The use of frames, or over-complete dictionaries, for sparse signal representation has been given considerable attention in recent years. The major challenges are good algorithms for sparse approximations, and good methods for choosing or designing frames. We are concerned with the latter, and have developed algorithms for training frames for a class of data and a specific application. The presented application is the denoising of images with additive Gaussian noise. We present a method for training of constrained overlapping frames to be used for denoising of images. Experiments show that the proposed method improves denoising results compared to adaptive Wiener filtering and wavelet denoising.

This paper describes a general design method for signal dependent frames, or over-complete dictionaries. The design method is developed for block-oriented frames, overlapping frames, and constrained frames, which can be regarded as extensions of, respectively, block-oriented transforms, filter banks, and general filter banks like wavelets. The frames are optimized for sparse representation of a signal class. Using the designed frames and a matching pursuit algorithm it is shown that superior, compared to other methods, sparse representations are achieved for an electrocardiogram signal. It is also demonstrated that compression based on these sparse representations gives excellent performance at low bit rates.

Iterative techniques for solving (large) sets of linear equations is an active research field in applied mathematics. Such techniques constitute an insignificant part, if any part at all, of the background of electrical and computer engineers. We argue that some exposure to such techniques is beneficial in the study of digital signal processing. While important in their own right, we show that the knowledge of such techniques facilitates a complementary understanding/interpretation of digital filters as equation solvers. Such connections between seemingly unrelated fields enhance the learning experience. Perhaps more importantly, we also show that elementary iterative equation solvers can be used as a vehicle for an introduction to adaptive filters at an elementary level.

In this contribution we present a novel algorithm for multichannel adaptive filtering. The algorithm is based on selective update of filter coefficients using a matching pursuit-like strategy operating on a time varying “dictionary” given by the current multichannel data matrix. The algorithm has low computational complexity and is robust in rank deficient situations. We present the adaptive filter in an application oriented setting in which the objective is to remove artifacts in electrocardiograms (ECG) resulting from cardiopulmonary resuscitation (CPR). We present simulation results on realistic data showing the superior performance of the algorithm.

We use a frame-based representation approach for compression of still images. The frames are optimized for use on images by using a training set of six natural images in the frame design algorithm we have called method of optimal directions (MOD). The optimized frames are investigated, and a compression experiment using a frame is done and compared to JPEG. A set of frames optimized using MOD are used in a multi frame compression (MFC) scheme. A test image is compressed using the MFC scheme with the optimized frames. For low bit rates the results show improved performance compared to JPEG.

Traditional signal decompositions generate signal expansions using the analysis-synthesis setting: the expansion coefficients are found by taking the inner product of the signal with the corresponding analysis vector. In this paper we try to free ourselves from the analysis-synthesis paradigm by concentrating on the synthesis or reconstruction part of the signal expansion. Ignoring the analysis issue completely, we construct sets of synthesis vectors, denoted waveform dictionaries, for sparse signal representation. The objective is to approximate a training signal using a small number of dictionary vectors. Our algorithm optimize the dictionary vectors with respect to the average non-linear approximation error. Using signals from a Gaussian, autoregressive process with correlation factor 0.95, it is demonstrated that for established signal expansions like the Karhunen-Loeve transform, the lapped orthogonal transform, and the biorthogonal 7/9 wavelet, it is possible to improve the approximation capabilities by up to 30% by optimizing the expansion vectors.

This paper deals with the problem of texture feature extraction in digital mammograms. Our main goal is to generate texture features that are able to "summarize" meaningful information in the mammogram. Subsequently, we use these features to discriminate between texture representing clusters of microcalcifications and texture representing normal tissue. Having a two-class problem, we suggest a texture feature extraction method based on a single filter optimized with respect to the Fisher criterion. The advantage of this criterion is that it uses both the feature mean and the feature variance to achieve good feature separation. Results from an experimental study indicate that the proposed method is useful for texture feature extraction in digital mammograms.

A frame design technique for use with vector selection algorithms, for example matching pursuits (MP), is presented. The design algorithm is iterative and requires a training set of signal vectors. The algorithm, called method of optimal directions (MOD), is an improvement of the algorithm presented by Engan, Aase and Husoy see (Proc. ICASSP '98, Seattle, USA, p.1817-20, 1998). The MOD is applied to speech and electrocardiogram (ECG) signals, and the designed frames are tested on signals outside the training sets. Experiments demonstrate that the approximation capabilities, in terms of mean squared error (MSE), of the optimized frames are significantly better than those obtained using frames designed by the algorithm of Engan et. al. Experiments show typical reduction in MSE by 20-50%.

We present a signal compression scheme based on coding linear segments approximating the signal. Although the approach is useful for many types of signals, we focus in this paper on compression of electrocardiogram (EGG) signals. The ECG signal compression has traditionally been tackled by heuristic approaches. However, it has been demonstrated that exact optimization algorithms outclass these heuristic approaches by a wide margin with respect to the reconstruction error. The exact optimization algorithm extracts signal samples from the original signal by formulating the sample selection problem as a graph theory problem. Thus known optimization theory can be applied in order to yield optimal compression. This paper generalizes the exact optimization scheme by removing the interpolation restriction when applying piecewise linear approximation. This guarantees a lower reconstruction error with respect to the number of extracted signal samples. The method shows superior performance compared to traditional ECG compression methods.

In this paper, we review most major filtering approaches to texture feature extraction and perform a comparative study. Filtering approaches included are Laws masks (1980), ring/wedge filters, dyadic Gabor filter banks, wavelet transforms, wavelet packets and wavelet frames, quadrature mirror filters, discrete cosine transform, eigenfilters, optimized Gabor filters, linear predictors, and optimized finite impulse response filters. The features are computed as the local energy of the filter responses. The effect of the filtering is highlighted, keeping the local energy function and the classification algorithm identical for most approaches. For reference, comparisons with two classical nonfiltering approaches, co-occurrence (statistical) and autoregressive (model based) features, are given. We present a ranking of the tested approaches based on extensive experiments.

The design of filters for texture feature extraction is addressed. Based on a new feature extraction model, optimization approaches utilizing various feature (energy) separation criteria are developed. Both two- and multiple-texture problems are addressed. The approaches are assessed by supervised segmentation experiments. The experiments also include results from alternative filter optimization approaches.

A technique for designing frames to use with vector selection algorithms, for example matching pursuits (MP), is presented. The design algorithm is iterative and requires a training set of signal vectors. An MP algorithm chooses frame vectors to approximate each training vector. Each vector in the frame is then adjusted by using the residuals for the training vectors which used that particular frame vector in their expansion. The frame design algorithm is applied to speech and electrocardiogram (ECG) signals, and the designed frames are tested on signals outside the training sets. Experiments demonstrate that the approximation capabilities, in terms of mean square error (MSE), of the optimized frames are significantly better than those found using frames designed by ad hoc techniques. Experiments show typical reduction in MSE by 20-50%.

Compression of image contours is an important problem in many contexts. An example is object oriented video coding, where efficient encoding of shape information of arbitrarily shaped objects is a major problem. This paper presents a method for compressing contours by extracting representative points from the original curve. By formulating the point selection problem as a graph theory problem, known optimization theory can be applied in order to yield optimal compression with respect to a given error bound. The contour is reconstructed based on linear interpolation among the extracted curve points. The method presented guarantees a minimal distortion for a given number of retained curve points. Compared to many other compression methods, this method shows superior performance.

A new scheme for color and texture feature extraction for image content search is presented. We introduce a scheme using the two chrominance components for color information and a computationally efficient infinite impulse response (IIR) quadrature mirror filter bank (QMF) energy measure of the luminance component for texture information. The color and texture information is combined into one feature vector, and the components are balanced with respect to dimensionality. We illustrate the utility of our features with experiments in searching for a specific color texture in a large database of images. Several different sub-band decompositions are evaluated. Features extracted using a previously published Gabor filter bank are also evaluated against the proposed scheme. We conclude that the proposed scheme outperforms the Gabor features in both quality and complexity.

An important category of texture features are features extracted by filters together with a filter response energy measure. Most approaches to texture filtering use filter banks which are selected by some heuristic criteria and which are not optimal with respect to the given data. Some approaches to optimal filter design have been presented. A few approaches to multi-texture optimal filter bank design have also been presented, but they are all restricted to very small sets of free parameters. In this paper a new technique for multiple texture optimal design of a bank of general finite impulse response (FIR) filters is presented. A closed form optimal solution is obtained by modeling the feature extraction for the textures.

This paper deals with the design of a finite impulse response filter for optimal feature extraction in texture segmentation/classification. Motivated by the Fisher criterion, we develop techniques for optimal filter design. Posing some restrictions on the data, we are able to find a closed form solution to the problem, and we develop a unifying framework for this and several other approaches. We also show how the optimal filters may be designed, using less restrictive assumptions and a gradient search.

The principle of subband coding has recently been applied for the purpose of image data compression. In this paper we present new results pertaining to our subband coder for images featuring an exact reconstruction parallel complex filter bank based on HR filters. This filter bank is characterized by its low complexity. The main advantage of subband coding is the possibility of separate coding of each subband such that the perceptually important coding noise is minimized. In this paper we exploit the nature of the complex valued subband signals of this particular coder by coding the module and phase rather than the real and imaginary parts. We determine the tolerable quantization noise levels for the module and phase signals in all subbands. These empiricaly derived data are employed in the coding simulations presented. Finally we present coding results for bit rates between 0.25 and 1.0 bits/pel.

Filter banks based on recursive filters have recently been applied with success in subband coding of still images [1, 2]. Their main feature, low computational complexity, make these filter banks extremely attractive for video coding applications. In. this paper we demonstrate the suitability of these filter banks in low bit rate image sequence coders operating in the 64 —200 Kbps range. In particular we compare the performance of two types of recursive filter banks with that of a more traditional one based on quadrature mirror FIR filters (QMF). It is shown that the performance of our hR based systems is comparable to that of the more complex FIR based systems. Also, we show that the encoding strategy of CCITT's reference model no. 7 can be adapted successfully to fit into our subband coding scheme. Finally we discuss alternative approaches to motion estimation in hybrid image sequence coders and show preliminary results in the context our video subband coder.