Multiresolution Filtering Research Articles

Balanced multiresolution for symmetric/antisymmetric filters

Given a set of symmetric/antisymmetric filter vectors containing only regular multiresolution filters, the method we present in this article can establish a balanced multiresolution scheme for images, allowing their balanced decomposition and subsequent perfect reconstruction without the use of any extraordinary boundary filters. We define balanced multiresolution such that it allows balanced decomposition i.e. decomposition of a high-resolution image into a low-resolution image and corresponding details of equal size. Such a balanced decomposition makes on-demand reconstruction of regions of interest efficient in both computational load and implementation aspects. We find this balanced decomposition and perfect reconstruction based on an appropriate combination of symmetric/antisymmetric extensions near the image and detail boundaries. In our method, exploiting such extensions correlates to performing sample (pixel/voxel) split operations. Our general approach is demonstrated for some commonly used symmetric/antisymmetric multiresolution filters. We also show the application of such a balanced multiresolution scheme in real-time focus+context visualization.

Focal-plane sensing-processing: a power-efficient approach for the implementation of privacy-aware networked visual sensors.

The capture, processing and distribution of visual information is one of the major challenges for the paradigm of the Internet of Things. Privacy emerges as a fundamental barrier to overcome. The idea of networked image sensors pervasively collecting data generates social rejection in the face of sensitive information being tampered by hackers or misused by legitimate users. Power consumption also constitutes a crucial aspect. Images contain a massive amount of data to be processed under strict timing requirements, demanding high-performance vision systems. In this paper, we describe a hardware-based strategy to concurrently address these two key issues. By conveying processing capabilities to the focal plane in addition to sensing, we can implement privacy protection measures just at the point where sensitive data are generated. Furthermore, such measures can be tailored for efficiently reducing the computational load of subsequent processing stages. As a proof of concept, a full-custom QVGA vision sensor chip is presented. It incorporates a mixed-signal focal-plane sensing-processing array providing programmable pixelation of multiple image regions in parallel. In addition to this functionality, the sensor exploits reconfigurability to implement other processing primitives, namely block-wise dynamic range adaptation, integral image computation and multi-resolution filtering. The proposed circuitry is also suitable to build a granular space, becoming the raw material for subsequent feature extraction and recognition of categorized objects.

Spiking neural network model of cortical auditory source segregation

Humans have the remarkable ability to tune into a particular voice even in loud noisy environments. The neural underpinnings of this amazing perceptual phenomenon are not yet fully understood. Recent EcoG [1] and MEG studies [2] have established that the neural representation of the attended speaker’s speech is much stronger than the unattended (distractor) speech when human subjects are asked to pay attention to a target speaker in a mixture of speech. How the brain sieves through the mixture waveform to enhance the target speaker’s speech and attenuate the background acoustic scene is still being investigated. In this work, we propose a spiking neural network architecture based on the theory of temporal coherence [3] to achieve auditory source segregation. Our model does not require training on the background noise or prior exposure to the target speech. Along with using bottom-up spectro-temporal features and pitch features, the model can also accommodate top-down attentional mechanisms to generate segregated phase locked neural representations to target speaker’s speech envelope. The model comprises of a feature extraction stage followed by clustering stage. The feature extraction stage mimics the auditory pathway starting from a cochlear representation followed by a multi-resolution analysis of the cochlear output using a bank of band-pass filters (cortical stage), to provide a rich timbre representation. Dominant pitch tracks are extracted from the sound mixture and processed through the same set of band-pass filters as the timbre channels. The output of the feature extraction stage comprising of the pitch and timbre channels are transduced into a spike-based representation using leaky integrate and fire neurons with time constants tuned to the bandwidth of the multi-resolution band-pass filters. The clustering stage comprises of a bank of coincidence detector neurons. Using the pitch signals as anchors the coincidence detector neurons can segregate the two sources from the mixture timbre representation. Thus, the output of the coincidence detector neurons comprises only of responses phase locked to the envelope of a single source. This model does not require any weight learning, is unsupervised and can segregate sources online. Previous studies on correlation based sound segregation employed network of neurons with intrinsic oscillator dynamics [4]. In this work, clustering of features belonging to a single source is driven only by the temporal coherence of spectro-temporal features of the given source. This spike-based representation provides an easy mechanism to group coherent features, which otherwise would require computationally expensive numerical routines for online, adaptive principal components analysis. Future work is aimed at reconstructing the speech waveform from the segregated spike trains.

An Image Denoising Framework with Multi-resolution Bilateral Filtering and Normal Shrink Approach

In this study, an image denoising algorithm is presented, which takes into account wavelet thresholding and bilateral filtering in transform domain. The proposed algorithm gives an extension of the bilateral filter i.e., multiresolution bilateral filter, in which bilateral filtering is applied to the approximation sub bands and normal shrink is used for thresholding the wavelet coefficients of the detail sub bands of an image decomposed using a wavelet filter bank up to 2-level of decomposition. The algorithm is tested against ultrasound image of gall bladder corrupted by different types of noise namely, gaussian, speckle, poisson and impulse. The result shows that with increase in decomposition levels the proposed method is effective in eliminating noise but gives overly smoothed image. The algorithm outperforms with speckle and poisson noise at 2- level decomposition in terms of PSNR.

Idealizing Ion Channel Recordings by a Jump Segmentation Multiresolution Filter

Based on a combination of jump segmentation and statistical multiresolution analysis for dependent data, a new approach called J-SMURF to idealize ion channel recordings has been developed. It is model-free in the sense that no a-priori assumptions about the channel’s characteristics have to be made; it thus complements existing methods which assume a model for the channel's dynamics, like hidden Markov models. The method accounts for the effect of an analog filter being applied before the data analysis, which results in colored noise, by adapting existing muliresolution statistics to this situation. J-SMURF’s ability to denoise the signal without missing events even when the signal-to-noise ratio is low is demonstrated on simulations as well as on ion current traces obtained from gramicidin A channels reconstituted into solvent-free planar membranes. When analyzing a newly synthesized acylated system of a fatty acid modified gramicidin channel, we are able to give statistical evidence for unknown gating characteristics such as subgating.

BinShrink: A multi-resolution filter with cache efficient averaging.

We present a new filter for the Insight Toolkit (ITK) for reducing the resolution of an image by an integer factor while averaging called BinShrink. This filter provides a new level of performance to ITK for reducing resolution and noise present in an image. The filter supports streaming, multi-threading and most of ITK’s pixel types including scalars, Vectors, SymmetricSecondRankTensors, and RGBPixels. The filter has been optimized to efficiently access the input image thereby greatly increasing performance over conventional methods.

Fuzzy Clustering with Multi-Resolution Bilateral Filtering for Medical Image Segmentation

Although fuzzy c-means (FCM) algorithm and some of its variants have been extensively widely used in unsupervised medical image segmentation applications in recent years, they more or less suffer from either noise sensitivity or loss of details, which always is a key point to medical image processing. This paper presents a novel FCM variation method that is suitable for medical image segmentation. The proposed method, typically by incorporating multi-resolution bilateral filter which is combined with wavelet thresholding, provides the following advantages: (1) it is less sensitive to both high- and low-frequency noise and removes spurious blobs and noisy spots, (2) it yields more homogeneous clustering regions, and (3) it preserves detail, thus significantly improving clustering performance. By the use of synthetic and multiple-feature magnetic resonance (MR) image data, the experimental results and quantitative analyses suggest that, compared to other fuzzy clustering algorithms, the proposed method further enhances the robustness to noisy images and capacity of detail preservation.

A novel image denoising scheme based on fusing multiresolution and spatial filters

The denoising of natural images corrupted by noise is a long established problem in signal or image processing. This paper proposes an effective denoising scheme to remove Gaussian noise by combining spatial filtering and multiresolution techniques. The spatial filter employed here is Joint Bilateral Filter. The Bilateral Filter is a nonlinear filter that does spatial averaging without smoothing edges; it has shown to be an effective image denoising technique. The Joint Bilateral Filter is similar to Bilateral Filter, but it needs a reference image for the parameter estimation. In the proposed scheme, noise-free image is taken as the reference image. The multiresolution techniques applied in this paper are Wavelet Transform, Contourlet Transform and Non-Subsampled Contourlet Transform. In the transformed domain, Bayes thresholding is performed on the detail subbands, while Joint Bilateral Filter is applied as the pre-filter and post-filter. The performance is evaluated in terms of Peak Signal to Noise Ratio, Image Quality Index and Edge Keeping Index. The experimental results proved that this algorithm is competitive with other denoising schemes.

Analytic Signal Based Detection of Extracellular Action Potentials

A method for calculating the instantaneous energy of extracellularly recorded action potentials using the analytic signal has been developed and tested. The energy is computed from the recorded signal with Hilbert filter based multi-resolution energy filters with optimized signal to noise ratio. The computed instantaneous energy is used for threshold based detection of action potentials in the signals.

Ultrasound Medical Image denoising using Hybrid Bilateral filtering

Medical imaging is placing a major role in diagnosing the diseases and in image guided surgery. There are various imaging modalities for different applications giving the anatomical and physiological conditions of the patient. All these modalities will introduce some amount of noise and artifacts during medical image acquisition. If the noise and artifacts are not minimised diagnosis will become difficult. One of the non-invasive modality is ultrasound where no question of radiation but suffers from speckle noise produced by the small particles in the tissues who’s size is less than the wavelength of the ultrasound. The presence of the speckle noise will cause the low contrast images where low contrast lesions and tumors can’t be detected in the diagnostic phase. So there is a strong need in developing the despeckling techniques to improve the quality of ultrasound images.Many image denoising techniques based on spatial filtering, total variational filtering, bilateral filtering and multiresolution filtering etc. In most of the filtering techniques the objective is removing the noise while preserving the edges in the image. Still research is going on in the improvement of denoising procedures without losing the diagnostic details. Here in this paper we are proposing a method which will combine the bilateral filtering and multiresolution approach (Discrete Wavelet Transform) to remove the noise from ultrasound medical images. The advantage of this method is it removes the noise in the approximation subband or low frequency subband in the wavelet decomposition. The performance of the filtering was evaluated using several image quality metrics and the results showed that the proposed hybrid filter is outperforming the methods based on wavelet transforms and spatial filtering.

A Multi-Resolution Fast Filter Bank for Spectrum Sensing in Military Radio Receivers

In this paper, we propose a multi-resolution filter bank (MRFB)-based on the fast filter bank design for multiple resolution spectrum sensing in military radio receivers. The proposed method overcomes the constraint of fixed sensing resolution in spectrum sensors based on conventional discrete Fourier transform filter banks (DFTFB). The flexibility in realizing multiple sensing resolution spectrum sensor is achieved by suitably designing the prototype filter and efficiently selecting the varying resolution subbands without hardware re-implementation. Design examples show that the sensing performance of proposed MRFB is comparable to that of conventional fixed resolution DFTFB. The complexity comparison shows that the proposed MRFB architecture has a gate count reduction of 36.5% over the DFTFB. The proposed MRFB architecture achieves an average power reduction of 20.8% over DFTFB.

An Optimization Algorithm for Orthogonal Trivariate Wavelets with Short Support

Wavelet analysis is nowadays a widely used tool in applied mathe-matics. The advantages of wavelet packets and their promising features in various application have attracted a lot of interest and effort in recent years.. The notion of vector-valued binary wavelets with two-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with multi-scale is discussed. A necessary and sufficient condition is presented by means of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal vector-valued wave-lets with compact support is proposed, and their properties are investigated.

A Procedure for Designing Vector-valued Compactly Supported Wavelets

Abstract Wavelet analysis has been applied to many aspects in science and technology. The notion of vector-valued wavelets with four-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with quarternary-scale is discussed. A necessary and sufficient condition is presented by means of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal vector-valued wavelets with compact support is proposed, and their orthogonal properties are discussed.

A Feasible Algorithm for Designing Biorthogonal Bivariate Vector-valued Finitely Supported Wavelets

Abstract Wavelet analysis has been developed a new branch for over twenty years. The concept of vector-valued binary wavelets with two-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with two-scale is discussed. A necessary and sufficient condition is provided by means of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal vector-valued wavelets with compact support is proposed, and their orthogonal properties are investigated.

Construction of a type of Biorthogonal Binary Wave Functions by Multiresolution Analysis Approach

Abstract Wavelet analysis is nowadays a widely used tool in applied mathematics. The concept of vector-valued binary wavelets with two-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with two-scale is discussed. A necessary and sufficient condition is provided by means of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal vector-valued wavelets with compact support is proposed, and their orthogonal properties are investigated.

Adaptive multiresolution non-local means filter for three-dimensional magnetic resonance image denoising

In this study, an adaptive multiresolution version of the blockwise non-local (NL)-means filter is presented for three-dimensional (3D) magnetic resonance (MR) images. On the basis of an adaptive soft wavelet coefficient mixing, the proposed filter implicitly adapts the amount of denoising according to the spatial and frequency information contained in the image. Two versions of the filter are described for Gaussian and Rician noise. Quantitative validation was carried out on BrainWeb datasets by using several quality metrics. The results show that the proposed multiresolution filter obtained competitive performance compared with recently proposed Rician NL-means filters. Finally, qualitative experiments on anatomical and diffusion-weighted MR images show that the proposed filter efficiently removes noise while preserving fine structures in classical and very noisy cases. The impact of the proposed denoising method on fibre tracking is also presented on a HARDI dataset.

Scalable Video Compression Framework With Adaptive Orientational Multiresolution Transform and Nonuniform Directional Filterbank Design

Although wavelet-based scalable video coding becomes the state-of-the-art video compression engine for its adaptability to heterogeneous networks and clients, a large number of attempts have been made to integrate local directionality onto discrete wavelet transform to explore the intrinsic geometrical structures. Taking into consideration that the contours and textures scattered in different scales change their directional resolutions as their curvatures change, we investigate adaptive directional resolutions along scales to achieve the dual (scale and orientation) multiresolution transform. This paper proposes nonuniform directional frequency decompositions for video representation and approximation, and exploits the nonuniformity of orientation multiresolution distribution and designs nonuniform directional filter banks to make the geometrical transform more sparse and efficient. The nonuniform directional frequency decomposition under arbitrary scales is fulfilled by a non-symmetric binary tree (NSBT) topology structure with nonuniform directional filterbank design. In turn, the proposed scalable video coding framework, called DMSVC, is enriched with the dual multiresolution transform. Each temporal subband through motion compensated temporal filtering is further decomposed into multiscale subbands, and the highpass wavelet subspaces are divided into an arbitrary number of directional subspaces in alignment with the orientation distribution via phase congruency to establish NSBT. The paraunitary perfect reconstruction condition is provided through a polyphase identical form of filter bank. Comparing with the isolated wavelet basis, our transform provides a greater correlated set of localized and anisotropic basis functions. The spatio-temporal subband coefficients are coded by a 3-D ESCOT entropy coding algorithm which is adopted to match the structure of NSBT. Experimental results show that the reconstructed video frames DMSVC in the proposed DMSVC scheme have better visual quality than existing scalable video coding schemes. It could produce higher compression ratio on video sequences full of directional edges and textures.

Smooth reverse Loop and Catmull–Clark subdivision

In this paper we present a new multiresolution technique for general topology surfaces based on reversing subdivision with energy minimization. We first introduce a general reverse subdivision approach that starts from a trial set of biorthogonal multiresolution filters and refines the resulting coarse points using local masks. The refinement step tries to find a good approximation of the fine points while minimizing the local energy of the coarse points in a least-squares sense. This approach is then used to find smooth reverse of the Loop and Catmull–Clark subdivisions. We discuss the advantages of using this technique in various surface editing and synthesis applications.

Ocultamiento del Mensaje de Señales de Voz usando la Transformada de Ondita Haar Discreta

This work introduces a message concealment method for voice signals transmission using codification through multi-resolution filter banks implementation for analysis and synthesis for the Discrete Haar Wavelet Transform. Through these multi-resolution filter banks of Haar wavelet the voice signal can be split in its components, and later a reversible distortion of the synthesis of its multi-resolution component signals is made, obtaining an output signal that, although maintains the same information of the original input signal, hides the message of the carried voice signal in itself. This method can be applied in codified transmission of voice, analog or digital signals, and due to the simplicity of the method it’s suitable to be implemented on digital electronic systems like FPGA, or ASIC.

Application of Wavelet in Highly Ill-Posed Inverse Heat Conduction Problem

In this work, the prefiltering of the sensor data is taken into consideration when solving an inverse heat conduction problem. The temperature data obtained from each sensor is considered as a discrete signal, and discrete wavelet transform in a multi-resolution filter bank structure is utilized for the signal analysis, after which wavelet denoising algorithm is applied to remove noise from data signal. Subsequently, noisy and denoised temperatures are separately used as input data to an inverse heat conduction problem for comparison. The inverse heat conduction problem considered in this article is an inverse volumetric heat source problem, and it is solved using the conjugate gradient method along with the associated adjoint problem used to obtain the gradient of the objective function. Three sets of results in two case studies are compared (i.e., the result obtained from non-noisy data, noisy data, and denoised data). In the case of noisy data, iterative regularization is used to regularize the solution. The root mean square error of the estimated heat source from denoised data is reduced approximately by a factor of seven to nine as compared to those obtained from noisy data.