A new framework for utilizing side information in sparse representation

An underdetermined system of linear equation has infinitely number of answers. To find a specific solution, regularization method is used. For this propose, we define a cost function based on desired features of the solution and that answer with the best matches to these function is selected as the desired solution. In case of sparse solution, zero-norm function is selected as the cost function. In many engineering cases, there is side information which are omitted because of the zero-norm function. Finding a way to conquer zero-norm function limitation, will help to improve estimation of the desired parameter. In this regard, we utilize maximum a posterior (MAP) estimation and modify the prior information such that both sparsity and side information are utilized. As a consequence, a framework to utilize side information into sparse representation algorithms is proposed. We also test our proposed framework in orthogonal frequency division multiplexing (OFDM) sparse channel estimation problem which indicates, by utilizing our proposed system, the performance of the system improves and fewer resources are required for estimating the channel.

Схема оценивания канала для систем связи MIMO с помощью методов обобщенного разложения Холецкого и обратной подстановки

В статье исследована и реализована новая схема полуслепого оценивания канала для системы связи MIMO (Multiple-Input Multiple-Output) для случая канала с квазистатическим рэлеевским замиранием. В этой схеме канальная матрица H остается относительно постоянной в пределах блока. Канальную матрицу H можно разложить на матрицу вращения Q и нижнюю треугольную матрицу R. Треугольная матрица R оценивается вслепую при использовании метода обобщенного разложения Холецкого GCD (generalized Cholesky decomposition) на основе QR-разложения выходной ковариационной матрицы, которая использует стохастический метод слепого разделения входных сигналов на основе анализа независимых компонентов ICA (Independent Component Analysis). Матрица Q оценивается по ортогональным пилотным символам при использовании нового подхода, основанного на QR-разложении, для минимизации целевой функции. При использовании этого нового подхода ортогональные пилотные символы можно разложить на детерминированную эрмитову матрицу и верхнюю треугольную матрицу, используя QR-разложение. Наконец, матрицу Q можно оценить, используя метод обратной подстановки, который представлен в данной работе. Проведено моделирование при использовании двух передающих антенн с пространственно-временным кодом Аламоути и комбинаций из 2 и 6 приемных антенн, чтобы исследовать эффективность работы новой схемы оценивания по сравнению со стандартными схемами оценивания на базе методов наименьших квадратов LS (Least Squares) и максимальной апостериорной оценки MAP (Maximum a posterior) при использовании схемы модуляции данных BPSK (двоичная фазовая манипуляция). Полученные результаты показали, что новая схема превосходит по эффективности работы другие схемы и демонстрирует значительно лучший результат в отношении характеристики коэффициента битовых ошибок BER. Таким образом, новая схема может быть весьма полезной для решения сложной задачи полуслепого оценивания канала MIMO с помощью метода QR-разложения матрицы. Кроме того, представлен анализ ошибок в терминах матрицы ковариации ошибки при рассмотрении шума для случая ненулевой ошибки (практический случай) по сравнению со случаем нулевой ошибки.

Accelerated Compressed Sensing Based CT Image Reconstruction

In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error .Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%.Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

Accelerated Compressed Sensing Based CT Image Reconstruction

In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error .Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%.Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

Regularization by denoising sub-sampled Newton method for spectral CT multi-material decomposition

Spectral Computed Tomography (CT) is an emerging technology that enables us to estimate the concentration of basis materials within a scanned object by exploiting different photon energy spectra. In this work, we aim at efficiently solving a model-based maximum-a-posterior problem to reconstruct multi-materials images with application to spectral CT. In particular, we propose to solve a regularized optimization problem based on a plug-in image-denoising function using a randomized second order method. By approximating the Newton step using a sketching of the Hessian of the likelihood function, it is possible to reduce the complexity while retaining the complex prior structure given by the data-driven regularizer. We exploit a non-uniform block sub-sampling of the Hessian with inexact but efficient conjugate gradient updates that require only Jacobian-vector products for denoising term. Finally, we show numerical and experimental results for spectral CT materials decomposition. This article is part of the theme issue ‘Synergistic tomographic image reconstruction: part 1’.

Design of A Parallel Decoding Method for LDPC Code Generated via Primitive Polynomial

An effective way of improving decoding performance of an LDPC code is to extend the single-decoder decoding method to a parallel decoding method with multiple sub-decoders. To this end, this paper proposes a parallel decoding method for the LDPC codes constructed by m-sequence. In this method, the sub-decoders have two types. The first one contains only one decoding module using the original parity-check constraints to implement a belief propagation (BP) algorithm. The second one consists of a pre-decode module and a decoding module. The parity-check matrices for pre-decode modules are generated by the parity-check constraints of the sub-sequences sampled from an m-sequence. Then, the number of iterations of the BP process in each pre-decode module is set as half of the girth of the parity-check matrix, resulting in the elimination of the impact of short cycles. Using maximum a posterior (MAP), the least metric selector (LMS) finally picks out a codeword from the outputs of sub-decoders. Our simulation results show that the performance gain of the proposed parallel decoding method with five sub-decoders is about 0.4 dB, compared to the single-decoder decoding method at the bit error rate (BER) of 10−5.

JPEG image steganography payload location based on optimal estimation of cover co-frequency sub-image

The excellent cover estimation is very important to the payload location of JPEG image steganography. But it is still hard to exactly estimate the quantized DCT coefficients in cover JPEG image. Therefore, this paper proposes a JPEG image steganography payload location method based on optimal estimation of cover co-frequency sub-image, which estimates the cover JPEG image based on the Markov model of co-frequency sub-image. The proposed method combines the coefficients of the same position in each 8 × 8 block in the JPEG image to obtain 64 co-frequency sub-images and then uses the maximum a posterior (MAP) probability algorithm to find the optimal estimations of cover co-frequency sub-images by the Markov model. Then, the residual of each DCT coefficient is obtained by computing the absolute difference between it and the estimated cover version of it, and the average residual over coefficients in the same position of multiple stego images embedded along the same path is used to estimate the stego position. The experimental results show that the proposed payload location method can significantly improve the locating accuracy of the stego positions in low frequencies.