This work presents a simple yet effective workflow for automatically scaling instruction-following data to elicit pixel-level grounding capabilities of VLMs under complex instructions. In particular, we address five critical real-world challenges in text-instruction-based grounding: hallucinated references, multi-object scenarios, reasoning, multi-granularity, and part-level references. By leveraging knowledge distillation from a pre-trained teacher model, our approach generates high-quality instruction-response pairs linked to existing pixel-level annotations, minimizing the need for costly human annotation. The resulting dataset, Ground-V, captures rich object localization knowledge and nuanced pixel-level referring expressions. Experiment results show that models trained on Ground-V exhibit substantial improvements across diverse grounding tasks. Specifically, incorporating Ground-V during training directly achieve an average accuracy boost of 4.4% for LISA and a 7.9% for PSALM across six benchmarks on the gIoU metric. It also sets new state-of-the-art results on standard benchmarks such as RefCOCO/+/g. Notably, on gRefCOCO, we achieve an N-Acc of 83.3%, exceeding the previous state-of-the-art by more than 20%.

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to a large error when using a small dataset (e.g., 5 samples per class) for extrapolation. This is because the log-performance error against the log-dataset size follows a nonlinear progression in the few-shot regime followed by a linear progression in the high-shot regime. We introduce a novel piecewise power law (PPL) that handles the two data regimes differently. To estimate the parameters of the PPL, we introduce a random forest regressor trained via meta learning that generalizes across classification/detection tasks, ResNet/ViT based architectures, and random/pre-trained initializations. The PPL improves the performance estimation on average by 37% across 16 classification and 33% across 10 detection datasets, compared to the power law. We further extend the PPL to provide a confidence bound and use it to limit the prediction horizon that reduces over-estimation of data by 76% on classification and 91% on detection datasets.

Visual anomaly classification and segmentation are vital for automating industrial quality inspection. The focus of prior research in the field has been on training custom models for each quality inspection task, which requires task-specific images and annotation. In this paper we move away from this regime, addressing zero-shot and few-normal-shot anomaly classification and segmentation. Recently CLIP, a vision-language model, has shown revolutionary generality with competitive zero-/few-shot performance in comparison to full-supervision. But CLIP falls short on anomaly classification and segmentation tasks. Hence, we propose window-based CLIP (WinCLIP) with (1) a compositional ensemble on state words and prompt templates and (2) efficient extraction and aggregation of window/patch/image-level features aligned with text. We also propose its few-normal-shot extension Win-CLIP+, which uses complementary information from normal images. In MVTec-AD (and VisA), without further tuning, WinCLIP achieves 91.8%/85.1% (78.1%/79.6%) AU-ROC in zero-shot anomaly classification and segmentation while WinCLIP + does 93.1%/95.2% (83.8%/96.4%) in 1-normal-shot, surpassing state-of-the-art by large margins.

Model selection is essential for reducing the search cost of the best pre-trained model over a large-scale model zoo for a downstream task. After analyzing recent hand-designed model selection criteria with 400+ ImageNet pre-trained models and 40 downstream tasks, we find that they can fail due to invalid assumptions and intrinsic limitations. The prior knowledge on model capacity and dataset also can not be easily integrated into the existing criteria. To address these issues, we propose to convert model selection as a recommendation problem and to learn from the past training history. Specifically, we characterize the meta information of datasets and models as features, and use their transfer learning performance as the guided score. With thousands of historical training jobs, a recommendation system can be learned to predict the model selection score given the features of the dataset and the model as input. Our approach enables integrating existing model selection scores as additional features and scales with more historical data. We evaluate the prediction accuracy with 22 pre-trained models over 40 downstream tasks. With extensive evaluations, we show that the learned approach can outperform prior hand-designed model selection methods significantly when relevant training history is available.

Autonomous vehicles rely on precise high definition (HD) 3D maps for navigation. This paper presents the mapping component of an end-to-end system for crowdsourcing precise 3D maps with semantically meaningful landmarks such as traffic signs (6 dof pose, shape and size) and traffic lanes (3D splines). The system uses consumer grade parts, and in particular, relies on a single front facing camera and a consumer grade GPS. Using real-time sign and lane triangulation on-device in the vehicle, with offline sign/lane clustering across multiple journeys and offline Bundle Adjustment across multiple journeys in the backend, we construct maps with mean absolute accuracy at sign corners of less than 20 cm from 25 journeys. To the best of our knowledge, this is the first end-to-end HD mapping pipeline in global coordinates in the automotive context using cost effective sensors.

In this article, we identify adaptive sampling strategies for haptic signals. Our approach relies on experiments wherein we record the response of several users to haptic stimuli. We then learn different classifiers to predict the user response based on a variety of causal signal features. The classifiers that have good prediction accuracy serve as candidates to be used in adaptive sampling. We compare the resultant adaptive samplers based on their rate-distortion tradeoff using synthetic as well as natural data. For our experiments, we use a haptic device with a maximum force level of 3 N and 10 users. Each user is subjected to several piecewise constant haptic signals and is required to click a button whenever he perceives a change in the signal. For classification, we not only use classifiers based on level crossings and Weber’s law but also random forests using a variety of causal signal features. The random forest typically yields the best prediction accuracy and a study of the importance of variables suggests that the level crossings and Weber’s classifier features are most dominant. The classifiers based on level crossings and Weber’s law have good accuracy (more than 90%) and are only marginally inferior to random forests. The level crossings classifier consistently outperforms the one based on Weber’s law even though the gap is small. Given their simple parametric form, the level crossings and Weber’s law--based classifiers are good candidates to be used for adaptive sampling. We study their rate-distortion performance and find that the level crossing sampler is superior. For example, for haptic signals obtained while exploring various rendered objects, for an average sampling rate of 10 samples per second, the level crossings adaptive sampler has a mean square error about 3dB less than the Weber sampler.

In this paper, we study collaborative filters that adapt future recommendations based on feedback from users. We consider discrete time and at each time a random user seeks a recommendation. The collaborative filter uses all past data available to make a recommendation, the user then provides binary feedback indicating whether he liked the item (rating 1) or not (rating 0), and this feedback is used by the collaborative filter for future decisions. In this setting, ideally the goal is to maximize the long run time average of the ratings, but practical considerations lead us to a moving horizon approximation. Our main result identifies a collaborative filter that optimizes a moving horizon cost in the limit as the noise in the ratings vanishes.

MIMO systems with several antennas at the transmitter and receiver have the potential to enable high throughputs. One of the challenges in realizing this potential is the design of receivers that scale in terms of computation and performance. Towards this end, in this paper, we propose a receiver that uses a committee of linear receivers, whose parameters are estimated from training data using a variant of the AdaBoost algorithm, a celebrated supervised classification algorithm in machine learning. We call our receiver boosted MMSE (B-MMSE) receiver and we study its performance via simulations. The channel matrix is estimated from the pilot using the MMSE technique. We find that for a 4 × 4 system with a Rayleigh fading channel, using BPSK at a bit error rate (BER) of 10-2, our receiver using the estimated channel matrix needs 2 dB less power than the plain MMSE receiver based on the estimated channel matrix. On an average, excluding the training phase, the receiver complexity equals 1.25 linear receivers. Thus the BMMSE receiver is slightly more complex than the MMSE receiver and substantially less complex than the maximum-likelihood receiver. We also show that the coded BER performance with an outer rate-3/4 Turbo-code has a gain of 5 dB at 10-4coded BER when the demodulated output from the proposed method is used in place of plain MMSE detection with MMSE estimated channel.

Multiple input multiple output (MIMO) systems with large number of antennas have been gaining wide attention as they enable very high throughputs. A major impediment is the complexity at the receiver needed to detect the transmitted data. To this end we propose a new receiver, called LRR (Linear Regression of MMSE Residual), which improves the MMSE receiver by learning a linear regression model for the error of the MMSE receiver. The LRR receiver uses pilot data to estimate the channel, and then uses locally generated training data (not transmitted over the channel), to find the linear regression parameters. The proposed receiver is suitable for applications where the channel remains constant for a long period (slowfading channels) and performs quite well: at a bit error rate (BER) of 10-3, the SNR gain over MMSE receiver is about 7 dB for a 16 × 16 system; for a 64 × 64 system the gain is about 8.5 dB. For large coherence time, the complexity order of the LRR receiver is the same as that of the MMSE receiver, and in simulations we find that it needs about 4 times as many floating point operations. We also show that further gain of about 4 dB is obtained by local search around the estimate given by the LRR receiver.

Motivated by the need to reduce power consumption in the receiver analog-to-digital converter (ADC) in multi-Gbps communication systems, in this paper, we study subcarrier power allocation based on channel side information (CSI) at the transmitter. We derive a fixed point equation for subcarrier power allocation that minimizes uncoded symbol error rate (SER) when a finite precision ADC is used at the receiver. We study the sensitivity of the optimal power allocation with respect to a parameter that depends on the ADC precision. Based on this, we propose a simple analytical approximation for the optimal power allocation, which performs within 0.5 dB of the exact case over a wide range of signal-to-noise ratio (SNR). The proposed power allocation leads to only a small increase in the peak-to-average power ratio (PAPR) (< 0.3 dB) for channel models suggested in IEEE 802.15.3c. Further, for a 16-QAM input, 7/8 rate low density parity check (LDPC) code and 3-bit precision ADC, it attains a coded bit error rate (BER) of 10^{-5} at a SNR of 23.5 dB, which compares favorably with the 25 dB required by a traditional system with equal power allocation across the subcarriers and infinite sampling precision. We also show the robustness of the performance gain to channel estimation errors.

Orthogonal frequency division multiplexing (OFDM) has been incorporated in standards/draft standards such as IEEE 80.15.3c, IEEE 802.11ad for building multi-Gigabit systems operating in a few GHz of bandwidth. The digital implementation of the receivers for such a system is challenging because high precision (6+ bits/sample) analog-to-digital conversion (ADC) at such high speeds is power hungry and expensive. In this paper, we show that by suitable subcarrier power allocation we can get good performance even with low precision ADC (1-4 bits/sample without oversampling). We derive an analytical expression for the uncoded SER of an M-QAM OFDM system with finite precision ADC. By accounting for automatic gain control (AGC), we show that equal received subcarrier power (ERSP) leads to less quantization noise power than equal transmit subcarrier power (ETSP). Furthermore, for high SNR, ERSP has a lower symbol error rate (SER) than ETSP. But for lower SNR, ETSP is better, and hence we also use convex combinations of ETSP and ERSP power allocations. We illustrate the accuracy of our analytical results with simulations for the Saleh-Valenzuela channel model with log-normal fading. Our results show that for 16-QAM, at SER of 0.01, with a 3-bit ADC and a combination of ERSP and ETSP, we can come within 1 dB of ETSP of the full precision case (while ETSP with 3-bit ADC has a SER floor above 0.04).

In this paper, we analyze a collaborative filter that answers the simple question: What is popular amongst your “friends”? While this basic principle seems to be prevalent in many practical implementations, there does not appear to be much theoretical analysis of its performance. In this paper, we partly fill this gap. While recent works on this topic, such as the low-rank matrix completion literature, consider the probability of error in recovering the entire rating matrix, we consider probability of an error in an individual recommendation [bit error rate (BER)]. For a mathematical model introduced by Aditya et al. in 2009 and 2011, we identify three regimes of operation for our algorithm (named Popularity Amongst Friends) in the limit as the matrix size grows to infinity. In a regime characterized by large number of samples and small degrees of freedom (defined precisely for the model in the paper), the asymptotic BER is zero; in a regime characterized by large number of samples and large degrees of freedom, the asymptotic BER is bounded away from 0 and 1/2 (and is identified exactly except for a special case); and in a regime characterized by a small number of samples, the algorithm fails. We then compare these results with the performance of the optimal recommender. We also present numerical results for the MovieLens and Netflix datasets. We discuss the empirical performance in light of our theoretical results and compare with an approach based on low-rank matrix completion.

We consider the problem of collaborative filtering from a channel coding perspective. We model the underlying rating matrix as a finite alphabet matrix with block constant structure. The observations are obtained from this underlying matrix through a discrete memoryless channel with a noisy part representing noisy user behavior and an erasure part representing missing data. Moreover, the clusters over which the underlying matrix is constant are unknown. We establish a threshold result for this model: if the largest cluster size is smaller than C1log(mn) (where the rating matrix is of size m × n), then the underlying matrix cannot be recovered with any estimator, but if the smallest cluster size is larger than C2log(mn), then we show a polynomial time estimator with asymptotically vanishing probability of error. In the case of uniform cluster size, not only the order of the threshold, but also the constant is identified.

We consider the problem of estimating the impulse response of a dispersive channel when the channel output is sampled using a low-precision analog-to-digital converter (ADC). While traditional channel estimation techniques require about 6 bits of ADC precision to approach full-precision performance, we are motivated by applications to multiGigabit communication, where we may be forced to use much lower precision (e.g., 1-3 bits) due to considerations of cost, power, and technological feasibility. We show that, even with such low ADC precision, it is possible to attain near full-precision performance using closed-loop estimation, where the ADC input is dithered and scaled. The dither signal is obtained using linear feedback based on the Minimum Mean Squared Error (MMSE) criterion. The dither feedback coefficients and the scaling gains are computed offline using Monte Carlo simulations based on a statistical model for the channel taps, and are found to work well over wide range of channel variations.

Motivated by applications such as recommendation systems, we consider the estimation of a binary random field X obtained by unknown row and column permutations of a block constant random matrix. The estimation of X is based on observations Y, which are obtained by passing entries of X through a binary symmetric channel (BSC) (representing noisy user behavior) and an erasure channel (representing missing data). We analyze an estimation algorithm based on local popularity. We study the bit error rate (BER) in the limit as the matrix size approaches infinity and the erasure rate approaches unity at a specified rate. Our main result identifies three regimes characterized by the cluster size and erasure rate. In one regime, the algorithm has asymptotically zero BER, in another regime the BER is bounded away from 0 and 1/2, while in the remaining regime, the algorithm fails and BER approaches 1/2. Numerical results for the Movielens dataset and comparison with earlier work is also given.

We consider the case when K sensors have strongly correlated measurements - they all observe a 0 or they all observe a 1. The two possibilities are to be tested at the output of a multiple access channel with Rayleigh fading coefficients, which are not known to the transmitter and the receiver. We study the problem of optimal transmitters for this case using the notion of generalized SNR (GSNR). Under certain symmetry and orthogonality restrictions on the transmitter, we find optimal and near-optimal transmission schemes. In particular, for low SNR, type-based multiple access is optimal, while for high SNR, the optimal strategy assigns orthogonal codewords across sensors. In between these two extremes, we identify optimal/near-optimal schemes for any fixed SNR. Simulation results for the probability of error are also given, which demonstrate the relevance of GSNR optimization.

Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size m × n) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix after unknown row and column permutations, erasures, and errors. We derive upper and lower bounds on the achievable probability of error. For fixed erasure and error probability, we show that there exists a constant C1such that if the cluster sizes are less than C1ln(mn), then for any algorithm the probability of error approaches one as m, n ¿ ¿. On the other hand, we show that a simple polynomial time algorithm gives probability of error diminishing to zero provided the cluster sizes are greater than C2ln(mn) for a suitable constant C2.

In this paper, we consider a non-saturated IEEE 802.11 based wireless network. We use a three-way fixed point to model the node behavior with Bernoulli packet arrivals and determine closed form expressions for the distribution of the time spent between two successful transmissions in an isolated network. The results of the analysis have been verified using extensive simulations in QualNet. The methodology presented in the paper is novel and we believe that the analysis like ours can be used as an approximation to model the behavior of sub-components of a larger mesh or hybrid network.

Consider a multiple input multiple output (MIMO) system with pulse amplitude modulation (PAM), where each transmit antenna is allowed to choose a different transmission delay. (We refer to this system as a MIMO system with asynchronous PAM.) Such MIMO systems have been studied before for increasing diversity and avoiding unintentional beamforming. We quantify the capacity/outage capacity improvement due to asynchronism and the corresponding spectral leakage (if any) for MIMO point-to-point and MIMO broadcast channels. We show that under commonly used transmitter spectral mask constraints, the channel has unbounded degrees of freedom. Synchronous PAM exploits only a finite number of these degrees of freedom, and asynchronism helps to improve capacity. For most cases of interest, two distinct shifts attain most of the capacity improvement. These gains are robust to interference from adjacent carriers. Analysis of the spectrum of the asynchronous PAM suggests that optimal water-filling based schemes are useful for improving capacity only in directional links due to possible spectral leakage, while uniform power allocation leads to capacity improvement without any extra spectral leakage.

As communication systems scale up in speed and bandwidth, the cost and power consumption of high-precision (e.g., 8-12 bits) analog-to-digital conversion (ADC) becomes the limiting factor in modern transceiver architectures based on digital signal processing. In this work, we explore the impact of lowering the precision of the ADC on the performance of the communication link. Specifically, we evaluate the communication limits imposed by low-precision ADC (e.g., 1-3 bits) for transmission over the real discrete-time additive white Gaussian noise (AWGN) channel, under an average power constraint on the input. For an ADC with K quantization bins (i.e., a precision of log2K bits), we show that the input distribution need not have any more than K+1 mass points to achieve the channel capacity. For 2-bin (1-bit) symmetric quantization, this result is tightened to show that binary antipodal signaling is optimum for any signal-to- noise ratio (SNR). For multi-bit quantization, a dual formulation of the channel capacity problem is used to obtain tight upper bounds on the capacity. The cutting-plane algorithm is employed to compute the capacity numerically, and the results obtained are used to make the following encouraging observations : (a) up to a moderately high SNR of 20 dB, 2-3 bit quantization results in only 10-20% reduction of spectral efficiency compared to unquantized observations, (b) standard equiprobable pulse amplitude modulated input with quantizer thresholds set to implement maximum likelihood hard decisions is asymptotically optimum at high SNR, and works well at low to moderate SNRs as well.

We investigate the limits of communication over the discrete-time additive white Gaussian noise (AWGN) channel, when the channel output is quantized using a small number of bits. We first provide a proof of our recent conjecture on the optimality of a discrete input distribution in this scenario. Specifically, we show that for any given output quantizer choice with K quantization bins (i.e., a precision of log2K bits), the input distribution, under an average power constraint, need not have any more than K + 1 mass points to achieve the channel capacity. The cutting-plane algorithm is employed to compute this capacity and to generate optimum input distributions. Numerical optimization over the choice of the quantizer is then performed (for 2-bit and 3-bit symmetric quantization), and the results we obtain show that the loss due to low-precision output quantization, which is small at low signal-to-noise ratio (SNR) as expected, can be quite acceptable even for moderate to high SNR values. For example, at SNRs up to 20 dB, 2-3 bit quantization achieves 80-90% of the capacity achievable using infinite-precision quantization.

Motivated by applications in sensor networks and communications, we consider multivariate signal parameter estimation when only dithered 1-bit quantized samples are available. The observation noise is taken to be a stationary, strongly mixing process, which covers a wide range of processes including autoregressive moving average (ARMA) models. The noise is allowed to be Gaussian or to have a heavy-tail (with possibly infinite variance). An estimate of the signal parameters is proposed and is shown to be weakly consistent. Joint asymptotic normality of the parameters estimate is also established and the asymptotic mean and covariance matrices are identified.

Random medium access, such as the one employed in IEEE 802.11 standard, is known to unfairly allocate channel resources under realistic channel conditions such as fading, shadowing and propagation loss. In this paper, we propose and analyze a scheme based on frequency binning to improve grade-of-service. For 802.11a/g, our scheme can be implemented with minor changes to the physical and MAC layers. The proposed frequency binning has positive as well as negative effects. But we show that the positive effect dominates in the spectral efficiency regime of interest and leads to better utilization of underlying channel dimensions. We provide a fixed point analysis of the MAC in steady state and quantify the advantages by studying the improvements in grade-of-service, cell-radius, user-capacity and mean throughput of user at cell-edge.

We consider distributed linear transceivers for sending a second-order wide-sense stationary process observed by two noisy sensors over a Gaussian multiple-access channel (MAC). We derive the minimum mean-square error (MSE) distributed linear transceiver. The optimal linear transmitter exploits bandwidth expansion by repeating transmission and the transmitters at the two sensors are the same except for a constant factor. When the source is white, encoded transmission is the best linear code for any SNR. But for a colored source, whitening transmit filter is sub-optimal. In high SNR regime, the magnitude response of the optimal transmission filter is inversely proportional to fourth-root of the power spectrum of the process (while that for the whitening filler is inversely proportional to the square-root of the spectrum). In the special case of n single sensor with Gaussian source, we also quantify the performance loss of linear source-channel codes with respect to the Shannon limit.

We examine the Shannon limits of communication systems when the precision of the analog-to-digital conversion (ADC) at the receiver is constrained. ADC is costly and power- hungry at high speeds, hence ADC precision is expected to be a limiting factor in the performance of receivers which are heavily based on digital signal processing. In this paper, we consider transmission over an ideal discrete-time real baseband additive white Gaussian noise (AWGN) channel, and provide capacity results when the receiver ADC employs a small number of bits, generalizing our prior work on one bit ADC. We show that dithered ADC does not increase capacity, and hence restrict attention to deterministic quantizers. To compute the capacity, we use a dual formulation of the channel capacity problem, which is attractive due to the discrete nature of the output alphabet. The numerical results we obtain strongly support our conjecture that the optimal input distribution is discrete, and has at most one mass point in each quantizer interval. This implies, for example, that it is not possible to support large alphabets such as 64-QAM using 2-bit quantization on the I and Q channels, at least with symbol rate sampling.

In random access schemes with no power control, such as the RTS/CTS method used in IEEE 802.11 for channel reservation, users with better channels have an advantage over those with bad channels. We propose the use of frequency binning in which a user randomly chooses one of M frequency bins to transmit the RTS. Such frequency binning has two competing effects: a) it reduces the chances of collision for the RTS, which increases the cell radius, b) it increases the signal power required for successful RTS reception due to higher spectral efficiency, which decreases the cell radius. We show that a) dominates in cases of interest and this leads to several advantages: i) it tends to provide equal grade-of-service to competing users in the presence of fading, shadowing, and propagation loss, which increases the cell radius, ii) it reduces access latency, and iii) it enables reception of multiple RTSs (with hardly any increase in transceiver complexity), which can be utilized for further improving the grade-of-service.

Motivated by the estimation of spatio-temporal events with cheap, simple sensors, we consider the problem of estimation of a parameter $\theta$ of a signal $s(x;\theta)$ corrupted by noise assuming that only 1-bit precision dithered quantized samples are available. An estimate that does not require the knowledge of the dither signal and the noise distribution is proposed, and it is analyzed in detail under variety of nonidealities. The consistency and asymptotic normality of the estimate is established for deterministic and random sampling, imprecise knowledge of sampling locations, Gaussian and non-Gaussian noise (with possibly infinite variance), a wide class of dither distributions, and under erroneous transmission of the binary observations via binary-symmetric channels (BSCs). It is also shown that if approximation to the log-likelihood equation in the full precision case yields a good estimate, then there is a corresponding good estimate based on 1-bit dithered samples. The proposed estimate requires no more computation than the maximum-likelihood estimate for the full precision case and suffers only a logarithmic rate loss compared to the full precision case when uniform dithering is used. It is shown that uniform dithering leads to the best rate among a broad class of dither distributions. A condition under which no dithering leads to a better estimate is also given.

We derive the precise asymptote of the pairwise error probability for high signal-to-noise ratio (SNR) and apply it to obtain new results concerning transmit beamforming and selective Rake receivers. For downlink beamforming (with N transmit antennas and independently identically distributed (i.i.d.) Rayleigh fading) based on quantized feedback from the mobile, we show that at least /spl lceil/log/sub 2/(N)/spl rceil/ bits of feedback (per coherence time) is required to obtain full diversity, and among all beamforming schemes using /spl lceil/log/sub 2/(N)/spl rceil/ bits of feedback, selection diversity is optimal. We give the exact expression for the SNR loss of selection diversity with respect to ideal beamforming based on perfect knowledge of fading coefficients. Further, we study selective Rake receivers for independent arbitrary fading distribution and arbitrary power delay profile (PDP). In particular, we show that the SNR loss of the SRake receiver with respect to the all-Rake receiver does not depend on the PDP, and we also propose a transformation to adapt the expressions known for the symbol error probability for the case of i.i.d. Rayleigh fading to the general case.

We consider the problem of hiding images in images. In addition to the usual design constraints such as imperceptible host degradation and robustness in presence of variety of attacks, we impose the condition that the quality of the recovered signature image should be better if the attack is milder. We present a simple hybrid analog-digital hiding technique for this purpose. The signature image is compressed efficiently (using JPEG) into a sequence of bits, which is hidden using a previously proposed digital hiding scheme. The residual error between the original and compressed signature image is then hidden using an analog hiding scheme. The results show (perceptual as well as mean-square error) improvement as the attack becomes milder.

In this paper we consider a hypothesis testing approach for detection of hiding in the least significant bit (LSB). This steganalysis problem is a composite hypothesis testing problem. We state a regularity condition on the image histogram, which reduces this problem to a simple hypothesis testing problem. We then develop a number of simple practical tests based on the estimation of the optimal log likelihood ratio statistic. We show that our tests significantly outperform Stegdetect, a popular hypothesis test available in the literature. Our approach also leads to good estimates of the hiding rate.

We study the global convergence of the stochastic gradient constant modulus algorithm (CMA) in the absence of channel noise as well as in the presence of channel noise. The case of fractionally spaced equalizer and/or multiple antenna at the receiver is considered. For the noiseless case, we show that with proper initialization, and with small step size, the algorithm converges to a zero-forcing filter with probability close to one. In the presence of channel noise such as additive Gaussian noise, we prove that the algorithm diverges almost surely on the infinite-time horizon. However, under suitable conditions, the algorithm visits a small neighborhood of the Wiener filters a large number of times before ultimately diverging.

For the least mean square (LMS) algorithm, we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state. We establish the convergence of the second-order statistics as the number of iterations increases, and we derive the exact asymptotic expressions for the mean square errors. In particular, the result for the excess signal estimation error gives conditions under which the LMS algorithm outperforms the Wiener filter with the same number of taps. We also analyze a new measure of transient speed. We do not assume a linear regression model: the desired signal and the data process are allowed to be nonlinearly related. The data is assumed to be an instantaneous transformation of a stationary Markov process satisfying certain ergodic conditions.

A definition of multiresolution analysis (MRA) of Gaussian processes is proposed. The problem, in a natural way, reduces to the MRA of the associated reproducing kernel Hilbert space. We then show that for processes synthesized from Gaussian white process by fractional integration of order /spl alpha//spl ges/1, this definition is applicable. The MRA results in an orthogonal expansion of these processes. The region of interest is the positive real line. Using this representation then a decomposition of a wider class of Gaussian processes is given. This representation is multiscale in two ways: firstly, the Gaussian process is split into various component processes characterized by the smoothness of their sample paths and secondly, each of these component processes has a MRA as defined in this paper.