Data-dependent Noise Research Articles

Cross-Domain Unpaired Learning for Low-Dose CT Imaging.

Supervised deep-learning techniques with paired training datasets have been widely studied for low-dose computed tomography (LDCT) imaging with excellent performance. However, the paired training datasets are usually difficult to obtain in clinical routine, which restricts the wide adoption of supervised deep-learning techniques in clinical practices. To address this issue, a general idea is to construct a pseudo paired training dataset based on the widely available unpaired data, after which, supervised deep-learning techniques can be adopted for improving the LDCT imaging performance by training on the pseudo paired training dataset. However, due to the complexity of noise properties in CT imaging, the LDCT data are difficult to generate in order to construct the pseudo paired training dataset. In this paper, we propose a simple yet effective cross-domain unpaired learning framework for pseudo LDCT data generation and LDCT image reconstruction, which is denoted as CrossDuL. Specifically, a dedicated pseudo LDCT sinogram generative module is constructed based on a data-dependent noise model in the sinogram domain, and then instead of in the sinogram domain, a pseudo paired dataset is constructed in the image domain to train an LDCT image restoration module. To validate the effectiveness of the proposed framework, clinical datasets are adopted. Experimental results demonstrate that the CrossDuL framework can obtain promising LDCT imaging performance in both quantitative and qualitative measurements.

ADASSM: Adversarial Data Augmentation in Statistical Shape Models From Images.

Statistical shape models (SSM) have been well-established as an excellent tool for identifying variations in the morphology of anatomy across the underlying population. Shape models use consistent shape representation across all the samples in a given cohort, which helps to compare shapes and identify the variations that can detect pathologies and help in formulating treatment plans. In medical imaging, computing these shape representations from CT/MRI scans requires time-intensive preprocessing operations, including but not limited to anatomy segmentation annotations, registration, and texture denoising. Deep learning models have demonstrated exceptional capabilities in learning shape representations directly from volumetric images, giving rise to highly effective and efficient Image-to-SSM networks. Nevertheless, these models are data-hungry and due to the limited availability of medical data, deep learning models tend to overfit. Offline data augmentation techniques, that use kernel density estimation based (KDE) methods for generating shape-augmented samples, have successfully aided Image-to-SSM networks in achieving comparable accuracy to traditional SSM methods. However, these augmentation methods focus on shape augmentation, whereas deep learning models exhibit image-based texture bias resulting in sub-optimal models. This paper introduces a novel strategy for on-the-fly data augmentation for the Image-to-SSM framework by leveraging data-dependent noise generation or texture augmentation. The proposed framework is trained as an adversary to the Image-to-SSM network, augmenting diverse and challenging noisy samples. Our approach achieves improved accuracy by encouraging the model to focus on the underlying geometry rather than relying solely on pixel values.

317 Gb/in2 Recording Areal Density on Strontium Ferrite Tape

The recording performance of a new prototype magnetic tape based on perpendicularly oriented strontium ferrite particles is investigated using a 29 nm wide tunneling magnetoresistive reader. At a linear density of 702 kbpi, a post-detection byte-error rate (BER) of 2.8e−2 is demonstrated based on measured recording data and a software read channel. The read channel uses a 64-state implementation of an extended version of a data-dependent noise-predictive maximum-likelihood detection scheme that tracks the first- and second-order statistics of the data-dependent noise. At the demonstrated post-detection BER, a post-error-correction-coding BER of less than 1e−20 can be achieved using an iterative decoding architecture. To facilitate aggressive track-density scaling, we made multiple advances in the area of track following. First, we developed a new timing-based servo pattern and implemented a novel quad channel averaging scheme. Second, we developed a new field programmable gate array prototyping platform to enable the implementation of quad channel averaging. Third, we enhanced our low disturbance tape transport with a pair of 20 mm diameter air bearing tape guides and a prototype track-following actuator. Fourth, we developed a novel low friction tape head and, finally, we designed a set of tape speed optimized track-following controllers using the model-based $H_{\infty }$ design framework. Combining these technologies, we achieved a position error signal (PES) characterized by a standard deviation ≤ 3.18 nm over a tape speed range of 1.2–4.1 m/s. This magnitude of PES in combination with a 29 nm wide reader enables reliable recording at a track width of 56.2 nm corresponding to a track density of 451.9 ktpi, for an equivalent areal density of 317.3 Gb/in2.

Fast Robust Subspace Tracking via PCA in Sparse Data-Dependent Noise

This work studies the robust subspace tracking (ST) problem. Robust ST can be simply understood as a (slow) time-varying subspace extension of robust PCA. It assumes that the true data lies in a low-dimensional subspace that is either fixed or changes slowly with time. The goal is to track the changing subspaces over time in the presence of additive sparse outliers and to do this quickly (with a short delay). We introduce a "fast" mini-batch robust ST solution that is provably correct under mild assumptions. Here "fast" means two things: (i) the subspace changes can be detected and the subspaces can be tracked with near-optimal delay, and (ii) the time complexity of doing this is the same as that of simple (non-robust) PCA. Our main result assumes piecewise constant subspaces (needed for identifiability), but we also provide a corollary for the case when there is a little change at each time. A second contribution is a novel non-asymptotic guarantee for PCA in linearly data-dependent noise. An important setting where this is useful is for linearly data dependent noise that is sparse with support that changes enough over time. The analysis of the subspace update step of our proposed robust ST solution uses this result.

Multiple-Coil Magnetic Resonance Image Denoising and Deblurring With Nonlocal Total Bounded Variation

One of the complex tasks in image restoration is to restore images under data correlated noise contaminations. In real-time medical imaging scenarios, such as Magnetic Resonance (MR), Ultrasound, Computed Tomography(CT) etc, it is observed that, the data of interest is severely degraded with data dependent noise interventions. A Nonlocal Total Bounded Variation (NLTBV) approach is being proposed in this paper to denoise as well as deblur multiple-coil MR images corrupted by non-central Chi distributed noise and linear Gaussian blur. The energy functional for the restoration model is derived by applying the Maximum A Posteriori (MAP) estimator on the Probability Density Function (PDF) of the non-central Chi distribution. The numerical implementation is performed using the split-Bregman iterative scheme to improve the convergence rate. The proposed model is compared with the other state of the art models in terms of both visual and statistical quantifications to demonstrate it's performance.

Noise classification and automatic restoration system using non-local regularization frameworks

ABSTRACTMedical, satellite or microscopic images differ in the imaging techniques used, hence their underlying noise distribution also are different. Most of the restoration methods including regularization models make prior assumptions about the noise to perform an efficient restoration. Here we propose a system that estimates and classifies the noise into different distributions by extracting the relevant features. The system provides information about the noise distribution and then it gets directed into the restoration module where an appropriate regularization method (based on the non-local framework) has been employed to provide an efficient restoration of the data. We have effectively addressed the distortion due to data-dependent noise distributions such as Poisson and Gamma along with data uncorrelated Gaussian noise. The studies have shown a 97.7% accuracy in classifying noise in the test data. Moreover, the system also shows the capability to cater to other popular noise distributions such as Rayleigh, Chi, etc.

Improved demapping for channels with data-dependent noise

A new demapper is presented for communication channels that can be modeled with data-dependent noise on the received symbols. This includes optical and satellite channels with various types of distortion. The demapper incorporates the covariance information of the received symbol clusters to capture noise variation across the constellation and any dependency between the in-phase and quadrature components. Two communication scenarios are considered, and it is shown that the demapper is advantageous when a system is dominated by distortion as opposed to thermal noise. Channel coding considerations are presented, and reductions up to 4 dB in the required SNR are achieved.

Necessary and sufficient conditions of proper estimators based on self density ratio for unnormalized statistical models

The largest family of density-ratio based estimators is obtained for unnormalized statistical models under the assumption of properness. They do not require normalization of the probability density function (PDF) because they are based on the density ratio of the same PDF at different points; therefore, the multiplicative normalization constant cancels out. In contrast with most existing work, a single necessary and sufficient condition is given here, rather than merely sufficient conditions for proper criteria for estimation. The condition implies that an extended Bregman divergence framework with data-dependent noise (Gutmann & Hirayama, 2011) gives the largest family of proper criteria in the present case. This properness yields consistent estimation as long as some mild conditions are satisfied. The present study shows that the above-mentioned framework gives an “upper bound” for attempts to extend Hyvärinen’s score matching and therefore provides a perspective for studies in this direction.

Joint Timing Recovery and Signal Detection for Two-Dimensional Magnetic Recording

Two-dimensional magnetic recording (TDMR) is a promising technology for boosting areal densities using sophisticated signal processing algorithms within a systems framework. The channel impairments comprise of 2-D intersymbol interference (ISI), 2-D synchronization errors along with media, and electronic noise sources, making it challenging for designing optimum algorithms and architectures for read/write channels. In this paper, we propose a novel iterative joint timing and signal detection algorithm to handle synchronization errors along with the 2-D ISI for TDMR channels. Our work is novel in two aspects: 1) we develop a discrete timing error model using 2-D random walk by incorporating correlated timing drifts due to phase and frequency offsets and 2) we develop a 2-D joint timing and signal detection engine for handling 2-D ISI constraints along with timing errors toward near maximum likelihood detection. The proposed 2-D joint timing-detection algorithm can be iteratively configured and observed to achieve a significant signal-to-noise ratio gain of > 1.2 dB in bit error rate performance (translating to similar to 10% increase in areal densities around the 1 Tb/in(2) regime with the grain sizes of 10 nm and the bit sizes of 25x25 nm) at the output of 2-D soft-output Viterbi algorithm (SOVA) as compared with a standalone timing loop coupled to a 2-D detector in an open-loop configuration. The efficacy of our proposed algorithm and system architecture is evaluated via simulations for TDMR configurations comprising of a 2-D generalized partial response equalization along the 2-D SOVA with data-dependent noise prediction capability over the Voronoi media model.

Novel iterative reconstruction method with optimal dose usage for partially redundant CT-acquisition

In CT imaging, a variety of applications exist which are strongly SNR limited. However, in some cases redundant data of the same body region provide additional quanta.Examples: in dual energy CT, the spatial resolution has to be compromised to provide good SNR for material decomposition. However, the respective spectral dataset of the same body region provides additional quanta which might be utilized to improve SNR of each spectral component. Perfusion CT is a high dose application, and dose reduction is highly desirable. However, a meaningful evaluation of perfusion parameters might be impaired by noisy time frames. On the other hand, the SNR of the average of all time frames is extremely high.In redundant CT acquisitions, multiple image datasets can be reconstructed and averaged to composite image data. These composite image data, however, might be compromised with respect to contrast resolution and/or spatial resolution and/or temporal resolution. These observations bring us to the idea of transferring high SNR of composite image data to low SNR ‘source’ image data, while maintaining their resolution.It has been shown that the noise characteristics of CT image data can be improved by iterative reconstruction (Popescu et al Book of s, 2nd CT Meeting (Salt Lake City, UT) p 148). In case of data dependent Gaussian noise it can be modelled with image-based iterative reconstruction at least in an approximate manner (Bruder et al Proc. SPIE 7961 79610J).We present a generalized update equation in image space, consisting of a linear combination of the previous update, a correction term which is constrained by the source image data, and a regularization prior, which is initialized by the composite image data. This iterative reconstruction approach we call bimodal reconstruction (BMR).Based on simulation data it is shown that BMR can improve low contrast detectability, substantially reduces the noise power and has the potential to recover spatial resolution of the source image data.For different CT applications: dual energy imaging, liver imaging, spiral imaging, cardiac imaging, we show that SNR can efficiently be transferred from the composite image to the source image data at constant patient dose, while maintaining resolution properties of the source data.

Signal Processing for Dedicated Servo Recording System

Perpendicular magnetic recording (PMR) in the hard disk drive is approaching its physical limits. In an earlier work, the dedicated servo (DS) recording system has been proposed to provide continuous position error signal for servo, enable higher servo sampling rate, and improve the overall servo performance. A further benefit is that the DS layer results in surface area savings at the data layer. However, it was also reported that the embedded servo layer introduces baseline variation and non-linear transition shift (NLTS) to the readback signal of the data layer. In this paper, we propose novel signal processing techniques to improve the bit error rate (BER) in DS recording. The synchronous averaging technique is proposed to improve the BER in the presence of baseline variation distortions. Further, the servo and data-dependent noise prediction method is proposed to mitigate the effect of the NLTS. Through the use of these techniques the linear density loss from the conventional PMR media is reduced.

An Image Dehazing Model considering Multiplicative Noise and Sensor Blur

A restoration model considering the data-dependent multiplicative noise, shift-invariant blur, and haze has been introduced in this paper. The proposed strategy adopts a two-step model to perform a single image dehazing under the blurred and noisy observations. The first step uses the well-known dark channel prior method to estimate the transmission of the medium and atmospheric light that signifies the global color of the haze and dehaze the images. The second step performs denoising and deblurring under a Gamma distributed noise setup and a linear blurring artefact. The restoration under the above mentioned setup has quite a few applications in satellite and long-distant telescopic imaging systems, where the captured images are noisy due to atmospheric pressure turbulence and hazy due to the presence of atmospheric dust formation; further they are blurred due to the common device artefacts. The proposed strategy is tested using a large amount of available image-sets and the performance of the model is analysed in detail in the results section.

A convex regularization model for image restoration

Many variational formulations are introduced over the last few years to handle multiplicative data-dependent noise. Some of these models seek to minimize the Total Variation (TV) norm of the absolute gradient function subject to given constraints. Since the TV-norm (well-defined in the space of bounded variations (BVs)) minimization eventually results in the formation of piece-wise constant patches during the evolution process, the filtered output appears blocky . In this work the block effect (commonly known as staircase effect) is being handled by using a convex combination of TV and Tikhonov filters, which are defined in BV and L2 (square-integrable functions) spaces, respectively. The constraint for the minimizing functional is derived based on a maximum a posteriori (MAP) regularization approach, duly considering the noise distributions. Therefore, this model is capable of denoising speckled images, whose intensity is Gamma distributed. The results are demonstrated both in terms of visual and quantitative measures.

Image Enhancement under Data-Dependent Multiplicative Gamma Noise

An edge enhancement filter is proposed for denoising and enhancing images corrupted with data-dependent noise which is observed to follow a Gamma distribution. The filter is equipped with three terms designed to perform three different tasks. The first term is an anisotropic diffusion term which is derived from a locally adaptivep-laplacian functional. The second term is an enhancement term or a shock term which imparts a shock effect at the edge points making them sharp. The third term is a reactive term which is derived based on the maximum a posteriori (MAP) estimator and this term helps the diffusive term to perform a Gamma distributive data-dependent multiplicative noise removal from images. And moreover, this reactive term ensures that deviation of the restored image from the original one is minimum. This proposed filter is compared with the state-of-the-art restoration models proposed for data-dependent multiplicative noise.

Statistical Characterization of Noise and Interference in NAND Flash Memory

Given the limited set of empirical input/output data from flash memory cells, we describe a technique to statistically analyze different sources that cause the mean-shifts and random fluctuations in the read values of the cells. In particular, for a given victim cell, we are able to quantify the amount of interference coming from any arbitrarily chosen set of potentially influencing cells. The effect of noise and interference on the victim cell after repeated program/erase cycles as well as baking is also investigated. The results presented here can be used to construct a channel model with data-dependent noise and interference characteristics, which in turn can be utilized in designing and evaluating advanced coding and signal processing methods for flash memory.

Generalized Belief Propagation Detector for TDMR Microcell Model

Signal processing in TDMR encounters several challenges such as read channel modeling and detection in the presence of severe two-dimensional intersymbol interference (2-D ISI). The contribution of this paper is twofold. 1) In this paper, we introduce a novel 2-D read channel model which we call the 2-D Microcell model. In this model, we use generalized 2-D microtracks called microcells to captures the properties of irregular grain boundaries of the medium in a relatively simple yet accurate manner. The data dependent noise (DDN) distributions are analytically derived for this model. The derivation of the DDN distributions makes the 2-D Microcell suitable for detector design purposes. 2) We propose a new framework for designing truly two-dimensional detectors for the Microcell model based on near-optimal generalized belief propagation (GBP). The GBP algorithm is purposefully applied for detection in this model in order to handle the data dependent media noise which is caused by irregular bit transitions in both dimensions. Results are provided to show that the incorporation of the DDN distributions into the GBP detection helps improving the detection performance.

Error Analysis for ML Sequence Detection in ISI Channels With Gauss Markov Noise

We consider error probability analysis for a class of ISI channels with data-dependent Gauss-Markov noise and propose an efficiently computable BER upper bound that is tight in the high SNR regime.

High Recording Density Tape Using Fine Barium-Ferrite Particles With Improved Thermal Stability

The effects of reducing barium-ferrite magnetic particle volume have been studied. We optimized barium-ferrite substitution elements and their amount and demonstrated thermal stability for very fine particles of the size 1.5 × 103 nm3. Using a giant magnetoresistive (GMR) head with a 0.2 ?m read track width, test tape containing these fine particles exhibited a bit error rate of 1.5 ×10-4 at a linear density of 360 kbpi using a noise predictive maximum likelihood (NPML) detection for nonstationary noise sources, i.e., data-dependent noise. This corresponds to a 15 Gb/in2 areal recording density in linear tape application.

Nonuniform Data-Dependent Noise Prediction in Magnetic Recording

In this paper, we report a method for nonuniform data-dependent noise prediction (DDNP), in which the noise predictive filters do not have an identical order (number of taps). To accommodate this new architecture, we implemented a partial decision feedback strategy for branch metric computations of the higher order predictive filters. Theoretical analysis and computer simulations show that our proposed DDNP can achieve a better tradeoff between detection performance and computational complexity compared with the previously reported DDNP

Data-Aided Timing Recovery for Recording Channels With Data-Dependent Noise

In high-density data storage systems, noise becomes highly correlated and data dependent as a result of media noise, channel nonlinearities, and front-end filters. In such environments, conventional timing recovery schemes will exhibit large residual timing jitter and, especially, data-dependent timing jitter. This paper presents a new data-aided timing recovery algorithm for data storage systems with data-dependent noise. We derive a maximum-likelihood timing recovery scheme based on a data-dependent Gauss-Markov model of the noise. The timing recovery algorithm incorporates data-dependent noise prediction parameters in the form of linear prediction filters and prediction error variances. Moreover, because noise can be nonstationary in practice, we propose an adaptive algorithm to estimate and track the noise prediction parameters. Simulation results, for an idealized optical storage channel incorporating a simple model of media noise, illustrate the merits of our algorithm