arXiv subjects

Alfred M. Bruckstein

Publications and source records attributed to Alfred M. Bruckstein.

51 records · Page 3Linked to original sources

arXiv2018

Optimized Pre-Compensating Compression

In imaging systems, following acquisition, an image/video is transmitted or stored and eventually presented to human observers using different and often imperfect display devices. While the resulting quality of the output image may severely be affected by the display, this degradation is usually ignored in the preceding compression. In this paper we model the sub-optimality of the display device as a known degradation operator applied on the decompressed image/video. We assume the use of a standard compression path, and augment it with a suitable pre-processing procedure, providing a compressed signal intended to compensate the degradation without any post-filtering. Our approach originates from an intricate rate-distortion problem, optimizing the modifications to the input image/video for reaching best end-to-end performance. We address this seemingly computationally intractable problem using the alternating direction method of multipliers (ADMM) approach, leading to a procedure in which a standard compression technique is iteratively applied. We demonstrate the proposed method for adjusting HEVC image/video compression to compensate post-decompression visual effects due to a common type of displays. Particularly, we use our method to reduce motion-blur perceived while viewing video on LCD devices. The experiments establish our method as a leading approach for preprocessing high bit-rate compression to counterbalance a post-decompression degradation.

cs.MM↗

arXiv2018

System-Aware Compression

Many information systems employ lossy compression as a crucial intermediate stage among other processing components. While the important distortion is defined by the system's input and output signals, the compression usually ignores the system structure, therefore, leading to an overall sub-optimal rate-distortion performance. In this paper we propose a compression methodology for an operational rate-distortion optimization considering a known system layout, modeled using linear operators and noise. Using the alternating direction method of multipliers (ADMM) technique, we show that the design of the new globally-optimized compression reduces to a standard compression of a "system adjusted" signal. Essentially, the proposed framework leverages standard compression techniques to address practical settings of the noisy source coding problem. We further explain the main ideas of our method by theoretically studying the case of a cyclo-stationary Gaussian signal. We present experimental results for coding of one-dimensional signals and for video compression using the HEVC standard, showing significant gains by the adjustment to an acquisition-rendering system.

cs.IT↗

arXiv2018

On High-Resolution Adaptive Sampling of Deterministic Signals

In this work we study the topic of high-resolution adaptive sampling of a given deterministic signal and establish a connection with classic approaches to high-rate quantization. Specifically, we formulate solutions for the task of optimal high-resolution sampling, counterparts of well-known results for high-rate quantization. Our results reveal that the optimal high-resolution sampling structure is determined by the density of the signal-gradient energy, just as the probability-density-function defines the optimal high-rate quantization form. This paper has three main contributions: the first is establishing a fundamental paradigm bridging the topics of sampling and quantization. The second is a theoretical analysis of nonuniform sampling relevant to the emerging field of high-resolution signal processing. The third is a new practical approach to nonuniform sampling of one-dimensional signals that enables reconstruction based only on the sampling time-points and the signal extrema locations and values. Experiments for signal sampling and coding showed that our method outperforms an optimized tree-structured sampling technique.

cs.IT↗

arXiv2018

Compression for Multiple Reconstructions

In this work we propose a method for optimizing the lossy compression for a network of diverse reconstruction systems. We focus on adapting a standard image compression method to a set of candidate displays, presenting the decompressed signals to viewers. Each display is modeled as a linear operator applied after decompression, and its probability to serve a network user. We formulate a complicated operational rate-distortion optimization trading-off the network's expected mean-squared reconstruction error and the compression bit-cost. Using the alternating direction method of multipliers (ADMM) we develop an iterative procedure where the network structure is separated from the compression method, enabling the reliance on standard compression techniques. We present experimental results showing our method to be the best approach for adjusting high bit-rate image compression (using the state-of-the-art HEVC standard) to a set of displays modeled as blur degradations.

cs.MM↗

arXiv2016

AntPaP: Patrolling and Fair Partitioning of Graphs by A(ge)nts Leaving Pheromone Traces

A team of identical and oblivious ant-like agents - a(ge)nts - leaving pheromone traces, are programmed to jointly patrol an area modeled as a graph. They perform this task using simple local interactions, while also achieving the important byproduct of partitioning the graph into roughly equal-sized disjoint sub-graphs. Each a(ge)nt begins to operate at an arbitrary initial location, and throughout its work does not acquire any information on either the shape or size of the graph, or the number or whereabouts of other a(ge)nts. Graph partitioning occurs spontaneously, as each of the a(ge)nts patrols and expands its own pheromone-marked sub-graph, or region. This graph partitioning algorithm is inspired by molecules hitting the borders of air filled elastic balloons: an a(ge)nt that hits a border edge from the interior of its region more frequently than an external a(ge)nt hits the same edge from an adjacent vertex in the neighboring region, may conquer that adjacent vertex, expanding its region at the expense of the neighbor. Since the rule of patrolling a region ensures that each vertex is visited with a frequency inversely proportional to the size of the region, in terms of vertex count, a smaller region will effectively exert higher "pressure" at its borders, and conquer adjacent vertices from a larger region, thereby increasing the smaller region and shrinking the larger. The algorithm, therefore, tends to equalize the sizes of the regions patrolled, resembling a set of perfectly elastic physical balloons, confined to a closed volume and filled with an equal amount of air. The pheromone based local interactions of agents eventually cause the system to evolve into a partition that is close to balanced rather quickly, and if the graph and the number of a(ge)nts remain unchanged, it is guaranteed that the system settles into a stable and balanced partition.

cs.MA↗

arXiv2016

Real-Time Depth Refinement for Specular Objects

The introduction of consumer RGB-D scanners set off a major boost in 3D computer vision research. Yet, the precision of existing depth scanners is not accurate enough to recover fine details of a scanned object. While modern shading based depth refinement methods have been proven to work well with Lambertian objects, they break down in the presence of specularities. We present a novel shape from shading framework that addresses this issue and enhances both diffuse and specular objects' depth profiles. We take advantage of the built-in monochromatic IR projector and IR images of the RGB-D scanners and present a lighting model that accounts for the specular regions in the input image. Using this model, we reconstruct the depth map in real-time. Both quantitative tests and visual evaluations prove that the proposed method produces state of the art depth reconstruction results.

cs.CV↗

arXiv2016

Postprocessing of Compressed Images via Sequential Denoising

In this work we propose a novel postprocessing technique for compression-artifact reduction. Our approach is based on posing this task as an inverse problem, with a regularization that leverages on existing state-of-the-art image denoising algorithms. We rely on the recently proposed Plug-and-Play Prior framework, suggesting the solution of general inverse problems via Alternating Direction Method of Multipliers (ADMM), leading to a sequence of Gaussian denoising steps. A key feature in our scheme is a linearization of the compression-decompression process, so as to get a formulation that can be optimized. In addition, we supply a thorough analysis of this linear approximation for several basic compression procedures. The proposed method is suitable for diverse compression techniques that rely on transform coding. Specifically, we demonstrate impressive gains in image quality for several leading compression methods - JPEG, JPEG2000, and HEVC.

cs.CV↗

arXiv2015

On Optimal Disc Covers and a New Characterization of the Steiner Center

Given N points in the plane $P_1 P_2...P_N$ and a location $Ω$, the union of discs with diameters $[ΩP_i], i = 1, 2,...N$ covers the convex hull of the points. The location $Ω_s$ minimizing the area covered by the union of discs, is shown to be the Steiner center of the convex hull of the points. Similar results for $d$-dimensional Euclidean space are conjectured.

cs.CG↗

arXiv2015

Sparsity Based Methods for Overparameterized Variational Problems

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the cosparse analysis framework, which may potentially help in bridging sparse approximation based methods to the traditional total-variation minimization. Based on this, we introduce a sparsity based framework for solving overparameterized variational problems. The latter has been used to improve the estimation of optical flow and also for general denoising of signals and images. However, the recovery of the space varying parameters involved was not adequately addressed by traditional variational methods. We first demonstrate the efficiency of the new framework for one dimensional signals in recovering a piecewise linear and polynomial function. Then, we illustrate how the new technique can be used for denoising and segmentation of images.

cs.CV↗

arXiv2015

Depth Perception in Autostereograms: 1/f-Noise is Best

An autostereogram is a single image that encodes depth information that pops out when looking at it. The trick is achieved by replicating a vertical strip that sets a basic two-dimensional pattern with disparity shifts that encode a three-dimensional scene. It is of interest to explore the dependency between the ease of perceiving depth in autostereograms and the choice of the basic pattern used for generating them. In this work we confirm a theory proposed by Bruckstein et al. to explain the process of autostereographic depth perception, providing a measure for the ease of "locking into" the depth profile, based on the spectral properties of the basic pattern used. We report the results of three sets of psychophysical experiments using autostereograms generated from two-dimensional random noise patterns having power spectra of the form $1/f^β$. The experiments were designed to test the ability of human subjects to identify smooth, low resolution surfaces, as well as detail, in the form of higher resolution objects in the depth profile, and to determine limits in identifying small objects as a function of their size. In accordance with the theory, we discover a significant advantage of the $1/f$ noise pattern (pink noise) for fast depth lock-in and fine detail detection, showing that such patterns are optimal choices for autostereogram design. Validating the theoretical model predictions strengthens its underlying assumptions, and contributes to a better understanding of the visual system's binocular disparity mechanisms.

cs.CV↗

arXiv2015

Improving Low Bit-Rate Video Coding using Spatio-Temporal Down-Scaling

Good quality video coding for low bit-rate applications is important for transmission over narrow-bandwidth channels and for storage with limited memory capacity. In this work, we develop a previous analysis for image compression at low bit-rates to adapt it to video signals. Improving compression using down-scaling in the spatial and temporal dimensions is examined. We show, both theoretically and experimentally, that at low bit-rates, we benefit from applying spatio-temporal scaling. The proposed method includes down-scaling before the compression and a corresponding up-scaling afterwards, while the codec itself is left unmodified. We propose analytic models for low bit-rate compression and spatio-temporal scaling operations. Specifically, we use theoretic models of motion-compensated prediction of available and absent frames as in coding and frame-rate up-conversion (FRUC) applications, respectively. The proposed models are designed for multi-resolution analysis. In addition, we formulate a bit-allocation procedure and propose a method for estimating good down-scaling factors of a given video based on its second-order statistics and the given bit-budget. We validate our model with experimental results of H.264 compression.

cs.MM↗

arXiv2014

Motion-Compensated Coding and Frame-Rate Up-Conversion: Models and Analysis

Block-based motion estimation (ME) and compensation (MC) techniques are widely used in modern video processing algorithms and compression systems. The great variety of video applications and devices results in numerous compression specifications. Specifically, there is a diversity of frame-rates and bit-rates. In this paper, we study the effect of frame-rate and compression bit-rate on block-based ME and MC as commonly utilized in inter-frame coding and frame-rate up conversion (FRUC). This joint examination yields a comprehensive foundation for comparing MC procedures in coding and FRUC. First, the video signal is modeled as a noisy translational motion of an image. Then, we theoretically model the motion-compensated prediction of an available and absent frames as in coding and FRUC applications, respectively. The theoretic MC-prediction error is further analyzed and its autocorrelation function is calculated for coding and FRUC applications. We show a linear relation between the variance of the MC-prediction error and temporal-distance. While the affecting distance in MC-coding is between the predicted and reference frames, MC-FRUC is affected by the distance between the available frames used for the interpolation. Moreover, the dependency in temporal-distance implies an inverse effect of the frame-rate. FRUC performance analysis considers the prediction error variance, since it equals to the mean-squared-error of the interpolation. However, MC-coding analysis requires the entire autocorrelation function of the error; hence, analytic simplicity is beneficial. Therefore, we propose two constructions of a separable autocorrelation function for prediction error in MC-coding. We conclude by comparing our estimations with experimental results.

cs.MM↗

arXiv2012

The Cooperative Cleaners Problem in Stochastic Dynamic Environments

In this paper we study the strengths and limitations of collaborative teams of simple agents. In particular, we discuss the efficient use of "ant robots" for covering a connected region on the $Z^{2}$ grid, whose area is unknown in advance and which expands stochastically. Specifically, we discuss the problem where an initial connected region of $S_0$ boundary tiles expand outward with probability $p$ at every time step. On this grid region a group of $k$ limited and simple agents operate, in order to clean the unmapped and dynamically expanding region. A preliminary version of this problem was discussed in [1],[2] involving a deterministic expansion of a region in the grid.In this work we extend the model and examine cases where the spread of the region is done stochastically, where each tile has some probability $p$ to expand, at every time step. For this extended model we obtain an analytic probabilistic lower bounds for the minimal number of agents and minimal time required to enable a collaborative coverage of the expanding region, regardless of the algorithm used and the robots' hardware and software specifications. In addition, we present an impossibility result, for a variety of regions that would be impossible to completely clean, regardless of the algorithm used. Finally, we validate the analytic bounds using extensive empirical computer simulation results.

cs.MA↗

arXiv2011

Simple and Robust Binary Self-Location Patterns

A simple method to generate a two-dimensional binary grid pattern, which allows for absolute and accurate self-location in a finite planar region, is proposed. The pattern encodes position information in a local way so that reading a small number of its black or white pixels at any place provides sufficient data from which the location can be decoded both efficiently and robustly.

cs.IT↗

arXiv2010

The Sample Complexity of Dictionary Learning

A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications, including classification, denoising and signal separation, learn a dictionary from a set of signals to be represented. Can we expect that the representation found by such a dictionary for a previously unseen example from the same source will have L_2 error of the same magnitude as those for the given examples? We assume signals are generated from a fixed distribution, and study this questions from a statistical learning theory perspective. We develop generalization bounds on the quality of the learned dictionary for two types of constraints on the coefficient selection, as measured by the expected L_2 error in representation when the dictionary is used. For the case of l_1 regularized coefficient selection we provide a generalization bound of the order of O(sqrt(np log(m lambda)/m)), where n is the dimension, p is the number of elements in the dictionary, lambda is a bound on the l_1 norm of the coefficient vector and m is the number of samples, which complements existing results. For the case of representing a new signal as a combination of at most k dictionary elements, we provide a bound of the order O(sqrt(np log(m k)/m)) under an assumption on the level of orthogonality of the dictionary (low Babel function). We further show that this assumption holds for most dictionaries in high dimensions in a strong probabilistic sense. Our results further yield fast rates of order 1/m as opposed to 1/sqrt(m) using localized Rademacher complexity. We provide similar results in a general setting using kernels with weak smoothness requirements.

stat.ML↗