Image reconstruction with imperfect forward models and applications in deblurring

نویسندگان

  • Yury Korolev
  • Jan Lellmann
چکیده

We present and analyse an approach to image reconstruction problems with imperfect forward models based on partially ordered spaces – Banach lattices. In this approach, errors in the data and in the forward models are described using order intervals. The method can be characterised as the lattice analogue of the residual method, where the feasible set is defined by linear inequality constraints. The study of this feasible set is the main contribution of this paper. Convexity of this feasible set is examined in several settings and modifications for introducing additional information about the forward operator are considered. Numerical examples demonstrate the performance of the method in deblurring with errors in the blurring kernel.

برای دانلود 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

Image Restoration with a New Class of Forward-Backward-Forward Diffusion Equations of Perona-Malik Type with Applications to Satellite Image Enhancement

A new class of anisotropic diffusion models is proposed for image processing which can either be viewed as a novel kind of regularization of the classical Perona-Malik model or, as it is advocated by the authors, as a new independent model. The models are diffusive in nature and are characterized by the presence of both forward and backward regimes. In contrast to the Perona-Malik model, in the...

متن کامل

MRA Based Wavelet Frames and Applications: Image Segmentation and Surface Reconstruction

Theory of wavelet frames and their applications to image restoration problems have been extensively studied for the past two decades. The success of wavelet frames in solving image restoration problems, which includes denoising, deblurring, inpainting, computed tomography, etc., is mainly due to their capability of sparsely approximating piecewise smooth functions such as images. However, in co...

متن کامل

A new model for image regularization

Introduction. Image processing is an active area of reseach with connections to a number of applications, such as medical imaging, machine learning, security, among others. Since the seminal paper [ROF92], image reconstruction based on total variation (TV) has become an extensively used technique for inpainting, deblurring, and denoising images. The model proposes as true image candidate a sign...

متن کامل

Iterative CT Reconstruction using Models of Source and Detector Blur and Correlated Noise.

Statistical model-based reconstruction methods derive much of their advantage over traditional methods through more accurate forward models of the imaging system. Typical forward models fail to integrate two important aspects of real imaging systems: system blur and noise correlations in the measurements. This work develops an approach that models both aspects using a two-stage approach that in...

متن کامل

Sparse inverse solution methods for signal and image processing applications

This paper addresses image and signal processing problems where the result most consistent with prior knowledge is the minimum order, or “maximally sparse” solution. These problems arise in such diverse areas as astronomical star image deblurring, neuromagnetic image reconstruction, seismic deconvolution, and thinned array beamformer design. An optimization theoretic formulation for sparse solu...

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

برای دانلود 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

عنوان ژورنال:
  • CoRR

دوره abs/1708.01244  شماره 

صفحات  -

تاریخ انتشار 2017