Amir Adler

Audio Inpainting

We propose the audio inpainting framework that recovers portions of audio data distorted due to impairments such as impulsive noise, clipping, and packet loss. In this framework, the distorted data are treated as missing and their location is assumed to be known. The signal is decomposed into overlapping time-domain frames and the restoration problem is then formulated as an inverse problem per audio frame. Sparse representation modeling is employed per frame, and each inverse problem is solved using the Orthogonal Matching Pursuit algorithm together with a discrete cosine or a Gabor dictionary. The Signal-to-Noise Ratio performance of this algorithm is shown to be comparable or better than state-of-the-art methods when blocks of samples of variable durations are missing. We also demonstrate that the size of the block of missing samples, rather than the overall number of missing samples, is a crucial parameter for high quality signal restoration. We further introduce a constrained Matching Pursuit approach for the special case of audio declipping that exploits the sign pattern of clipped audio samples and their maximal absolute value, as well as allowing the user to specify the maximum amplitude of the signal. This approach is shown to outperform state-of-the-art and commercially available methods for audio declipping in terms of Signal-to-Noise Ratio.

Sparse coding with anomaly detection

We consider the problem of simultaneous sparse coding and anomaly detection in a collection of data vectors. The majority of the data vectors are assumed to conform with a sparse representation model, whereas the anomaly is caused by an unknown subset of the data vectors—the outliers—which significantly deviate from this model. The proposed approach utilizes the Alternating Direction Method of Multipliers (ADMM) to recover simultaneously the sparse representations and the outliers components for the entire collection. This approach provides a unified solution both for jointly sparse and independently sparse data vectors. We demonstrate the usefulness of the proposed approach for irregular heartbeats detection in Electrocardiogram (ECG) as well as for specular reflectance and shadows removal from natural images.

A constrained matching pursuit approach to audio declipping

We present a novel sparse representation based approach for the restoration of clipped audio signals. In the proposed approach, the clipped signal is decomposed into overlapping frames and the declipping problem is formulated as an inverse problem, per audio frame. This problem is further solved by a constrained matching pursuit algorithm, that exploits the sign pattern of the clipped samples and their maximal absolute value. Performance evaluation with a collection of music and speech signals demonstrate superior results compared to existing algorithms, over a wide range of clipping levels.

Probabilistic Subspace Clustering Via Sparse Representations

We present a probabilistic subspace clustering approach that is capable of rapidly clustering very large signal collections. Each signal is represented by a sparse combination of basis elements (atoms), which form the columns of a dictionary matrix. The set of sparse representations is utilized to derive the co-occurrences matrix of atoms and signals, which is modeled as emerging from a mixture model. The components of the mixture model are obtained via a non-negative matrix factorization (NNMF) of the co-occurrences matrix, and the subspace of each signal is estimated according to a maximum-likelihood (ML) criterion. Performance evaluation demonstrate comparable clustering accuracies to state-of-the-art at a fraction of the computational load.

A shrinkage learning approach for single image super-resolution with overcomplete representations

We present a novel approach for online shrinkage functions learning in single image super-resolution. The proposed approach leverages the classical Wavelet Shrinkage denoising technique where a set of scalar shrinkage functions is applied to the wavelet coefficients of a noisy image. In the proposed approach, a unique set of learned shrinkage functions is applied to the overcomplete representation coefficients of the interpolated input image. The super-resolution image is reconstructed from the post-shrinkage coefficients. During the learning stage, the lowresolution input image is treated as a reference high-resolution image and a super-resolution reconstruction process is applied to a scaled-down version of it. The shapes of all shrinkage functions are jointly learned by solving a Least Squares optimization problem that minimizes the sum of squared errors between the reference image and its super-resolution approximation. Computer simulations demonstrate superior performance compared to state-of-the-art results.

Linear-Time Subspace Clustering via Bipartite Graph Modeling

We present a linear-time subspace clustering approach that combines sparse representations and bipartite graph modeling. The signals are modeled as drawn from a union of low-dimensional subspaces, and each signal is represented by a sparse combination of basis elements, termed atoms, which form the columns of a dictionary matrix. The sparse representation coefficients are arranged in a sparse affinity matrix, which defines a bipartite graph of two disjoint sets: (1) atoms and (2) signals. Subspace clustering is obtained by applying low-complexity spectral bipartite graph clustering that exploits the small number of atoms for complexity reduction. The complexity of the proposed approach is linear in the number of signals, thus it can rapidly cluster very large data collections. Performance evaluation of face clustering and temporal video segmentation demonstrates comparable clustering accuracies to state-of-the-art at a significantly lower computational load.

A weighted discriminative approach for image denoising with overcomplete representations

We present a novel weighted approach for shrinkage functions learning in image denoising. The proposed approach optimizes the shape of the shrinkage functions and maximizes denoising performance by emphasizing the contribution of sparse overcomplete representation components. In contrast to previous work, we apply the weights in the overcomplete domain and formulate the restored image as a weighted combination of the post-shrinkage overcomplete representations. We further utilize this formulation in an offline Least Squares learning stage of the shrinkage functions, thus adapting their shape to the weighting process. The denoised image is reconstructed with the learned weighted shrinkage functions. Computer simulations demonstrate superior shrinkage-based denoising performance.

Block-based compressed sensing of images via deep learning

Compressed sensing (CS) is a signal processing framework for efficiently reconstructing a signal from a small number of measurements, obtained by linear projections of the signal. Block-based CS is a lightweight CS approach that is mostly suitable for processing very high-dimensional images and videos: it operates on local patches, employs a low-complexity reconstruction operator and requires significantly less memory to store the sensing matrix. In this paper we present a deep learning approach for block-based CS, in which a fully-connected network performs both the block-based linear sensing and non-linear reconstruction stages. During the training phase, the sensing matrix and the non-linear reconstruction operator are jointly optimized, and the proposed approach out-performs state-of-the-art both in terms of reconstruction quality and computation time. For example, at a 25% sensing rate the average PSNR advantage is 0.77dB and computation time is over 200-times faster.