Priyam Chatterjee

Is Denoising Dead

Image denoising has been a well studied problem in the field of image processing. Yet researchers continue to focus attention on it to better the current state-of-the-art. Recently proposed methods take different approaches to the problem and yet their denoising performances are comparable. A pertinent question then to ask is whether there is a theoretical limit to denoising performance and, more importantly, are we there yet? As camera manufacturers continue to pack increasing numbers of pixels per unit area, an increase in noise sensitivity manifests itself in the form of a noisier image. We study the performance bounds for the image denoising problem. Our work in this paper estimates a lower bound on the mean squared error of the denoised result and compares the performance of current state-of-the-art denoising methods with this bound. We show that despite the phenomenal recent progress in the quality of denoising algorithms, some room for improvement still remains for a wide class of general images, and at certain signal-to-noise levels. Therefore, image denoising is not dead - yet.

Clustering-Based Denoising With Locally Learned Dictionaries

In this paper, we propose K-LLD: a patch-based, locally adaptive denoising method based on clustering the given noisy image into regions of similar geometric structure. In order to effectively perform such clustering, we employ as features the local weight functions derived from our earlier work on steering kernel regression . These weights are exceedingly informative and robust in conveying reliable local structural information about the image even in the presence of significant amounts of noise. Next, we model each region (or cluster)-which may not be spatially contiguous-by ldquolearningrdquo a best basis describing the patches within that cluster using principal components analysis. This learned basis (or ldquodictionaryrdquo) is then employed to optimally estimate the underlying pixel values using a kernel regression framework. An iterated version of the proposed algorithm is also presented which leads to further performance enhancements. We also introduce a novel mechanism for optimally choosing the local patch size for each cluster using Steins unbiased risk estimator (SURE). We illustrate the overall algorithms capabilities with several examples. These indicate that the proposed method appears to be competitive with some of the most recently published state of the art denoising methods.

Patch-Based Near-Optimal Image Denoising

In this paper, we propose a denoising method motivated by our previous analysis of the performance bounds for image denoising. Insights from that study are used here to derive a high-performance practical denoising algorithm. We propose a patch-based Wiener filter that exploits patch redundancy for image denoising. Our framework uses both geometrically and photometrically similar patches to estimate the different filter parameters. We describe how these parameters can be accurately estimated directly from the input noisy image. Our denoising approach, designed for near-optimal performance (in the mean-squared error sense), has a sound statistical foundation that is analyzed in detail. The performance of our approach is experimentally verified on a variety of images and noise levels. The results presented here demonstrate that our proposed method is on par or exceeding the current state of the art, both visually and quantitatively.

Application Of Papoulis–Gerchberg Method In Image Super-Resolution and Inpainting

In this paper, we study the Papoulis–Gerchberg (PG) method and its applications to domains of image restoration such as super-resolution (SR) and inpainting. We show that the method performs well under certain conditions. We then suggest improvements to the method to achieve better SR and inpainting results. The modification applied to the SR process also allows us to apply the method to a larger class of images by doing away with some of the restrictions inherent in the classical PG method. We also present results to demonstrate the performance of the proposed techniques.

A generalization of non-local means via kernel regression

The Non-Local Means (NLM) method of denoising has received considerable attention in the image processing community due to its performance, despite its simplicity. In this paper, we show that NLM is a zero-th order kernel regression method, with a very specific choice of kernel. As such, it can be generalized. The original method of NLM, we show, implicitly assumes local constancy of the underlying image data. Once put in the context of kernel regression, we extend the existing Non-Local Means algorithm to higher orders of regression which allows us to approximate the image data locally by a polynomial or other localized basis of a given order. These extra degrees of freedom allow us to perform better denoising in texture regions. Overall the higher order method displays consistently better denoising capabilities compared to the zero-th order method. The power of the higher order method is amply illustrated with the help of various denoising experiments.

Practical Bounds on Image Denoising: From Estimation to Information

Recently, in a previous work, we proposed a way to bound how well any given image can be denoised. The bound was computed directly from the noise-free image that was assumed to be available. In this work, we extend the formulation to the more practical case where no ground truth is available. We show that the parameters of the bounds, namely the cluster covariances and level of redundancy for patches in the image, can be estimated directly from the noise corrupted image. Further, we analyze the bounds formulation to show that these two parameters are interdependent and they, along with the bounds formulation as a whole, have a nice information-theoretic interpretation as well. The results are verified through a variety of well-motivated experiments.

Noise suppression in low-light images through joint denoising and demosaicing

We address the effects of noise in low-light images in this paper. Color images are usually captured by a sensor with a color filter array (CFA). This requires a demosaicing process to generate a full color image. The captured images typically have low signal-to-noise ratio, and the demosaicing step further corrupts the image, which we show to be the leading cause of visually objectionable random noise patterns (splotches). To avoid this problem, we propose a combined framework of denoising and demosaicing, where we use information about the image inferred in the denoising step to perform demosaicing. Our experiments show that such a framework results in sharper low-light images that are devoid of splotches and other noise artifacts.

A Comparison of Some State of the Art Image Denoising Methods

We briefly describe and compare some recent advances in image denoising. In particular, we discuss three leading denoising algorithms, and describe their similarities and differences in terms of both structure and performance. Following a summary of each of these methods, several examples with various images corrupted with simulated and real noise of different strengths are presented. With the help of these experiments, we are able to identify the strengths and weaknesses of these state of the art methods, as well as seek the way ahead towards a definitive solution to the long-standing problem of image denoising.

Fundamental limits of image denoising: Are we there yet?

In this paper, we study the fundamental performance limits of image denoising where the aim is to recover the original image from its noisy observation. Our study is based on a general class of estimators whose bias can be modeled to be affine. A bound on the performance in terms of mean squared error (MSE) of the recovered image is derived in a Bayesian framework. In this work, we assume that the original image is available, from which we learn the image statistics. Performances of some current state-of-the-art methods are compared to our MSE bounds for some commonly used experimental images. These show that some gain in denoising performance is yet to be achieved.

Bias modeling for image denoising

In this paper, we study the bias characteristics of image denoising algorithms. Recently introduced state-of-the-art denoising methods produce biased estimates of pixel intensities. The bias in each case is dependent on the underlying image geometry. Hence, we cluster the image into groups of patches that share a common underlying structure and study the bias independently in each cluster. We show that the bias in each cluster can be modeled effectively by an affine function, where the parameters of the model differ between clusters and algorithms. We validate our model through experimental results, both visually and quantitatively.