USING BLOCK PSEUDOREVERSION IN SEQUENTIAL DATA PROCESSING

Предложен алгоритм последовательной обработки данных на основе блочного псевдообращения матриц полного столбцового ранга. Показывается, что формула блочного псевдообращения, лежащая в основе алгоритма, является обобщением одного шага алгоритма Гревиля псевдообращения в невырожденном случае и потому может быть использована для обобщения метода нахождения весов нейросетевой функции LSHDI (linear solutions to higher dimensional interlayer networks), основанного на алгоритме Гревиля. Представленный алгоритм на каждом этапе использует найденные на предыдущих этапах псевдообратные к блокам матрицы и, следовательно, позволяет сократить вычисления не только за счет работы с матрицами меньшего размера, но и за счет повторного использования уже найденной информации. Приводятся примеры применения алгоритма для восстановления искаженных работой фильтра (шума) одномерных сигналов и двумерных сигналов (изображений). Рассматриваются случаи, когда фильтр является статическим, но на практике встречаются ситуации, когда матрица фильтра меняется с течением времени. Описанный алгоритм позволяет непосредственно в процессе получения входного сигнала перестраивать псевдообратную матрицу с учетом изменения одного или нескольких блоков матрицы фильтра, и потому алгоритм может быть использован и в случае зависящих от времени параметров фильтра (шума). Кроме того, как показывают вычислительные эксперименты, формула блочного псевдообращения, на которой основан описываемый алгоритм, хорошо работает и в случае плохо обусловленных матриц, что часто встречается на практике The paper proposes an algorithm for sequential data processing based on block pseudoinverse of full column rank matrixes. It is shown that the block pseudoinverse formula underlying the algorithm is a generalization of one step of the Greville’s pseudoinverse algorithm in the nonsingular case and can also be used as a generalization for finding weights of neural network function in the LSHDI algorithm (linear solutions to higher dimensional interlayer networks). The presented algorithm uses the pseudoinversed matrixes found at each step, and therefore allows one to reduce the computations not only by working with matrixes of smaller size but also by reusing the already found information. Examples of application of the algorithm for signal and image reconstruction are given. The article deals with cases where noise is static but the algorithm is similarly well suited to dynamically changing noises, allowing one to process input data in blocks on the fly, depending on changes. The block pseudoreverse formula, on which the described algorithm is based, works well in the case of ill-conditioned matrixes, which is often encountered in practice

Simulated Annealing-Based Image Reconstruction for Patients With COVID-19 as a Model for Ultralow-Dose Computed Tomography

The proposed algorithm of inverse problem of computed tomography (CT), using limited views, is based on stochastic techniques, namely simulated annealing (SA). The selection of an optimal cost function for SA-based image reconstruction is of prime importance. It can reduce annealing time, and also X-ray dose rate accompanying better image quality. In this paper, effectiveness of various cost functions, namely universal image quality index (UIQI), root-mean-squared error (RMSE), structural similarity index measure (SSIM), mean absolute error (MAE), relative squared error (RSE), relative absolute error (RAE), and root-mean-squared logarithmic error (RMSLE), has been critically analyzed and evaluated for ultralow-dose X-ray CT of patients with COVID-19. For sensitivity analysis of this ill-posed problem, the stochastically estimated images of lung phantom have been reconstructed. The cost function analysis in terms of computational and spatial complexity has been performed using image quality measures, namely peak signal-to-noise ratio (PSNR), Euclidean error (EuE), and weighted peak signal-to-noise ratio (WPSNR). It has been generalized for cost functions that RMSLE exhibits WPSNR of 64.33 ± 3.98 dB and 63.41 ± 2.88 dB for 8 × 8 and 16 × 16 lung phantoms, respectively, and it has been applied for actual CT-based image reconstruction of patients with COVID-19. We successfully reconstructed chest CT images of patients with COVID-19 using RMSLE with eighteen projections, a 10-fold reduction in radiation dose exposure. This approach will be suitable for accurate diagnosis of patients with COVID-19 having less immunity and sensitive to radiation dose.

Optimization of Spatial Resolution and Image Reconstruction Parameters for the Small-Animal MetisTM PET/CT System

The aim of this study was to investigate the optimization of spatial resolution and image reconstruction parameters related to image quality in an iterative reconstruction algorithm for the small-animal MetisTM PET/CT system. We used a homemade Derenzo phantom to evaluate the image quality by visual assessment, signal-to-noise ratio, contrast, coefficient of variation, and contrast-to-noise ratio of the 0.8 mm hot rods of 8 slices in the centre of the phantom PET images. A healthy mouse study was performed to analyze the influence of optimal reconstruction parameters and Gaussian post-filter FWHM. In the phantom study, the best image quality was obtained by placing the phantom at one end, keeping the central axis parallel to X-axis of the system, selecting iterations between 30 and 40, with a reconstruction voxel of 0.314 mm and a Gaussian post-filter FWHM of 1.57 mm. The optimization of spatial resolution can reach 0.6-mm. In the animal study, it was suitable to choose a voxel size of 0.472-mm, iterations between 30 and 40, and 2.36-mm Gaussian post-filter FWHM. Our results indicate that optimal imaging conditions and reconstruction parameters are necessary to obtain high-resolution images and quantitative accuracy, especially for the high-precision identification of tiny lesions.

Ultra-limited-angle CT image reconstruction algorithm based on reweighting and edge-preserving

BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π 2 is severely ill-posed. Due to the considerably large condition number of a linear system for image reconstruction, it is extremely challenging to generate a valid reconstructed image by traditional iterative reconstruction algorithms. OBJECTIVE: To develop and test a valid ultra-limited-angle CT image reconstruction algorithm. METHODS: We propose a new optimized reconstruction model and Reweighted Alternating Edge-preserving Diffusion and Smoothing algorithm in which a reweighted method of improving the condition number is incorporated into the idea of AEDS image reconstruction algorithm. The AEDS algorithm utilizes the property of image sparsity to improve partially the results. In experiments, the different algorithms (the Pre-Landweber, AEDS algorithms and our algorithm) are used to reconstruct the Shepp-Logan phantom from the simulated projection data with noises and the flat object with a large ratio between length and width from the real projection data. PSNR and SSIM are used as the quantitative indices to evaluate quality of reconstructed images. RESULTS: Experiment results showed that for simulated projection data, our algorithm improves PSNR and SSIM from 22.46db to 39.38db and from 0.71 to 0.96, respectively. For real projection data, our algorithm yields the highest PSNR and SSIM of 30.89db and 0.88, which obtains a valid reconstructed result. CONCLUSIONS: Our algorithm successfully combines the merits of several image processing and reconstruction algorithms. Thus, our new algorithm outperforms significantly other two algorithms and is valid for ultra-limited-angle CT image reconstruction.