Optimally Stabilized PET Image Denoising Using Trilateral Filtering

Low-resolution and signal-dependent noise distribution in positron emission tomography (PET) images makes denoising process an inevitable step prior to qualitative and quantitative image analysis tasks. Conventional PET denoising methods either over-smooth small-sized structures due to resolution limitation or make incorrect assumptions about the noise characteristics. Therefore, clinically important quantitative information may be corrupted. To address these challenges, we introduced a novel approach to remove signal-dependent noise in the PET images where the noise distribution was considered as Poisson-Gaussian mixed. Meanwhile, the generalized Anscombe's transformation (GAT) was used to stabilize varying nature of the PET noise. Other than noise stabilization, it is also desirable for the noise removal filter to preserve the boundaries of the structures while smoothing the noisy regions. Indeed, it is important to avoid significant loss of quantitative information such as standard uptake value (SUV)-based metrics as well as metabolic lesion volume. To satisfy all these properties, we extended bilateral filtering method into trilateral filtering through multiscaling and optimal Gaussianization process. The proposed method was tested on more than 50 PET-CT images from various patients having different cancers and achieved the superior performance compared to the widely used denoising techniques in the literature.Comment: 8 pages, 3 figures; to appear in the Lecture Notes in Computer Science (MICCAI 2014

Recursive Non-Local Means Filter for Video Denoising with Poisson-Gaussian Noise

In this paper, we describe a new recursive Non-Local means (RNLM) algorithm for video denoising that has been developed by the current authors. Furthermore, we extend this work by incorporating a Poisson-Gaussian noise model. Our new RNLM method provides a computationally efficient means for video denoising, and yields improved performance compared with the single frame NLM and BM3D benchmarks methods. Non-Local means (NLM) based methods of denoising have been applied successfully in various image and video sequence denoising applications. However, direct extension of this method from 2D to 3D for video processing can be computationally demanding. The RNLM approach takes advantage of recursion for computational savings, and spatio-temporal correlations for improved performance. In our approach, the first frame is processed with single frame NLM. Subsequent frames are estimated using a weighted combination of the current frame NLM, and the previous frame estimate. Block matching registration with the prior estimate is done for each current pixel estimate to maximize the temporal correlation. To address the Poisson-Gaussian noise model, we make use of the Anscombe transformation prior to filtering to stabilize the noise variance. Experimental results are presented that demonstrate the effectiveness of our proposed method. We show that the new method outperforms single frame NLM and BM3D

Efficient Burst Raw Denoising with Variance Stabilization and Multi-frequency Denoising Network

With the growing popularity of smartphones, capturing high-quality images is of vital importance to smartphones. The cameras of smartphones have small apertures and small sensor cells, which lead to the noisy images in low light environment. Denoising based on a burst of multiple frames generally outperforms single frame denoising but with the larger compututional cost. In this paper, we propose an efficient yet effective burst denoising system. We adopt a three-stage design: noise prior integration, multi-frame alignment and multi-frame denoising. First, we integrate noise prior by pre-processing raw signals into a variance-stabilization space, which allows using a small-scale network to achieve competitive performance. Second, we observe that it is essential to adopt an explicit alignment for burst denoising, but it is not necessary to integrate a learning-based method to perform multi-frame alignment. Instead, we resort to a conventional and efficient alignment method and combine it with our multi-frame denoising network. At last, we propose a denoising strategy that processes multiple frames sequentially. Sequential denoising avoids filtering a large number of frames by decomposing multiple frames denoising into several efficient sub-network denoising. As for each sub-network, we propose an efficient multi-frequency denoising network to remove noise of different frequencies. Our three-stage design is efficient and shows strong performance on burst denoising. Experiments on synthetic and real raw datasets demonstrate that our method outperforms state-of-the-art methods, with less computational cost. Furthermore, the low complexity and high-quality performance make deployment on smartphones possible.Comment: Accepted for publication in International Journal of Computer Visio

Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data

The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of interest. In this article, we first show how the so-called Skellam distribution arises from the fact that Haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts. We then provide two main theorems on Skellam shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting and the other providing for unbiased risk estimation in a frequentist context. These results serve to yield new estimators in the Haar transform domain, including an unbiased risk estimate for shrinkage of Haar-Fisz variance-stabilized data, along with accompanying low-complexity algorithms for inference. We conclude with a simulation study demonstrating the efficacy of our Skellam shrinkage estimators both for the standard univariate wavelet test functions as well as a variety of test images taken from the image processing literature, confirming that they offer substantial performance improvements over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for publicatio

Image denoising with multi-layer perceptrons, part 1: comparison with existing algorithms and with bounds

Image denoising can be described as the problem of mapping from a noisy image to a noise-free image. The best currently available denoising methods approximate this mapping with cleverly engineered algorithms. In this work we attempt to learn this mapping directly with plain multi layer perceptrons (MLP) applied to image patches. We will show that by training on large image databases we are able to outperform the current state-of-the-art image denoising methods. In addition, our method achieves results that are superior to one type of theoretical bound and goes a large way toward closing the gap with a second type of theoretical bound. Our approach is easily adapted to less extensively studied types of noise, such as mixed Poisson-Gaussian noise, JPEG artifacts, salt-and-pepper noise and noise resembling stripes, for which we achieve excellent results as well. We will show that combining a block-matching procedure with MLPs can further improve the results on certain images. In a second paper, we detail the training trade-offs and the inner mechanisms of our MLPs

A proximal iteration for deconvolving Poisson noisy images using sparse representations

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a {\it non-linear} degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a non-smooth sparsity-promoting penalties over the image representation coefficients (e.g. $\ell_1$-norm). Third, a fast iterative backward-forward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy

Postreconstruction filtering of 3D PET images by using weighted higher-order singular value decomposition

Additional file 1. Original 3D PET images data used in this work to generate the results