Wavelet domain image restoration using adaptively regularized constrained total least squares

This thesis is concerned with image restoration techniques using adaptively regularized constrained total least squares (ARCTLS) and wavelet transforms. The objective of the thesis is to improve the conventional ARCTLS algorithm by exploiting the subband properties of both the degraded image and the point spread function (PSF) of the degradation system. First of all, two most frequently used restoration algorithms, namely, the regularized constrained total least squares (RCTLS) and its adaptive version (ARCTLS) are investigated. The solutions of the two techniques in the DFT domain are emphasized in order to reduce the computational complexity. It is shown that both techniques are very suitable for the degradation situation where the (PSF) and the observed degraded image are subject to the same type of error. Secondly, a wavelet-domain image restoration technique using ARCTLS is presented. The 1-D and 2-D wavelet transform matrix representations are formulated for both the degraded image and the degradation convolution operator. A class of orthonormal wavelet based quadrature mirror filter bank is investigated and applied to the subband decomposition of the degraded image and the PSF as well such that the conventional ARCTLS algorithm can be employed for each subband image restoration

Improving Image Restoration with Soft-Rounding

Several important classes of images such as text, barcode and pattern images have the property that pixels can only take a distinct subset of values. This knowledge can benefit the restoration of such images, but it has not been widely considered in current restoration methods. In this work, we describe an effective and efficient approach to incorporate the knowledge of distinct pixel values of the pristine images into the general regularized least squares restoration framework. We introduce a new regularizer that attains zero at the designated pixel values and becomes a quadratic penalty function in the intervals between them. When incorporated into the regularized least squares restoration framework, this regularizer leads to a simple and efficient step that resembles and extends the rounding operation, which we term as soft-rounding. We apply the soft-rounding enhanced solution to the restoration of binary text/barcode images and pattern images with multiple distinct pixel values. Experimental results show that soft-rounding enhanced restoration methods achieve significant improvement in both visual quality and quantitative measures (PSNR and SSIM). Furthermore, we show that this regularizer can also benefit the restoration of general natural images.Comment: 9 pages, 6 figure

An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, non-smoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called "alternating direction method of multipliers", for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art.Comment: 13 pages, 8 figure, 8 tables. Submitted to the IEEE Transactions on Image Processin