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101
Generalizing the nonlocalmeans to superresolution reconstruction
 IN IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2009
"... Superresolution reconstruction proposes a fusion of several lowquality images into one higher quality result with better optical resolution. Classic superresolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inacc ..."
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Cited by 80 (5 self)
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Superresolution reconstruction proposes a fusion of several lowquality images into one higher quality result with better optical resolution. Classic superresolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inaccurately, as often happens for nonglobal motion fields, annoying artifacts appear in the superresolved outcome. Encouraged by recent developments on the video denoising problem, where stateoftheart algorithms are formed with no explicit motion estimation, we seek a superresolution algorithm of similar nature that will allow processing sequences with general motion patterns. In this paper, we base our solution on the NonlocalMeans (NLM) algorithm. We show how this denoising method is generalized to become a relatively simple superresolution algorithm with no explicit motion estimation. Results on several test movies show that the proposed method is very successful in providing superresolution on general sequences.
The Cosparse Analysis Model and Algorithms
, 2011
"... After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to ..."
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Cited by 64 (14 self)
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After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This workproposeseffectivepursuitmethodsthat aimtosolveinverseproblemsregularized with the analysismodel prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments.
Nonlocal Regularization of Inverse Problems
, 2008
"... This article proposes a new framework to regularize linear inverse problems using the total variation on nonlocal graphs. This nonlocal graph allows to adapt the penalization to the geometry of the underlying function to recover. A fast algorithm computes iteratively both the solution of the regul ..."
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Cited by 56 (3 self)
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This article proposes a new framework to regularize linear inverse problems using the total variation on nonlocal graphs. This nonlocal graph allows to adapt the penalization to the geometry of the underlying function to recover. A fast algorithm computes iteratively both the solution of the regularization process and the nonlocal graph adapted to this solution. We show numerical applications of this method to the resolution of image processing inverse problems such as inpainting, superresolution and compressive sampling.
Light field superresolution
 In IEEE ICCP
, 2009
"... Figure 1. From left to right: Light field image captured with a plenoptic camera (detail); the light field image on the left is rearranged as a collection of several views; central view extracted from the light field, with one pixel per microlens, as in a traditional rendering [23]; central view sup ..."
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Cited by 33 (0 self)
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Figure 1. From left to right: Light field image captured with a plenoptic camera (detail); the light field image on the left is rearranged as a collection of several views; central view extracted from the light field, with one pixel per microlens, as in a traditional rendering [23]; central view superresolved with our method. Light field cameras have been recently shown to be very effective in applications such as digital refocusing and 3D reconstruction. In a single snapshot these cameras provide a sample of the light field of a scene by trading off spatial resolution with angular resolution. Current methods produce images at a resolution that is much lower than that of traditional imaging devices. However, by explicitly modeling the image formation process and incorporating priors such as Lambertianity and texture statistics, these types of images can be reconstructed at a higher resolution. We formulate this method in a variational Bayesian framework and perform the reconstruction of both the surface of the scene and the (superresolved) light field. The method is demonstrated on both synthetic and real images captured with our lightfield camera prototype. 1.
Examplebased regularization deployed to superresolution reconstruction of a single image. The Computer Journal
, 2007
"... In superresolution (SR) reconstruction of images, regularization becomes crucial when insufficient number of measured lowresolution images is supplied. Beyond making the problem algebraically well posed, a properly chosen regularization can direct the solution toward a better quality outcome. Even ..."
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Cited by 30 (4 self)
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In superresolution (SR) reconstruction of images, regularization becomes crucial when insufficient number of measured lowresolution images is supplied. Beyond making the problem algebraically well posed, a properly chosen regularization can direct the solution toward a better quality outcome. Even the extreme case—a SR reconstruction from a single measured image—can be made successful with a wellchosen regularization. Much of the progress made in the past two decades on inverse problems in image processing can be attributed to the advances in forming or choosing the way to practice the regularization. A Bayesian point of view interpret this as a way of including the prior distribution of images, which sheds some light on the complications involved. This paper reviews an emerging powerful family of regularization techniques that is drawing attention in recent years—the examplebased approach. We describe how examples can and have been used effectively for regularization of inverse problems, reviewing the main contributions along these lines in the literature, and organizing this information into major trends and directions. A description of the stateoftheart in this field, along with supporting simulation results on the image scaleup problem are given. This paper concludes with an outline of the outstanding challenges this field faces today.
SuperResolution From Unregistered and Totally Aliased Signals Using Subspace Methods
, 2007
"... In many applications, the sampling frequency is limited by the physical characteristics of the components: the pixel pitch, the rate of the analogtodigital (A/D) converter, etc. A lowpass filter is usually applied before the sampling operation to avoid aliasing. However, when multiple copies are ..."
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Cited by 28 (8 self)
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In many applications, the sampling frequency is limited by the physical characteristics of the components: the pixel pitch, the rate of the analogtodigital (A/D) converter, etc. A lowpass filter is usually applied before the sampling operation to avoid aliasing. However, when multiple copies are available, it is possible to use the information that is inherently present in the aliasing to reconstruct a higher resolution signal. If the different copies have unknown relative offsets, this is a nonlinear problem in the offsets and the signal coefficients. They are not easily separable in the set of equations describing the superresolution problem. Thus, we perform joint registration and reconstruction from multiple unregistered sets of samples. We give a mathematical formulation for the problem when there are sets of samples of a signal that is described by expansion coefficients. We prove that the solution of the registration and reconstruction problem is generically unique
On single image scaleup using sparserepresentations,” Curves and Surfaces
, 2012
"... Abstract. This paper deals with the single image scaleup problem using sparserepresentation modeling. The goal is to recover an original image from its blurred and downscaled noisy version. Since this problem is highly illposed, a prior is needed in order to regularize it. The literature offers ..."
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Cited by 26 (2 self)
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Abstract. This paper deals with the single image scaleup problem using sparserepresentation modeling. The goal is to recover an original image from its blurred and downscaled noisy version. Since this problem is highly illposed, a prior is needed in order to regularize it. The literature offers various ways to address this problem, ranging from simple linear spaceinvariant interpolation schemes (e.g., bicubic interpolation), to spatiallyadaptive and nonlinear filters of various sorts. We embark from a recentlyproposed successful algorithm by Yang et. al. [1,2], and similarly assume a local SparseLand model on image patches, serving as regularization. Several important modifications to the abovementioned solution are introduced, and are shown to lead to improved results. These modifications include a major simplification of the overall process both in terms of the computational complexity and the algorithm architecture, using a different training approach for the dictionarypair, and introducing the ability to operate without a trainingset by bootstrapping the scaleup task from the given lowresolution image. We demonstrate the results on true images, showing both visual and PSNR improvements. 1
Superresolution with sparse mixing estimators
 IEEE Trans on IP
, 2010
"... Abstract—We introduce a class of inverse problem estimators computed by mixing adaptively a family of linear estimators corresponding to different priors. Sparse mixing weights are calculated over blocks of coefficients in a frame providing a sparse signal representation. They minimize an norm takin ..."
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Cited by 21 (1 self)
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Abstract—We introduce a class of inverse problem estimators computed by mixing adaptively a family of linear estimators corresponding to different priors. Sparse mixing weights are calculated over blocks of coefficients in a frame providing a sparse signal representation. They minimize an norm taking into account the signal regularity in each block. Adaptive directional image interpolations are computed over a wavelet frame with an algorithm, providing stateoftheart numerical results. Index Terms—Block matching pursuit, interpolation, inverse problem, mixing estimator, structured sparsity, superresolution, Tikhonov regularization, wavelet. I.
Numerical methods for coupled superresolution
 Inverse Probl
, 2006
"... The process of combining, via mathematical software tools, a set of low resolution images into a single high resolution image is often referred to as superresolution. Algorithms for superresolution involve two key steps: registration and reconstruction. Most approaches proposed in the literature d ..."
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Cited by 19 (5 self)
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The process of combining, via mathematical software tools, a set of low resolution images into a single high resolution image is often referred to as superresolution. Algorithms for superresolution involve two key steps: registration and reconstruction. Most approaches proposed in the literature decouple these steps, solving each independently. This can be effective if there are very simple, linear displacements between the low resolution images. However, for more complex, nonlinear, nonuniform transformations, estimating the displacements can be very difficult, leading to severe inaccuracies in the reconstructed high resolution image. This paper presents a mathematical framework and optimization algorithms that can be used to jointly estimate these quantities. Efficient implementation details are considered, and numerical experiments are provided to illustrate the effectiveness of our approach.
Super Resolution With Probabilistic Motion Estimation
"... Abstract—Superresolution reconstruction (SRR) has long been relying on very accurate motion estimation between the frames for a successful process. However, recent works propose SRR that bypasses the need for an explicit motion estimation [11], [15]. In this correspondence, we present a new framewo ..."
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Cited by 12 (0 self)
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Abstract—Superresolution reconstruction (SRR) has long been relying on very accurate motion estimation between the frames for a successful process. However, recent works propose SRR that bypasses the need for an explicit motion estimation [11], [15]. In this correspondence, we present a new framework that ultimately leads to the same algorithm as in our prior work [11]. The contribution of this paper is twofold. First, the suggested approach is much simpler and more intuitive, relying on the classic SRR formulation, and using a probabilistic and crude motion estimation. Second, the new approach offers various extensions not covered in our previous work, such as more general resampling tasks (e.g., deinterlacing). Index Terms—Deinterlacing, probabilistic motion estimation, super resolution. I.