Study on analytical noise propagation in convolutional neural network methods used in computed tomography imaging

Neural network methods have recently emerged as a hot topic in computed tomography(CT) imaging owing to their powerful fitting ability;however, their potential applications still need to be carefully studied because their results are often difficult to interpret and are ambiguous in generalizability. Thus, quality assessments of the results obtained from a neural network are necessary to evaluate the neural network. Assessing the image quality of neural networks using traditional objective measurements is not appropriate because neural networks are nonstationary and nonlinear. In contrast, subjective assessments are trustworthy, although they are time-and energy-consuming for radiologists. Model observers that mimic subjective assessment require the mean and covariance of images, which are calculated from numerous image samples;however, this has not yet been applied to the evaluation of neural networks. In this study, we propose an analytical method for noise propagation from a single projection to efficiently evaluate convolutional neural networks(CNNs) in the CT imaging field. We propagate noise through nonlinear layers in a CNN using the Taylor expansion. Nesting of the linear and nonlinear layer noise propagation constitutes the covariance estimation of the CNN. A commonly used U-net structure is adopted for validation. The results reveal that the covariance estimation obtained from the proposed analytical method agrees well with that obtained from the image samples for different phantoms, noise levels, and activation functions, demonstrating that propagating noise from only a single projection is feasible for CNN methods in CT reconstruction. In addition, we use covariance estimation to provide three measurements for the qualitative and quantitative performance evaluation of U-net. The results indicate that the network cannot be applied to projections with high noise levels and possesses limitations in terms of efficiency for processing low-noise projections. U-net is more effective in improving the image quality of smooth regions compared with that of the edge. LeakyReLU outperforms Swish in terms of noise reduction.

Viewing the noise propagation mechanism in a unidirectional transition cascade from the perspective of stability

Noise and noise propagation are inevitable and play a constructive role in various biological processes.The stability of cell homeostasis is also a critical issue.In the unidirectional transition cascade of colon cells,stem cells(SCs)are the source.They differentiate into transit-amplifying cells(TACs),and TACs differentiate into fully differentiated cells(FDCs).Two differentiation processes are irreversible.The stability factor is introduced so that the noise propagation mechanism from the perspective of stability is studied according to the noise propagation formulas.It is found that the value of the stability factor corresponding to the minimum noise in FDCs may be the best choice to enable colon cells to maintain high stability and low noise of the cascade.Moreover,for the source cell,the total noise only includes intrinsic noise;for the downstream cell with self-proliferation capability,the total noise mainly depends on its intrinsic noise and transmitted noise from upstream cells,and its intrinsic noise is dominant.For the downstream cell without self-proliferation capability,the total noise is mainly determined by transmitted noises from upstream cells,and there is a minimum value.This work provides a new approach for studying the mechanism of noise propagation while considering the stability of cell homeostasis in biological systems.

Noise decomposition algorithm and propagation mechanism in feed-forward gene transcriptional regulatory loop

Feed-forward gene transcriptional regulatory networks, as a set of common signal motifs, are widely distributed in the biological systems. In this paper, the noise characteristics and propagation mechanism of various feed-forward gene transcriptional regulatory loops are investigated, including （i） coherent feed-forward loops with AND-gate, （ii） coherent feed-forward loops with OR-gate logic, and （iii） incoherent feed-forward loops with AND-gate logic. By introducing logarithmic gain coefficient and using linear noise approximation, the theoretical formulas of noise decomposition are derived and the theoretical results are verified by Gillespie simulation. From the theoretical and numerical results of noise decomposition algorithm, three general characteristics about noise transmission in these different kinds of feed-forward loops are observed, i） The two-step noise propagation of upstream factor is negative in the incoherent feed-forward loops with AND-gate logic, that is, upstream factor can indirectly suppress the noise of downstream factors, ii） The one-step propagation noise of upstream factor is non-monotonic in the coherent feed-forward loops with OR-gate logic, iii） When the branch of the feed-forward loop is negatively controlled, the total noise of the downstream factor monotonically increases for each of all feed-forward loops. These findings are robust to variations of model parameters. These observations reveal the universal rules of noise propagation in the feed-forward loops, and may contribute to our understanding of design principle of gene circuits.

Adaptive digital backward propagation based on variance of intensity noise

An adaptive digital backward propagation(ADBP) algorithm is proposed and experimentally demonstrated based on the variance of the intensity noise. The proposed algorithm can self-determine the unknown nonlinear coefficient γ and the nonlinear compensation parameter ξ. Compared to the scheme based on the variance of phase noise, the proposed algorithm can avoid the repeated frequency offset compensation and carrier phase recovery. The simulation results show that the system’s performance compensated by the proposed method is comparable to conventional ADBP schemes. The performance of the proposed algorithm is simulated in40/112 Gb/s polarization-division multiplexing(PDM)-quadrature phase-shift keying(QPSK) and 224 Gb/s PDM-16-quadrature amplitude modulation(QAM) systems and further experimentally verified in a 40 Gb/s PDM-QPSK coherent optical communication system over a 720 km single-mode fiber.