HYDRA: Hybrid Deep Magnetic Resonance Fingerprinting

Purpose: Magnetic resonance fingerprinting (MRF) methods typically rely on dictio-nary matching to map the temporal MRF signals to quantitative tissue parameters. Such approaches suffer from inherent discretization errors, as well as high computational complexity as the dictionary size grows. To alleviate these issues, we propose a HYbrid Deep magnetic ResonAnce fingerprinting approach, referred to as HYDRA. Methods: HYDRA involves two stages: a model-based signature restoration phase and a learning-based parameter restoration phase. Signal restoration is implemented using low-rank based de-aliasing techniques while parameter restoration is performed using a deep nonlocal residual convolutional neural network. The designed network is trained on synthesized MRF data simulated with the Bloch equations and fast imaging with steady state precession (FISP) sequences. In test mode, it takes a temporal MRF signal as input and produces the corresponding tissue parameters. Results: We validated our approach on both synthetic data and anatomical data generated from a healthy subject. The results demonstrate that, in contrast to conventional dictionary-matching based MRF techniques, our approach significantly improves inference speed by eliminating the time-consuming dictionary matching operation, and alleviates discretization errors by outputting continuous-valued parameters. We further avoid the need to store a large dictionary, thus reducing memory requirements. Conclusions: Our approach demonstrates advantages in terms of inference speed, accuracy and storage requirements over competing MRF method

Optimal quantum detectors for unambiguous detection of mixed states

We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that maximizes the probability of correct detection. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.Comment: Submitted to Phys. Rev.

What's Psychology Worth? A Field Experiment in the Consumer Credit Market

Numerous laboratory studies report on behaviors inconsistent with rational economic models. How much do these inconsistencies matter in natural settings, when consumers make large, real decisions and have the opportunity to learn from experiences? We report on a field experiment designed to address this question. Incumbent clients of a lender in South Africa were sent letters offering them large, short-term loans at randomly chosen interest rates. Psychological “features” on the letter, which did not affect offer terms or economic content, were also independently randomized. Consistent with standard economics, the interest rate significantly affected loan take-up. Inconsistent with standard economics, the psychological features also significantly affected take-up. The independent randomizations allow us to quantify the relative importance of psychological features and prices. Our core finding is the sheer magnitude of the psychological effects. On average, any one psychological manipulation has the same effect as a one half percentage point change in the monthly interest rate. Interestingly, the psychological features appear to have greater impact in the context of less advantageous offers. Moreover, the psychological features do not appear to draw in marginally worse clients, nor does the magnitude of the psychological effects vary systematically with income or education. In short, even in a market setting with large stakes and experienced customers, subtle psychological features that normatively ought to have no impact appear to be extremely powerful drivers of behavior.Behavioral economics, psychology, microfinance, marketing, field experiment, credit markets

On Model-Based RIP-1 Matrices

The Restricted Isometry Property (RIP) is a fundamental property of a matrix enabling sparse recovery. Informally, an m x n matrix satisfies RIP of order k in the l_p norm if ||Ax||_p \approx ||x||_p for any vector x that is k-sparse, i.e., that has at most k non-zeros. The minimal number of rows m necessary for the property to hold has been extensively investigated, and tight bounds are known. Motivated by signal processing models, a recent work of Baraniuk et al has generalized this notion to the case where the support of x must belong to a given model, i.e., a given family of supports. This more general notion is much less understood, especially for norms other than l_2. In this paper we present tight bounds for the model-based RIP property in the l_1 norm. Our bounds hold for the two most frequently investigated models: tree-sparsity and block-sparsity. We also show implications of our results to sparse recovery problems.Comment: Version 3 corrects a few errors present in the earlier version. In particular, it states and proves correct upper and lower bounds for the number of rows in RIP-1 matrices for the block-sparse model. The bounds are of the form k log_b n, not k log_k n as stated in the earlier versio

Undersampled Phase Retrieval with Outliers

We propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations (to address the nonconvexity of the phase retrieval problem), repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization using the alternating directions method of multipliers. Exploiting the generality of this framework, we investigate using a Laplace measurement noise model better adapted to outliers present in the data than the conventional Gaussian noise model. Using simulations, we explore the sensitivity of the method to both the regularization and penalty parameters. We include 1D Monte Carlo and 2D image reconstruction comparisons with alternative phase retrieval algorithms. The results suggest the proposed method, with the Laplace noise model, both increases the likelihood of correct support recovery and reduces the mean squared error from measurements containing outliers. We also describe exciting extensions made possible by the generality of the proposed framework, including regularization using analysis-form sparsity priors that are incompatible with many existing approaches.Comment: 11 pages, 9 figure

The Case for Behaviorally Informed Regulation

Policymakers approach human behavior largely through the perspective of the “rational agent” model, which relies on normative, a priori analyses of the making of rational decisions. This perspective is promoted in the social sciences and in professional schools, and has come to dominate much of the formulation and conduct of policy. An alternative view, developed mostly through empirical behavioral research, provides a substantially different perspective on individual behavior and its policy implications. Behavior, according to the empirical perspective, is the outcome of perceptions, impulses, and other processes that characterize the impressive machinery that we carry behind the eyes and between the ears. These proclivities, research has shown, intrude upon and shape behavior, often quite independently of deliberative intent, and in contrast with normative ideals that people endorse upon reflection. The results are systematic behaviors that are unforeseen and misunderstood by classical policy thinking. A more nuanced behavioral perspective, such research suggests, can yield deeper understanding and improved regulatory insight

Behaviorally Informed Financial Services Regulation

Financial services decisions can have enourmous consequences for household well-being. Households need a range of financial services - to conduct basic transactions, such as receiving their income, storing it, and paying bills; to save for emergency needs and long-term goals; to access credit; and to insure against life\u27s key risks. But the financial services system is exceedingly complicated and often not well-designed to optimize house-hold behavior. In response to the complexity of out financial system, there has been a long running debate about the appropriate role and form of regulation. Regulation is largely stuck in two competing models - disclosure, and usury or product restrictions. This paper explores a different approach, based on insights from behavioral economics on one hand, and an understanding of industrial organization on the other. At the core of the analysis is the interaction between individual psychology and market competition. This is in contrast to the classic model, which relies on the interaction between rational choice and market competition. The introduction of richer psychology complicates the impact of competition. It helps us understand that firms compete based on how individuals will respond to products in the marketplace, and competitive outcomes may not always and in all contexts closely align with improved decisional choice and increased consumer welfare. This paper adopts a behavioral economic framework that considers firm incentives to respond to regulation. Under this framework, outcomes are an equilibrium interaction between individuals with specific psychologies and firms that responds to those psychologies within specific market contexts. Regulation must then address failures in this equilibrium. The model suggests, for example, that in some contexts market participants seek to overcome common human failings (as for example, with under-saving) while in other contexts market participants seek to exploit those failings (as for example, with over-borrowing). Behaviorally informed regulation needs to take account of these different contexts. The paper discusses the specific application of these forces to the case of mortage, credit card, and banking markets. The purpose of this paper is not to champion politics, but to illustrate how a behaviorally informed regulatory analysis would lead to a deeper understanding of the costs and benefits of specific policies

Quantum Detection with Unknown States

We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the probability of a detection error have been derived. In this work, we assume that each of the states in our collection is a mixture of a known state and an unknown state. We investigate two criteria for optimality. The first is minimization of the worst-case probability of a detection error. For the second we assume a probability distribution on the unknown states, and minimize of the expected probability of a detection error. We find that under both criteria, the optimal detectors are equivalent to the optimal detectors of an ``effective ensemble''. In the worst-case, the effective ensemble is comprised of the known states with altered prior probabilities, and in the average case it is made up of altered states with the original prior probabilities.Comment: Refereed version. Improved numerical examples and figures. A few typos fixe