CIF: Small: Adaptive signal representation for accelerated multidimensional imaging

高分辨率多维图像数据的采集在若干生物医学应用中变得越来越重要（例如，光谱成像和心脏成像）。通常，成像设备在追求高时空/空间光谱分辨率时被推到其极限，导致若干伪影和SNR损失。最近，使用约束图像模型从次奈奎斯特采样测量中恢复图像数据已经成为一种有前途的替代方案。使用预定模型的一个挑战是表示和数据集之间的不匹配;通常需要许多系数来表示手头的信号。这项工作的主要重点是开发一种新的理论框架和有效的算法，以适应图像表示欠采样测量。我们特别关注盲表示或自适应表示，这与基于预定字典的经典方法有很大不同。通过使信号模型适应测量，我们期望从更少数量的测量中获得无偏重建。我们制定的联合估计的表示和信号从整个欠采样的数据作为一个单一的优化问题，其中的标准是只依赖于恢复的信号。这使得开发高效的优化算法、使用定制的成本函数进行性能优化以及确定完美恢复的条件成为可能。这种方法有望大大提高几种多维成像方案的分辨率，这将促进几种具有非常重要意义的基础科学和临床应用;拟议的研究是真正的变革。通过软件共享和数据共享，研究与教学的整合以及精心设计的外展计划，加强了这项工作的影响。

The acquisition of high resolution multi-dimensional image data is becoming increasingly important in several bio-medical applications (e.g., spectroscopic imaging and cardiac imaging). Very often, imaging devices are pushed to their limits in the quest for high spatio-temporal/spatial-spectral resolution, resulting in several artifacts and SNR loss. Recently, the recovery of the image data from sub-Nyquist sampled measurements using constrained image models has emerged as a promising alternative. A challenge in using pre-determined models is the misfit between the representation and dataset; many coefficients are often required to represent the signal at hand. The main focus of this work is to develop a novel theoretical framework and efficient algorithms to adapt image representations to under-sampled measurements. We specifically focus on blind or adaptive representations, which are a significant departure from classical approaches based on pre-determined dictionaries. By adapting the signal model to measurements, we expect to obtain unbiased reconstructions from far smaller numbers of measurements. We formulate the joint estimation of the representation and the signal from the entire under-sampled data as a single optimization problem, where the criterion is only dependent on the recovered signal. This enables the development of efficient optimization algorithms, performance optimization using tailored cost functions, and determination of the conditions for perfect recovery. This approach is expected to considerably improve the resolution in several multi-dimensional imaging schemes, which will facilitate several basic science and clinical applications of very high significance; the proposed research is truly transformative. The impact of this work is strengthened by the sharing of software and data-sharing, integration of research and teaching, and well-designed out-reach program.