# Biblio

Hierarchical approaches for representation learning have the ability to encode relevant features at multiple scales or levels of abstraction. However, most hierarchical approaches exploit only the last level in the hierarchy, or provide a multiscale representation that holds a significant amount of redundancy. We argue that removing redundancy across the multiple levels of abstraction is important for an efficient representation of compositionality in object-based representations. With the perspective of feature learning as a data compression operation, we propose a new greedy inference algorithm for hierarchical sparse coding. Convolutional matching pursuit with a L0-norm constraint was used to encode the input signal into compact and non-redundant codes distributed across levels of the hierarchy. Simple and complex synthetic datasets of temporal signals were created to evaluate the encoding efficiency and compare with the theoretical lower bounds on the information rate for those signals. Empirical evidence have shown that the algorithm is able to infer near-optimal codes for simple signals. However, it failed for complex signals with strong overlapping between objects. We explain the inefficiency of convolutional matching pursuit that occurred in such case. This brings new insights about the NP-hard optimization problem related to using L0-norm constraint in inferring optimally compact and distributed object-based representations.

This paper proposes a fast and robust procedure for sensing and reconstruction of sparse or compressible magnetic resonance images based on the compressive sampling theory. The algorithm starts with incoherent undersampling of the k-space data of the image using a random matrix. The undersampled data is sparsified using Haar transformation. The Haar transform coefficients of the k-space data are then reconstructed using the orthogonal matching Pursuit algorithm. The reconstructed coefficients are inverse transformed into k-space data and then into the image in spatial domain. Finally, a median filter is used to suppress the recovery noise artifacts. Experimental results show that the proposed procedure greatly reduces the image data acquisition time without significantly reducing the image quality. The results also show that the error in the reconstructed image is reduced by median filtering.

In this paper, a new approach based on Sub-sampled Inverse Fast Fourier Transform (SSIFFT) for efficiently acquiring compressive measurements is proposed, which is motivated by random filter based method and sub-sampled FFT. In our approach, to start with, we multiply the FFT of input signal and that of random-tap FIR filter in frequency domain and then utilize SSIFFT to obtain compressive measurements in the time domain. It requires less data storage and computation than the existing methods based on random filter. Moreover, it is suitable for both one-dimensional and two-dimensional signals. Experimental results show that the proposed approach is effective and efficient.