Recently, much progress has been made in unsupervised restoration learning. However, existing methods more or less rely on some assumptions on the signal and/or degradation model, which limits their practical performance. How to construct an optimal
criterion for unsupervised restoration learning without any prior knowledge on the degradation model is still an open question. Toward answering this question, this work proposes a criterion for unsupervised restoration learning based on the optimal transport theory. This criterion has favorable properties, e.g., approximately maximal preservation of the information of the signal, whilst achieving perceptual reconstruction. Furthermore, though a relaxed unconstrained formulation is used in practical implementation, we show that the relaxed formulation in theory has the same solution as the original constrained formulation. Experiments on synthetic and real-world data, including realistic photographic, microscopy, depth, and raw depth images, demonstrate that the proposed method even compares favorably with supervised methods, e.g., approaching the PSNR of supervised methods while having better perceptual quality. Particularly, for spatially correlated noise and realistic microscopy images, the proposed method not only achieves better perceptual quality but also has higher PSNR than supervised methods. Besides, it shows remarkable superiority in harsh practical conditions with complex noise, e.g., raw depth images.
Lossy compression algorithms are typically designed to achieve the lowest possible distortion at a given bit rate. However, recent studies show that pursuing high perceptual quality would lead to increase of the lowest achievable distortion (e.g., MS
E). This paper provides nontrivial results theoretically revealing that, textit{1}) the cost of achieving perfect perception quality is exactly a doubling of the lowest achievable MSE distortion, textit{2}) an optimal encoder for the classic rate-distortion problem is also optimal for the perceptual compression problem, textit{3}) distortion loss is unnecessary for training a perceptual decoder. Further, we propose a novel training framework to achieve the lowest MSE distortion under perfect perception constraint at a given bit rate. This framework uses a GAN with discriminator conditioned on an MSE-optimized encoder, which is superior over the traditional framework using distortion plus adversarial loss. Experiments are provided to verify the theoretical finding and demonstrate the superiority of the proposed training framework.
The quantity $T_0$, the cosmic microwave background (CMB) monopole, is an often neglected seventh parameter of the standard cosmological model. As well as its variation affecting the physics of the CMB, the measurement of $T_0$ is also used to calibr
ate the anisotropies, via the orbital dipole. We point out that it is easy to misestimate the effect of $T_0$ because the CMB anisotropies are conventionally provided in temperature units. In fact the anisotropies are most naturally described as dimensionless and we argue for restoring the convention of working with $Delta T/T$ rather than $Delta T$. As a free cosmological parameter, $T_0$ most naturally only impacts the CMB power spectra through late-time effects. Thus if we ignore the COBE-FIRAS measurement, current CMB data only weakly constrain $T_0$. Even ideal future CMB data can at best provide a percent-level constraint on $T_0$, although adding large-scale structure data will lead to further improvement. The FIRAS measurement is so precise that its uncertainty negligibly effects most, but not all, cosmological parameter inferences for current CMB experiments. However, if we eventually want to extract all available information from CMB power spectra measured to multipoles $ellsimeq5000$, then we will need a better determination of $T_0$ than is currently available.
Hybrid memory systems, comprised of emerging non-volatile memory (NVM) and DRAM, have been proposed to address the growing memory demand of applications. Emerging NVM technologies, such as phase-change memories (PCM), memristor, and 3D XPoint, have h
igher capacity density, minimal static power consumption and lower cost per GB. However, NVM has longer access latency and limited write endurance as opposed to DRAM. The different characteristics of two memory classes point towards the design of hybrid memory systems containing multiple classes of main memory. In the iterative and incremental development of new architectures, the timeliness of simulation completion is critical to project progression. Hence, a highly efficient simulation method is needed to evaluate the performance of different hybrid memory system designs. Design exploration for hybrid memory systems is challenging, because it requires emulation of the full system stack, including the OS, memory controller, and interconnect. Moreover, benchmark applications for memory performance test typically have much larger working sets, thus taking even longer simulation warm-up period. In this paper, we propose a FPGA-based hybrid memory system emulation platform. We target at the mobile computing system, which is sensitive to energy consumption and is likely to adopt NVM for its power efficiency. Here, because the focus of our platform is on the design of the hybrid memory system, we leverage the on-board hard IP ARM processors to both improve simulation performance while improving accuracy of the results. Thus, users can implement their data placement/migration policies with the FPGA logic elements and evaluate new designs quickly and effectively. Results show that our emulation platform provides a speedup of 9280x in simulation time compared to the software counterpart Gem5.
Maximum consensus (MC) robust fitting is a fundamental problem in low-level vision to process raw-data. Typically, it firstly finds a consensus set of inliers and then fits a model on the consensus set. This work proposes a new formulation to achieve
simultaneous maximum consensus and model estimation (MCME), which has two significant features compared with traditional MC robust fitting. First, it takes fitting residual into account in finding inliers, hence its lowest achievable residual in model fitting is lower than that of MC robust fitting. Second, it has an unconstrained formulation involving binary variables, which facilitates the use of the effective semidefinite relaxation (SDR) method to handle the underlying challenging combinatorial optimization problem. Though still nonconvex after SDR, it becomes biconvex in some applications, for which we use an alternating minimization algorithm to solve. Further, the sparsity of the problem is exploited in combination with low-rank factorization to develop an efficient algorithm. Experiments show that MCME significantly outperforms RANSAC and deterministic approximate MC methods at high outlier ratios. Besides, in rotation and Euclidean registration, it also compares favorably with state-of-the-art registration methods, especially in high noise and outliers. Code is available at textit{https://github.com/FWen/mcme.git}.
The current mobile applications have rapidly growing memory footprints, posing a great challenge for memory system design. Insufficient DRAM main memory will incur frequent data swaps between memory and storage, a process that hurts performance, cons
umes energy and deteriorates the write endurance of typical flash storage devices. Alternately, a larger DRAM has higher leakage power and drains the battery faster. Further, DRAM scaling trends make further growth of DRAMin the mobile space prohibitive due to cost. Emerging non-volatile memory (NVM) has the potential to alleviate these issues due to its higher capacity per cost than DRAM and mini-mal static power. Recently, a wide spectrum of NVM technologies, including phase-change memories (PCM), memristor, and 3D XPoint have emerged. Despite the mentioned advantages, NVM has longer access latency compared to DRAMand NVM writes can incur higher latencies and wear costs. Therefore integration of these new memory technologies in the memory hierarchy requires a fundamental rearchitect-ing of traditional system designs. In this work, we propose a hardware-accelerated memory manager (HMMU) that addresses both types of memory in a flat space address space. We design a set of data placement and data migration policies within this memory manager, such that we may exploit the advantages of each memory technology. By augmenting the system with this HMMU, we reduce the overall memory latency while also reducing writes to the NVM. Experimental results show that our design achieves a 39% reduction in energy consumption with only a 12% performance degradation versus an all-DRAM baseline that is likely untenable in the future.
Blind image deblurring is a long standing challenging problem in image processing and low-level vision. Recently, sophisticated priors such as dark channel prior, extreme channel prior, and local maximum gradient prior, have shown promising effective
ness. However, these methods are computationally expensive. Meanwhile, since these priors involved subproblems cannot be solved explicitly, approximate solution is commonly used, which limits the best exploitation of their capability. To address these problems, this work firstly proposes a simplified sparsity prior of local minimal pixels, namely patch-wise minimal pixels (PMP). The PMP of clear images is much more sparse than that of blurred ones, and hence is very effective in discriminating between clear and blurred images. Then, a novel algorithm is designed to efficiently exploit the sparsity of PMP in deblurring. The new algorithm flexibly imposes sparsity inducing on the PMP under the MAP framework rather than directly uses the half quadratic splitting algorithm. By this, it avoids non-rigorous approximation solution in existing algorithms, while being much more computationally efficient. Extensive experiments demonstrate that the proposed algorithm can achieve better practical stability compared with state-of-the-arts. In terms of deblurring quality, robustness and computational efficiency, the new algorithm is superior to state-of-the-arts. Code for reproducing the results of the new method is available at https://github.com/FWen/deblur-pmp.git.
Recently, multi-user multiple input multiple output (MU-MIMO) systems with low-resolution digital-to-analog converters (DACs) has received considerable attention, owing to the capability of dramatically reducing the hardware cost. Besides, it has bee
n shown that the use of low-resolution DACs enable great reduction in power consumption while maintain the performance loss within acceptable margin, under the assumption of perfect knowledge of channel state information (CSI). In this paper, we investigate the precoding problem for the coarsely quantized MU-MIMO system without such an assumption. The channel uncertainties are modeled to be a random matrix with finite second-order statistics. By leveraging a favorable relation between the multi-bit DACs outputs and the single-bit ones, we first reformulate the original complex precoding problem into a nonconvex binary optimization problem. Then, using the S-procedure lemma, the nonconvex problem is recast into a tractable formulation with convex constraints and finally solved by the semidefinite relaxation (SDR) method. Compared with existing representative methods, the proposed precoder is robust to various channel uncertainties and is able to support a MUMIMO system with higher-order modulations, e.g., 16QAM.
Matrix completion has attracted much interest in the past decade in machine learning and computer vision. For low-rank promotion in matrix completion, the nuclear norm penalty is convenient due to its convexity but has a bias problem. Recently, vario
us algorithms using nonconvex penalties have been proposed, among which the proximal gradient descent (PGD) algorithm is one of the most efficient and effective. For the nonconvex PGD algorithm, whether it converges to a local minimizer and its convergence rate are still unclear. This work provides a nontrivial analysis on the PGD algorithm in the nonconvex case. Besides the convergence to a stationary point for a generalized nonconvex penalty, we provide more deep analysis on a popular and important class of nonconvex penalties which have discontinuous thresholding functions. For such penalties, we establish the finite rank convergence, convergence to restricted strictly local minimizer and eventually linear convergence rate of the PGD algorithm. Meanwhile, convergence to a local minimizer has been proved for the hard-thresholding penalty. Our result is the first shows that, nonconvex regularized matrix completion only has restricted strictly local minimizers, and the PGD algorithm can converge to such minimizers with eventually linear rate under certain conditions. Illustration of the PGD algorithm via experiments has also been provided. Code is available at https://github.com/FWen/nmc.
In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the $ell_1$ norm and nuclear
norm are of the most popular regularization penalties due to their convexity. While the $ell_1$ and nuclear norm are convenient as the related convex optimization problems are usually tractable, it has been shown in many applications that a nonconvex penalty can yield significantly better performance. In recent, nonconvex regularization based sparse and low-rank recovery is of considerable interest and it in fact is a main driver of the recent progress in nonconvex and nonsmooth optimization. This paper gives an overview of this topic in various fields in signal processing, statistics and machine learning, including compressive sensing (CS), sparse regression and variable selection, sparse signals separation, sparse principal component analysis (PCA), large covariance and inverse covariance matrices estimation, matrix completion, and robust PCA. We present recent developments of nonconvex regularization based sparse and low-rank recovery in these fields, addressing the issues of penalty selection, applications and the convergence of nonconvex algorithms. Code is available at https://github.com/FWen/ncreg.git.
