NASA's Soil Moisture Active Passive (SMAP) satellite mission combines a passive L-band radiometer and an active Synthetic Aperture Radar (SAR) instrument in order to monitor the near-surface soil moisture and freeze-thaw states globally, with a revisit frequency of 2-3 days. SMAP provides three soil moisture products: a high-resolution from the radar, a low-resolution from the radiometer, and an intermediate-resolution from the fusion of the radar and radiometer measurements. Unfortunately, SMAP's SAR instrument halted its transmissions after a short operating period. In order to address this limitation, we introduce a novel post-acquisition computational technique aiming to synthesize the active measurements of SMAP, by exploiting the mathematical frameworks of Sparse Representations and Dictionary Learning. We propose a coupled dictionary learning model which considers joint feature spaces, composed of active and passive images, in order to recover the missing active measurements. We formulate our coupled dictionary learning problem within the context of the Alternating Direction Method of Multipliers. Our experimental results demonstrate the ability of the proposed approach to reconstruct the active measurements, achieving better performance compared to state-of-the-art coupled dictionary learning techniques.
Sparse coding - modelling data vectors as sparse linear combinations of basis elements - has been widely and successfully used in image classification, noise reduction, texture synthesis, audio processing, etc. Although traditional sparse coding with fixed dictionaries like wavelet and curvelet can produce promising results, unsupervised sparse coding has shown its advantage by optimizing the dictionary based on target data provided. However, most of the existing unsupervised sparse coding method failed to consider the high dimensional manifold information. Recently, graph regularized sparse coding has been proposed to incorporate manifold information. Better classification and clustering results have been shown compared with naive unsupervised sparse coding. The authors utilize modified feature-sign search and Lagrange dual algorithm to solve the objective function as two consecutive convex functions. This method relies on large number of iterations to get state-of-art classification and clustering results, which is computational intensive. In this paper, we proposed a novel modified online dictionary learning method which iteratively utilizes modified least angle regression and block coordinate descent method to solve the problem. Instead of getting entire coefficient matrix then generate dictionary matrix, our method updates coefficient vector and dictionary matrix in each inner iteration. Thus, efficiency and accuracy are reserved at same time.