Venkat Chandar

Segmenting and tracking the left ventricle by learning the dynamics in cardiac images

Having accurate left ventricle (LV) segmentations across a cardiac cycle provides useful quantitative (e.g. ejection fraction) and qualitative information for diagnosis of certain heart conditions. Existing LV segmentation techniques are founded mostly upon algorithms for segmenting static images. In order to exploit the dynamic structure of the heart in a principled manner, we approach the problem of LV segmentation as a recursive estimation problem. In our framework, LV boundaries constitute the dynamic system state to be estimated, and a sequence of observed cardiac images constitute the data. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past segmentations. This requires a dynamical system model of the LV, which we propose to learn from training data through an information-theoretic approach. To incorporate the learned dynamic model into our segmentation framework and obtain predictions, we use ideas from particle filtering. Our framework uses a curve evolution method to combine such predictions with the observed images to estimate the LV boundaries at each time. We demonstrate the effectiveness of the proposed approach on a large set of cardiac images. We observe that our approach provides more accurate segmentations than those from static image segmentation techniques, especially when the observed data are of limited quality.

Communication Under Strong Asynchronism

A formulation of the problem of asynchronous point-to-point communication is developed. In the system model of interest, the message codeword is transmitted over a channel starting at a randomly chosen time within a prescribed window. The length of the window scales exponentially with the codeword length, where the scaling parameter is referred to as the asynchronism exponent. The receiver knows the transmission window, but not the transmission time. Communication rate is defined as the ratio between the message size and the elapsed time between when transmission commences and when the decoder makes a decision. Under this model, several aspects of the achievable tradeoff between the rate of reliable communication and the asynchronism exponent are quantified. First, the use of generalized constant-composition codebooks and sequential decoding is shown to be sufficient for achieving reliable communication under strictly positive asynchronism exponents at all rates less than the capacity of the synchronized channel. Second, the largest asynchronism exponent under which reliable communication is possible, regardless of rate, is characterized. In contrast to traditional communication architectures, there is no separate synchronization phase in the coding scheme. Rather, synchronization and communication are implemented jointly. The results are relevant to a variety of sensor network and other applications in which intermittent communication is involved.

A simple message-passing algorithm for compressed sensing

We consider the recovery of a nonnegative vector x from measurements y = Ax, where A ∈ {0, 1}^m×n. We establish that when A corresponds to the adjacency matrix of a bipartite graph with sufficient expansion, a simple message-passing algorithm produces an estimate x^ of x satisfying ∥x-x^∥<inf>1</inf> = O(n over k) ∥x−x^(k)∥1, where x^(k) is the best k-sparse approximation of x. The algorithm performs O(n(log(n over k))² log(k)) computation in total, and the number of measurements required is m = O(k log(n over k)). In the special case when x is k-sparse, the algorithm recovers x exactly in time O(n log(n over k) log(k)). Ultimately, this work is a further step in the direction of more formally developing the broader role of message-passing algorithms in solving compressed sensing problems.

Optimal Sequential Frame Synchronization

We consider the ldquoone-shot frame synchronization problem,rdquo where a decoder wants to locate a sync pattern at the output of a memoryless channel on the basis of sequential observations. The sync pattern of length N starts being emitted at a random time within some interval of size A, where A characterizes the asynchronism level. We show that a sequential decoder can optimally locate the sync pattern, i.e., exactly, without delay, and with probability approaching one as N rarr infin, if the asynchronism level grows as O(eNalpha), with alpha below the synchronization threshold, a constant that admits a simple expression depending on the channel. If alpha exceeds the synchronization threshold, any decoder, sequential or nonsequential, locates the sync pattern with an error that tends to one as Nrarr infin. Hence, a sequential decoder can locate a sync pattern as well as the (nonsequential) maximum-likelihood decoder that operates on the basis of output sequences of maximum length A+N-1, but with far fewer observations.

Asynchronous Capacity per Unit Cost

The capacity per unit cost, or, equivalently, the minimum cost to transmit one bit, is a well-studied quantity under the assumption of full synchrony between the transmitter and the receiver. In many applications, such as sensor networks, transmissions are very bursty, with amounts of bits arriving infrequently at random times. In such scenarios, the cost of acquiring synchronization is significant and one is interested in the fundamental limits on communication without assuming a priori synchronization. In this paper, the minimum cost to transmit B bits of information asynchronously is shown to be equal to (B +H) ksync, where ksync is the synchronous minimum cost per bit and H is a measure of timing uncertainty equal to the entropy for most reasonable arrival time distributions. This result holds when the transmitter can stay idle at no cost and is a particular case of a general result which holds for arbitrary cost functions.

Information Embedding Codes on Graphs with Iterative Encoding and Decoding

We show that linear complexity capacity-approaching information embedding codes exist for information embedding problems. Specifically, we introduce the double-erasure information embedding channel model, and show that in at least some parameter regimes one can achieve rates arbitrarily close to capacity using suitably defined codes on graphs. Furthermore, we show that both encoding and decoding can be implemented with linear complexity by exploiting belief propagation techniques

Update-Efficiency and Local Repairability Limits for Capacity Approaching Codes

Motivated by distributed storage applications, we investigate the degree to which capacity achieving codes can be efficiently updated when a single information symbol changes, and the degree to which such codes can be efficiently repaired when a single encoded symbol is lost. Specifically, we first develop conditions under which optimum error-correction and update-efficiency are possible. We establish that the number of encoded bits that should change in response to a change in a single information bit must scale logarithmically in the block-length of the code, if we are to achieve any nontrivial rate with vanishing probability of error over the binary erasure or binary symmetric channels. Moreover, we show that there exist capacity-achieving codes with this scaling. With respect to local repairability, we develop tight upper and lower bounds on the number of remaining encoded bits that are needed to recover a single lost encoded bit. In particular, we show that when the rate of an optimal code is ε below capacity, the maximum number of codeword symbols required to recover one lost symbol must scale as log1/ε. Several variations on-and extensions of-these results are also developed, including to the problem of rate-distortion coding.

Asynchronous Communication: Capacity Bounds and Suboptimality of Training

Several aspects of the problem of asynchronous point-to-point communication without feedback are developed when the source is highly intermittent. In the system model of interest, the codeword is transmitted at a random time within a prescribed window whose length corresponds to the level of asynchronism between the transmitter and the receiver. The decoder operates sequentially and communication rate is defined as the ratio between the message size and the elapsed time between when transmission commences and when the decoder makes a decision. For such systems, general upper and lower bounds on capacity as a function of the level of asynchronism are established, and are shown to coincide in some nontrivial cases. From these bounds, several properties of this asynchronous capacity are derived. In addition, the performance of training-based schemes is investigated. It is shown that such schemes, which implement synchronization and information transmission on separate degrees of freedom in the encoding, cannot achieve the asynchronous capacity in general, and that the penalty is particularly significant in the high-rate regime.

Error exponents in asynchronous communication

Based on recent work on asynchronous communication, this paper proposes a slotted asynchronous channel model and investigates the fundamental limits of asynchronous communication, in terms of miss and false alarm error exponents. We propose coding schemes that are suitable for various asynchronous communication scenarios, and quantify more precisely the suboptimality of training-based schemes, i.e., communication strategies that separate synchronization from information transmission. In particular, we show that under a broad set of conditions, training-based schemes are suboptimal at all positive rates. Finally, we demonstrate these performance differences by specializing our results to BSCs and AWGN channels.

Local recovery properties of capacity achieving codes

A code is called locally recoverable or repairable if any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed storage where a most frequent error-event is a single storage node failure. A common objective is to repair the node by downloading data from as few other storage node as possible. In this paper we study the basic error-correcting properties of a locally recoverable code. We provide tight upper and lower bound on the local-recoverability of a code that achieves capacity of a symmetric channel. In particular it is shown that, if the code-rate is e less than the capacity then for the optimal codes, the maximum number of codeword symbols required to recover one lost symbol must scale as log 1/ϵ.