosynthesis using a star pattern image to plot modulation in the frequency domain. The FSD samples the spatial resolution of a star-pattern image tangentially over an acute angle and for a range of spatial frequencies in a 2D image or 3D image reconstruction slice. The FSD graph portrays all frequencies present in a star pattern quadrant. In addition to the fundamental input frequency of the star pattern, the FSD graph shows spectral leakage, square wave harmonics, and residual noise. The contrast transfer function (CTF) is obtained using the FSD graph. The CTF is analogous to the modulation transfer function (MTF), but it is not normalized to unity at zero spatial frequency. Unlike the MTF, this metric separates the fundamental input-frequency from the other signals in the Fourier domain. This metric helps determine optimal image reconstruction parameters, the in-plane limit of spatial resolution with respect to aliased signals, and a threshold criterion for an image to support super resolution and reduce aliasing artifacts. Various sampling parameters were evaluated to optimize this metric and ascertain measurement accuracy. The FSD adequately compares resolution properties of 2D images and 3D image reconstruction slices for various x ray imaging modes without suppressing aliased signals.

Effect of Automatic Extraction Accuracy by Different Image Reconstruction Methods Using a Three-dimensional Image Analysis System for Pulmonary Segmentectomy Preoperative CT Angiography

This study aimed to determine the optimal image reconstruction method for preoperative computed tomography (CT) angiography for pulmonary segmentectomy. This study enrolled 20 patients who underwent contrast-enhanced CT examination for pulmonary segmentectomy. The optimal image reconstruction algorithm among four different reconstruction algorithms (filtered back projection, hybrid iterative reconstruction, model- based iterative reconstruction, and deep learning reconstruction [DLR]) was investigated by assessing the CT numbers, vessel extraction ratios, and misclassification ratios. The vessel extraction ratios for main and subsegment branches reconstructed using DLR were significantly higher than those using other reconstruction algorithms (96.7% and 90.8% for pulmonary artery and vein, respectively). The misclassification ratios at the right upper lobe pulmonary vessels (V1 and V2) were especially high because they were close to the superior vena cava, and their CT numbers were similar in all four reconstructions. In conclusion, the DLR allows a high extraction rate of pulmonary blood vessels and a low misclassification rate of automatic extraction.

Determination of Bone SPECT Image Reconstruction Conditions in the Head and Neck Region

Quantitative analysis using a standardized uptake value (SUV) has become possible for single-photon emission computed tomography-computed tomography (SPECT-CT) of bone. However, previous research was targeted to the trunk area, and there are few studies for the head and neck region. Therefore, the purpose of this study was to determine the optimal image reconstruction conditions for bone SPECT of the head and neck using a phantom study. The radioactivity concentration of the 99mTc solution enclosed in the cylindrical phantom was set to the same count rate as in clinical cases, and six hot spheres (10, 13, 17, 22, 28, 37 mm) with four times the concentration were placed within it. The image reconstruction was 3D-OSEM, and the reconstruction conditions were varied by the number of iterative updates and the width of the Gaussian filter. Quantitative evaluations of the image quality were performed using the % contrast, background variability, and SUV for the hot spheres and background. A visual evaluation was performed by four observers to determine the optimal image reconstruction conditions for bone SPECT of the head and neck region. The concentration of the 99mTc solution enclosed in the phantom was 6.95 (kBq/ml). Based on the results of the quantitative and visual evaluations, the optimal image reconstruction conditions were iterative updates=60 (subset: 10, iteration: 6) and a Gaussian filter of 7.8 mm. The optimal image reconstruction conditions were subset=10, iterations=6, and a Gaussian filter of 7.8 mm.

Artificial intelligence in cardiac radiology.

Artificial intelligence (AI) is entering the clinical arena, and in the early stage, its implementation will be focused on the automatization tasks, improving diagnostic accuracy and reducing reading time. Many studies investigate the potential role of AI to support cardiac radiologist in their day-to-day tasks, assisting in segmentation, quantification, and reporting tasks. In addition, AI algorithms can be also utilized to optimize image reconstruction and image quality. Since these algorithms will play an important role in the field of cardiac radiology, it is increasingly important for radiologists to be familiar with the potential applications of AI. The main focus of this article is to provide an overview of cardiac-related AI applications for CT and MRI studies, as well as non-imaging-based applications for reporting and image optimization.

Optimal texture image reconstruction method for improvement of SAR image matching

Image matching is an important step that is taken in most synthetic aperture radar (SAR) images applications. In this study, a method is proposed for texture image reconstruction to improve SAR image matching. This method consists of three major steps. First, textural features are extracted. Second optimal texture images (OTIs) are created using extracted features. Texture optimisation is conducted using a cat swarm optimisation algorithm. The cost function is the number of correct matched points that are obtained from speeded-up robust features (SURFs) image matching algorithm. Finally, corresponding points on stereo OTI pairs are matched. Experiments were conducted on spaceborne SAR image pairs consist of RADARSAT-2, ALOS-PALSAR, and Sentinel-1. Results demonstrate that the proposed method has better results in terms of the number of matched points compared to the result of the original SURF and scale-invariant feature transform methods as two common matching methods.

Superresolution using supergrowth and intensity contrast imaging

This article explores the possibility of another kind of superresolution functionality that exists in superoscillatory functions besides the “faster than Fourier” feature. We posit the ability to resolve images with resolution beyond the wavelength of light used via the exponentially rising and falling parts of superoscillatory and related functions. We give some preliminary results that this technique can indeed be useful using intensity contrast imaging. The exponential growth or decay of these functions can give higher resolution of the image, provided the rate of falloff is faster than the smallest wavenumber of the light that is used: “supergrowth”. One limitation of this proposal is the high dynamic range the detector would need to possess to map out several decades of intensity. An outstanding question is to find the optimal image reconstruction method using a superoscillatory point spread function that makes optimal use of the function’s unique properties. We give a number of conjectures about this new kind of supergrowth imaging technique as an outlook for future research.

Selection Criteria for Determination of Optimal Reconstruction Method for Cu-64 Trastuzumab Dosimetry on Siemens Inveon PET Scanner.

The goal of this study was to suggest criteria for the determination of the optimal image reconstruction algorithm for image-based dosimetry of Cu-64 trastuzumab PET in a mouse model. Image qualities, such as recovery coefficient (RC), spill-over ratio (SOR), and non-uniformity (NU), were measured according to National Electrical Manufacturers Association (NEMA) NU4-2008. Mice bearing a subcutaneous tumor (, HER2 NCI N87) were injected with monoclonal antibodies (trastuzumab) with Cu-64. Preclinical mouse PET images were acquired at 4 time points after injection (2, 15, 40 and 64 h). Phantom and Cu-64 trastuzumab PET images were reconstructed using various reconstruction algorithms (filtered back projection (FBP), 3D reprojection algorithm (FBP-3DRP), 2D ordered subset expectation maximization (OSEM 2D), and OSEM 3D maximum a posteriori (OSEM3D-MAP)) and filters. The absorbed dose for the tumor and the effective dose for organs for Cu-64 trastuzumab PET were calculated using the OLINDA/EXM program with various reconstruction algorithms. Absorbed dose for the tumor ranged from 923 mGy/MBq to 1830 mGy/MBq with application of reconstruction algorithms and filters. When OSEM2D was used, the effective osteogenic dose increased from 0.0031 to 0.0245 with an increase in the iteration number (1 to 10). In the region of kidney, the effective dose increased from 0.1870 to 1.4100 when OSEM2D was used with iteration number 1 to 10. To determine the optimal reconstruction algorithms and filters, a correlation between RC and NU was plotted and selection criteria (0.9 < RC < 1.0 and < 10% of NU) were suggested. According to the selection criteria, OSEM2D (iteration 1) was chosen for the optimal reconstruction algorithm. OSEM2D (iteration 10) provided 154.7% overestimated effective dose and FBP with a Butterworth filter provided 20.9% underestimated effective dose. We suggested OSEM2D (iteration 1) for the calculation of the effective dose of Cu-64 trastuzumab on an Inveon PET scanner.

223Ra-dichloride therapy of bone metastasis: optimization of SPECT images for quantification

Background223Ra imaging is crucial to evaluate the successfulness of the therapy of bone metastasis of castration-resistant prostate cancer (CRPC). The goals of this study were to establish a quantitative tomographic 223Ra imaging protocol with clinically achievable conditions, as well as to investigate its usefulness and limitations.We performed several experiments using the Infinia Hawkeye 4 gamma camera (GE) and physical phantoms in order to assess the optimal image acquisition and reconstruction parameters, such as the windows setting, as well as the iteration number and filter of the reconstruction algorithm. Then, based on the MIRD pamphlet 23, we used a NEMA phantom and an anthropomorphic TORSO® phantom to calibrate the gamma camera and investigate the accuracy of quantification.ResultsExperiences showed that the 85 keV ± 20%, 154 keV ± 10%, and 270 keV ± 10% energy windows are the most suitable for 223Ra imaging.The study with the NEMA phantom showed that the OSEM algorithm with 2 iterations, 10 subsets, and the Butterworth filter offered the best compromise between contrast and noise. Moreover, the calibration factors for different sphere sizes (26.5 ml, 11.5 ml, and 5.6 ml) were constant for 223Ra concentrations ranging between 6.5 and 22.8 kBq/ml. The values found are 73.7 cts/s/MBq, 43.8 cts/s/MBq, and 43.4 cts/s/MBq for 26.5 ml, 11.5 ml, and 5.6 ml sphere, respectively. For concentration lower than 6.5 kBq/ml, the calibration factors exhibited greater variability pointing out the limitations of SPECT/CT imaging for quantification.By the use of a TORSO® phantom, we simulated several tumors to normal tissue ratios as close as possible to clinical conditions. Using the calibration factors obtained with the NEMA phantom, for 223Ra concentrations higher than 8 kBq/ml, we were able to quantify the activity with an error inferior to 18.8% in a 5.6 ml lesion.ConclusionsAbsolute quantitative 223Ra SPECT imaging appears feasible once the dimension of the target is determined. Further evaluation should be needed to apply the calibration factor-based quantitation to clinical 223Ra SPECT/CT imaging. This will open the possibility for patient-specific 223Ra treatment planning and therapeutic outcome prediction in patients.

Towards a Combination of Low Rank and Sparsity in EIT Imaging

Electrical impedance tomography (EIT) calculates the internal conductivity distribution of a body using electrical contact measurement and has become increasingly attractive in the biomedical field. However, the design of optimal tomography image reconstruction algorithms has not achieved an adequate level of progress and maturity. The spatial-temporal properties are crucial for the improvement of reconstruction quality and efficiency in dynamic EIT reconstruction. However, these properties have not been fully utilized in previous research. In this paper, a mathematical model for EIT reconstruction is built upon a combination of the low-rank and the sparsity theories. In addition to the low-rank method based on the nuclear norm constraint, the patch-based sparse method is also used to obtain the spatial features of a reconstructed image, according to the characteristic of an irregular boundary for the EIT image. The mathematical model of the new method is solved using the variable split (VS) algorithm. The imaging results are compared with the reconstruction results of the traditional algorithms. The experimental results demonstrate better performance of the new method compared with the traditional methods. The effectiveness of the proposed scheme is verified.

Comparison of reconstruction and acquisition choices for quantitative T2* maps and synthetic contrasts

Aim and scopeA Gradient Echo Plural Contrast Imaging technique (GEPCI) is a post-processing method, which can be used to obtain quantitative T2* values and generate multiple synthetic contrasts from a single acquisition. However, scan duration and image reconstruction from k-space data present challenges in a clinical workflow. This study aimed at optimizing image reconstruction and acquisition duration to facilitate a post-processing method for synthetic image contrast creation in clinical settings. Materials and methodsThis study consists of tests using the American College of Radiology (ACR) image quality phantom, two healthy volunteers, four mild traumatic brain injury patients and four small vessel disease patients. The measurements were carried out on a 3.0 T scanner with multiple echo times. Reconstruction from k-space data and DICOM data with two different coil-channel combination modes were investigated. Partial Fourier techniques were tested to optimize the scanning time. ConclusionsSum of squares coil-channel combination produced artifacts in phase images, but images created with adaptive combination were artifact-free. The voxel-wise median signed difference of T2* between the vendor’s adaptive channel combination and k-space reconstruction modes was 2.9 ± 0.7 ms for white matter and 4.5 ± 0.6 ms for gray matter. Relative white matter/gray matter contrast of all synthetic images and contrast-to-noise ratio of synthetic T1-weighted images were almost equal between reconstruction modes. Our results indicate that synthetic contrasts can be generated from the vendor’s DICOM data with the adaptive combination mode without affecting the quantitative T2* values or white matter/gray matter contrast.

On monotone and primal-dual active set schemes for ell ^p-type problems, p in (0,1

Nonsmooth nonconvex optimization problems involving the ell ^p quasi-norm, p in (0, 1], of a linear map are considered. A monotonically convergent scheme for a regularized version of the original problem is developed and necessary optimality conditions for the original problem in the form of a complementary system amenable for computation are given. Then an algorithm for solving the above mentioned necessary optimality conditions is proposed. It is based on a combination of the monotone scheme and a primal-dual active set strategy. The performance of the two algorithms is studied by means of a series of numerical tests in different cases, including optimal control problems, fracture mechanics and microscopy image reconstruction.