Systematic Construction of Real Lapped Tight Frame Transforms

We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.

A multiresolution approach to automated classification of protein subcellular location images

Background

Fluorescence microscopy is widely used to determine the subcellular location of proteins. Efforts to determine location on a proteome-wide basis create a need for automated methods to analyze the resulting images. Over the past ten years, the feasibility of using machine learning methods to recognize all major subcellular location patterns has been convincingly demonstrated, using diverse feature sets and classifiers. On a well-studied data set of 2D HeLa single-cell images, the best performance to date, 91.5%, was obtained by including a set of multiresolution features. This demonstrates the value of multiresolution approaches to this important problem.

Results

We report here a novel approach for the classification of subcellular location patterns by classifying in multiresolution subspaces. Our system is able to work with any feature set and any classifier. It consists of multiresolution (MR) decomposition, followed by feature computation and classification in each MR subspace, yielding local decisions that are then combined into a global decision. With 26 texture features alone and a neural network classifier, we obtained an increase in accuracy on the 2D HeLa data set to 95.3%.

Conclusion

We demonstrate that the space-frequency localized information in the multiresolution subspaces adds significantly to the discriminative power of the system. Moreover, we show that a vastly reduced set of features is sufficient, consisting of our novel modified Haralick texture features. Our proposed system is general, allowing for any combinations of sets of features and any combination of classifiers.