Solution Dynamics, Causality, and Critical Behavior of the Regularization Parameter in Total Variation Denoising Problems

نویسندگان

  • ANDY M. YIP
  • FREDERICK PARK
چکیده

We analyze the role of the regularization parameter λ in the total variation (TV) denoising model. There are several contributions in this paper. (1) We realize that, beyond controlling the smoothness of the solution, λ exhibits another significant behavior — causality. This property allows us to solve the problem by incrementally increasing λ so that each solution at a given regularization parameter can be used to solve the problem at a larger parameter efficiently. We call such a technique parameter marching. (2) While λ is allowed to take a continuum of non-negative values, we show that only a unique finite number of them are critical and useful in the sense that they correspond to meaningful changes in signal features. Furthermore, we present the construction of these critical λ’s. (3) Since the analysis of the TV model is carried out by deriving exact solutions and investigating the dynamics of the solutions as λ varies, many properties of the model which previously have not been studied to a rigorous extent are clearly revealed. A discussion of other possible further research within the parameter marching framework is also given. In particular, we present some insights into the improvement of the TV model provided by our analysis. We also discuss the possibility of applying parameter marching techniques to solving general Tikhonov-type regularization problems.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A new principle for choosing regularization parameter in certain inverse problems

A new parameter choice rule for inverse problems is introduced. This parameter choice rule was developed for total variation regularization in electron tomography and might in general be useful for L regularization of inverse problems with high levels of noise in the data.

متن کامل

A Novel Mechanical Fault Diagnosis Scheme Based on the Convex 1-D Second-Order Total Variation Denoising Algorithm

Convex 1-D first-order total variation (TV) denoising is an effective method for eliminating signal noise, which can be defined as convex optimization consisting of a quadratic data fidelity term and a non-convex regularization term. It not only ensures strict convex for optimization problems, but also improves the sparseness of the total variation term by introducing the non-convex penalty fun...

متن کامل

Statistical Tests for Total Variation Regularization Parameter Selection

Total Variation (TV) is an effective method of removing noise in digital image processing while preserving edges [23]. The choice of scaling or regularization parameter in the TV process defines the amount of denoising, with value of zero giving a result equivalent to the input signal. Here we explore three algorithms for specifying this parameter based on the statistics of the signal in the to...

متن کامل

Spatially dependent regularization parameter selection in total generalized variation models for image restoration

The automated spatially dependent regularization parameter selection framework of [9] for multi-scale image restoration is applied to total generalized variation (TGV) of order two. Well-posedness of the underlying continuous models is discussed and an algorithm for the numerical solution is developed. Experiments confirm that due to the spatially adapted regularization parameter the method all...

متن کامل

The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws

This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003