Image Deblurring Using Derivative Compressed Sensing for Optical Imaging Application

Reconstruction of multidimensional signals from the samples of their partial derivatives is known to be a standard problem in inverse theory. Such and similar problems routinely arise in numerous areas of applied sciences, including optical imaging, laser interferometry, computer vision, remote sensing and control. Though being ill-posed in nature, the above problem can be solved in a unique and stable manner, provided proper regularization and relevant boundary conditions. In this paper, however, a more challenging setup is addressed, in which one has to recover an image of interest from its noisy and blurry version, while the only information available about the imaging system at hand is the amplitude of the generalized pupil function (GPF) along with partial observations of the gradient of GPF's phase. In this case, the phase-related information is collected using a simplified version of the Shack-Hartmann interferometer, followed by recovering the entire phase by means of derivative compressed sensing. Subsequently, the estimated phase can be combined with the amplitude of the GPF to produce an estimate of the point spread function (PSF), whose knowledge is essential for subsequent image deconvolution. In summary, the principal contribution of this work is twofold. First, we demonstrate how to simplify the construction of the Shack-Hartmann interferometer so as to make it less expensive and hence more accessible. Second, it is shown by means of numerical experiments that the above simplification and its associated solution scheme produce image reconstructions of the quality comparable to those obtained using dense sampling of the GPF phase

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

CTprintNet: An Accurate and Stable Deep Unfolding Approach for Few-View CT Reconstruction

In this paper, we propose a new deep learning approach based on unfolded neural networks for the reconstruction of X-ray computed tomography images from few views. We start from a model-based approach in a compressed sensing framework, described by the minimization of a least squares function plus an edge-preserving prior on the solution. In particular, the proposed network automatically estimates the internal parameters of a proximal interior point method for the solution of the optimization problem. The numerical tests performed on both a synthetic and a real dataset show the effectiveness of the framework in terms of accuracy and robustness with respect to noise on the input sinogram when compared to other different data-driven approaches

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented

Compressed Sensing in the Presence of Side Information

Reconstruction of continuous signals from a number of their discrete samples is central to digital signal processing. Digital devices can only process discrete data and thus processing the continuous signals requires discretization. After discretization, possibility of unique reconstruction of the source signals from their samples is crucial. The classical sampling theory provides bounds on the sampling rate for unique source reconstruction, known as the Nyquist sampling rate. Recently a new sampling scheme, Compressive Sensing (CS), has been formulated for sparse signals. CS is an active area of research in signal processing. It has revolutionized the classical sampling theorems and has provided a new scheme to sample and reconstruct sparse signals uniquely, below Nyquist sampling rates. A signal is called (approximately) sparse when a relatively large number of its elements are (approximately) equal to zero. For the class of sparse signals, sparsity can be viewed as prior information about the source signal. CS has found numerous applications and has improved some image acquisition devices. Interesting instances of CS can happen, when apart from sparsity, side information is available about the source signals. The side information can be about the source structure, distribution, etc. Such cases can be viewed as extensions of the classical CS. In such cases we are interested in incorporating the side information to either improve the quality of the source reconstruction or decrease the number of the required samples for accurate reconstruction. A general CS problem can be transformed to an equivalent optimization problem. In this thesis, a special case of CS with side information about the feasible region of the equivalent optimization problem is studied. It is shown that in such cases uniqueness and stability of the equivalent optimization problem still holds. Then, an efficient reconstruction method is proposed. To demonstrate the practical value of the proposed scheme, the algorithm is applied on two real world applications: image deblurring in optical imaging and surface reconstruction in the gradient field. Experimental results are provided to further investigate and confirm the effectiveness and usefulness of the proposed scheme