Pointwise shape-adaptive DCT for high-quality denoising and deblocking of grayscale and color images

Low-dimensional-structure self-learning and thresholding: regularization beyond compressed sensing for MRI reconstruction

An improved image reconstruction method from undersampled k-space data, low-dimensional-structure self-learning and thresholding (LOST), which utilizes the structure from the underlying image is presented. A low-resolution image from the fully sampled k-space center is reconstructed to learn image patches of similar anatomical characteristics. These patches are arranged into "similarity clusters," which are subsequently processed for dealiasing and artifact removal, using underlying low-dimensional properties. The efficacy of the proposed method in scan time reduction was assessed in a pilot coronary MRI study. Initially, in a retrospective study on 10 healthy adult subjects, we evaluated retrospective undersampling and reconstruction using LOST, wavelet-based l(1)-norm minimization, and total variation compressed sensing. Quantitative measures of vessel sharpness and mean square error, and qualitative image scores were used to compare reconstruction for rates of 2, 3, and 4. Subsequently, in a prospective study, coronary MRI data were acquired using these rates, and LOST-reconstructed images were compared with an accelerated data acquisition using uniform undersampling and sensitivity encoding reconstruction. Subjective image quality and sharpness data indicate that LOST outperforms the alternative techniques for all rates. The prospective LOST yields images with superior quality compared with sensitivity encoding or l(1)-minimization compressed sensing. The proposed LOST technique greatly improves image reconstruction for accelerated coronary MRI acquisitions.

Fine-granularity and spatially-adaptive regularization for projection-based image deblurring

This paper studies two classes of regularization strategies to achieve an improved tradeoff between image recovery and noise suppression in projection-based image deblurring. The first is based on a simple fact that r-times Landweber iteration leads to a fixed level of regularization, which allows us to achieve fine-granularity control of projection-based iterative deblurring by varying the value r. The regularization behavior is explained by using the theory of Lagrangian multiplier for variational schemes. The second class of regularization strategy is based on the observation that various regularized filters can be viewed as nonexpansive mappings in the metric space. A deeper understanding about different regularization filters can be gained by probing into their asymptotic behavior--the fixed point of nonexpansive mappings. By making an analogy to the states of matter in statistical physics, we can observe that different image structures (smooth regions, regular edges and textures) correspond to different fixed points of nonexpansive mappings when the temperature(regularization) parameter varies. Such an analogy motivates us to propose a deterministic annealing based approach toward spatial adaptation in projection-based image deblurring. Significant performance improvements over the current state-of-the-art schemes have been observed in our experiments, which substantiates the effectiveness of the proposed regularization strategies.

Fast query for exemplar-based image completion

In this paper, we present a fast algorithm for filling unknown regions in an image using the strategy of exemplar-matching. Unlike the original exemplar-based method using exhaustive search, we decompose exemplars into the frequency coefficients and select fewer coefficients which are the most significant to evaluate the matching score. We have also developed a local gradient-based algorithm to fill the unknown pixels in a query image block. These two techniques bring the ability of input with varied dimensions to the fast query of similar image exemplars. The fast query is based upon a search-array data structure, and can be conducted very efficiently. Moreover, the evaluation of search-arrays runs in parallel maps well on the modern graphics hardware with graphics processing units (GPU). The functionality of the approach has been demonstrated by experimental results on real photographs.

Adaptive 2-D wavelet transform based on the lifting scheme with preserved vanishing moments

In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.

Novel Bayesian deringing method in image interpolation and compression using a SGLI prior

This paper provides a novel Bayesian deringing method to reduce ringing artifacts caused by image interpolation and JPEG compression. To remove the ringing artifacts, the proposed method uses a Bayesian framework based on a SGLI (spatial-gradient-local-inhomogeneity) prior. The SGLI prior employs two complementary discontinuity measures: spatial gradient and local inhomogeniety. The spatial gradient measure effectively detects strong edge components in images. In addition, the local inhomogeniety measure successfully detects locations of the significant discontinuities by taking uniformity of small regions into consideration. The two complementary measures are elaborately combined to create prior probabilities of the Bayesian deringing framework. Thus, the proposed deringing method can effectively preserve the significant discontinuities such as textures of objects as well as the strong edge components in images while reducing the ringing artifacts. Experimental results show that the proposed deringing method achieves average PSNR gains of 0.09 dB in image interpolation artifact reduction and 0.21 dB in JPEG compression artifact reduction.

Iterative weighted maximum likelihood denoising with probabilistic patch-based weights

Image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation. This paper presents a new approach for image denoising in the case of a known uncorrelated noise model. The proposed filter is an extension of the nonlocal means (NL means) algorithm introduced by Buades , which performs a weighted average of the values of similar pixels. Pixel similarity is defined in NL means as the Euclidean distance between patches (rectangular windows centered on each two pixels). In this paper, a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model. The denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a data-driven way. These weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate. We show that this iterative process noticeably improves the denoising performance, especially in the case of low signal-to-noise ratio images such as synthetic aperture radar (SAR) images. Numerical experiments illustrate that the technique can be successfully applied to the classical case of additive Gaussian noise but also to cases such as multiplicative speckle noise. The proposed denoising technique seems to improve on the state of the art performance in that latter case.

Image restoration using space-variant Gaussian scale mixtures in overcomplete pyramids

In recent years, Bayes least squares-Gaussian scale mixtures (BLS-GSM) has emerged as one of the most powerful methods for image restoration. Its strength relies on providing a simple and, yet, very effective local statistical description of oriented pyramid coefficient neighborhoods via a GSM vector. This can be viewed as a fine adaptation of the model to the signal variance at each scale, orientation, and spatial location. Here, we present an enhancement of the model by introducing a coarser adaptation level, where a larger neighborhood is used to estimate the local signal covariance within every subband. We formulate our model as a BLS estimator using space-variant GSM. The model can be also applied to image deconvolution, by first performing a global blur compensation, and then doing local adaptive denoising. We demonstrate through simulations that the proposed method, besides being model-based and noniterative, it is also robust and efficient. Its performance, measured visually and in L2-norm terms, is significantly higher than the original BLS-GSM method, both for denoising and deconvolution.

Weighted averaging for denoising with overcomplete dictionaries

We consider the scenario where additive, independent, and identically distributed (i.i.d) noise in an image is removed using an overcomplete set of linear transforms and thresholding. Rather than the standard approach, where one obtains the denoised signal by ad hoc averaging of the denoised estimates provided by denoising with each of the transforms, we formulate the optimal combination as a conditional linear estimation problem and solve it for optimal estimates. Our approach is independent of the utilized transforms and the thresholding scheme, and as we illustrate using oracle-based denoisers, it extends established work by exploiting a separate degree of freedom that is, in general, not reachable using previous techniques. Our derivation of the optimal estimates specifically relies on the assumption that the utilized transforms provide sparse decompositions. At the same time, our work is robust as it does not require any assumptions about image statistics beyond sparsity. Unlike existing work, which tries to devise ever more sophisticated transforms and thresholding algorithms to deal with the myriad types of image singularities, our work uses basic tools to obtain very high performance on singularities by taking better advantage of the sparsity that surrounds them. With well-established transforms, we obtain results that are competitive with state-of-the-art methods.

Image denoising by sparse 3-D transform-domain collaborative filtering

We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2-D image fragments (e.g., blocks) into 3-D data arrays which we call "groups." Collaborative filtering is a special procedure developed to deal with these 3-D groups. We realize it using the three successive steps: 3-D transformation of a group, shrinkage of the transform spectrum, and inverse 3-D transformation. The result is a 3-D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

Pointwise shape-adaptive DCT for high-quality denoising and deblocking of grayscale and color images

The shape-adaptive discrete cosine transform ISA-DCT) transform can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable block-DCT (B-DCT). Despite the near-optimal decorrelation and energy compaction properties, application of the SA-DCT has been rather limited, targeted nearly exclusively to video compression. In this paper, we present a novel approach to image filtering based on the SA-DCT. We use the SA-DCT in conjunction with the Anisotropic Local Polynomial Approximation-Intersection of Confidence Intervals technique, which defines the shape of the transform's support in a pointwise adaptive manner. The thresholded or attenuated SA-DCT coefficients are used to reconstruct a local estimate of the signal within the adaptive-shape support. Since supports corresponding to different points are in general overlapping, the local estimates are averaged together using adaptive weights that depend on the region's statistics. This approach can be used for various image-processing tasks. In this paper, we consider, in particular, image denoising and image deblocking and deringing from block-DCT compression. A special structural constraint in luminance-chrominance space is also proposed to enable an accurate filtering of color images. Simulation experiments show a state-of-the-art quality of the final estimate, both in terms of objective criteria and visual appearance. Thanks to the adaptive support, reconstructed edges are clean, and no unpleasant ringing artifacts are introduced by the fitted transform.