An algorithm for hybrid regularizers based image restoration with Poisson noise

Pham, Cong Thang; Tran, Thi Thu Thao

doi:10.14736/kyb-2021-3-0446

Cited by 2 publications

(2 citation statements)

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“…К таким процессам относятся, в частности, передача нервных импульсов [1], образование капель в метеорологии [2], другие явления в гидрологии и гидроклиматологии [3]. Пуассоновские процессы используются в разработке моделей распределения пикселей в электронной микроскопии и улучшении качества изображения [4,5,6,7], визуализации медицинской томографии [8,9].…”

Section: Introductionunclassified

Algorithm for Calculating Noise Immunity of Cognitive Dynamic Systems in the State Space

Solodov,

Trembach,

Zhovnovatiy

2023

Otkryt. obraz. (Mosk.)

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The research method consists in applying the state space method, widely used in the study of automatic dynamical systems, to describe the behavior of cognitive systems. It is assumed, that at the input of the cognitive system, there is a signal and interference described by Poisson point processes, modeling the amount of information, the amount of emotional stress, etc., corresponding to each event. The cognitive properties of the system in the paper are taken into account by two circumstances. Firstly, events localized in time are characterized in the paper not only by the Poisson distribution of the times of their occurrence, but also by some random variables that characterize the importance (significance) events for the system. A typical example is the attribution of a certain amount of information to each event, if an information processing system is modeled. Another example is the emotional reaction of a person to the appearance of stress, described in a classic work on psychology. In this case, the point is the event that causes stress, and the effects of stress on the system are modeled by the relative magnitude of stress in accordance with the Holmes and Rahe scale. Secondly, the cognitive system processes, assimilates, adapts to the impact that each event has on it with its inherent speed. In this paper, this phenomenon is modeled as the passage of a point process through a dynamic system described by differential equations. Such processes are called filtered point processes. Examples of impacts are given and, for simplicity, an assumption is made about the magnitude of the impact as the amount of information received by the system when an event occurs. Thus, the model of a cognitive system is a dynamic system described by a differential equation in the state space, at the input of which messages with a certain information load appear at random discrete moments of time.As for any technical system, the cognitive system faces the task of evaluating the quality of its work. In this regard, the paper substantiates the use of a convenient quality index from an engineering point of view and an appropriate criterion in the form of a signal – interference ratio. The new results are differential equations in the state space for the mathematical expectations of the signal and interference, as well as an algorithm for calculating the noise immunity of the cognitive system. As an example, a graph of the noise immunity of a particular cognitive system is calculated and presented, confirming an intuitive idea of its behavior.In conclusion, it is noted that the main result of the paper is an algorithm for calculating the noise immunity of cognitive systems using differential equations that allow calculating the behavior of non-stationary cognitive systems under any point impacts described by a non-stationary function of the intensities of the appearance of points. The equations of behavior of the mathematical expectation of the processed information are reduced to a canonical form, which allows them to be applied to a variety of practical tasks, for example, to the description of hierarchical cognitive structures when the output of one level is the input of another.

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Section: Introductionunclassified

Algorithm for Calculating Noise Immunity of Cognitive Dynamic Systems in the State Space

Solodov,

Trembach,

Zhovnovatiy

2023

Otkryt. obraz. (Mosk.)

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“…For many years, many variational methods have been proposed to handle the restoration problem with Poisson noise [16][17][18][19][20][21][22][23]. One of variational models for Poissonian image reconstruction is the one based on the total variation (TV) norm as regularization term [24]:…”

Section: Introductionmentioning

confidence: 99%

Combined total variation of first and fractional orders for Poisson noise removal in digital images

Pham

Tran

Pham

et al. 2021

ICS

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Introduction: Many methods have been proposed to handle the image restoration problem with Poisson noise. A popular approach to Poissonian image reconstruction is the one based on Total Variation. This method can provide significantly sharp edges and visually fine images, but it results in piecewise-constant regions in the resulting images. Purpose: Developing an adaptive total variation-based model for the reconstruction of images contaminated by Poisson noise, and an algorithm for solving the optimization problem. Results: We proposed an effective way to restore images degraded by Poisson noise. Using the Bayesian framework, we proposed an adaptive model based on a combination of first-order total variation and fractional order total variation. The first-order total variation model is efficient for suppressing the noise and preserving the keen edges simultaneously. However, the first-order total variation method usually causes artifact problems in the obtained results. To avoid this drawback, we can use high-order total variation models, one of which is the fractional-order total variation-based model for image restoration. In the fractional-order total variation model, the derivatives have an order greater than or equal to one. It leads to the convenience of computation with a compact discrete form. However, methods based on the fractional-order total variation may cause image blurring. Thus, the proposed model incorporates the advantages of two total variation regularization models, having a significant effect on the edge-preserving image restoration. In order to solve the considered optimization problem, the Split Bregman method is used. Experimental results are provided, demonstrating the effectiveness of the proposed method. Practical relevance: The proposed method allows you to restore Poissonian images preserving their edges. The presented numerical simulation demonstrates the competitive performance of the model proposed for image reconstruction. Discussion: From the experimental results, we can see that the proposed algorithm is effective in suppressing noise and preserving the image edges. However, the weighted parameters in the proposed model were not automatically selected at each iteration of the proposed algorithm. This requires additional research.

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An algorithm for hybrid regularizers based image restoration with Poisson noise

Cited by 2 publications

References 0 publications

Algorithm for Calculating Noise Immunity of Cognitive Dynamic Systems in the State Space

Algorithm for Calculating Noise Immunity of Cognitive Dynamic Systems in the State Space

Combined total variation of first and fractional orders for Poisson noise removal in digital images

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