121 results about "Generalized inverse" patented technology

The invention discloses a robust controller of a permanent magnet synchronous motor based on a fuzzy-neural network generalized inverse and a construction method thereof. The construction method of the invention comprises the following steps of: combining an internal model controller and a fuzzy-neural network generalized inverse to form a compound controlled object; serially connecting two linear transfer functions and one integrator with the fuzzy-neural network with determined parameters and weight coefficients to form the fuzzy-neural network generalized inverse, serially connecting the fuzzy-neural network generalized inverse and the compound controlled object to form a generalized pseudo-linear system, linearizing a PMSM (permanent magnet synchronous motor), and decoupling and equalizing the linearized PMSM into a second-order speed pseudo-linear subsystem and a first-order current pseudo-linear subsystem; and respectively introducing an internal-model control method in the two pseudo-linear subsystems to construct the internal model controller. The robust controller of the invention has the advantages of overcoming the dependence and local convergence of the optimal gradient method on initial values and solving the problems of randomness and probability caused by using the simple genetic algorithm, obtaining the high performance control, anti-disturbance performance and adaptability of the motor and simplifying the control difficulty, along with simple structure and high system robustness.

The invention discloses a constructing method of a nerval net generalized inversing bearingless permanent magnet synchronous motor decoupling controlling device, which takes two Clark inverse transformations, two electric current tracing type inverters, a bearingless permanent magnet and a load model as a whole to form a composite controlled object, a nerval net generalized inverse of the composite controlled object is formed through adopting static nerval net added with a plurality of linear links, then the nerval net generalized inverse is reversely arranged before the composite controlled object to form a generalized pseudolinear system, the generalized pseudolinear system is decoupled to three single input and output subsystems through linearization, finally a nerval net generalized inverse, the two Clark inverse transformations and the two electric current tracing type inverters are all formed to a nerval net generalized inversing bearingless permanent magnet synchronous motor controlling device, the controlling device can not only realize dynamic decoupling between a radial position system of a motor and torque moment system and between radial forces, but also be taken as a nonlinear open-cycle controlling device to use directly, and stable suspension and operation of a rotor of a motor can be ensured.

The invention relates to a PSO (Particle Swarm Optimization) extremity learning machine based strip steel exit thickness predicting method, which basically comprises the steps below: 1) analyzing a strip steel data signal by utilizing a data processing software, selecting four parameters which greatly influence the thickness of the strip steel exit and includes a roll force, a roll gap, a roll speed and a motor current, and inputting the four parameters as input variables into an extremity learning machine in the prediction of the thickness of the strip steel exit; 2) performing selective optimization on parameter input weights and a hidden layer offset value in the extremity learning machine by using the PSO, analyzing and determining output weights by applying a generalized inverse way to obtain an output weight matrix with a minimum norm value in the extremity learning machine, and accordingly obtain optimal parameters of the extremity learning machine; 3) modeling the obtained optimal extremity learning machine; 4) predicting the thickness of the strip steel exit by inputting the four parameters in the step 1) into the optimized extremity learning machine. By applying the PSO extremity learning machine based strip steel exit thickness predicting method, analysis aiming at the rolling production process is carried out, the prediction for the thickness of a rolled piece exit is performed, relevant technical parameters affecting the quality of the strip steel are further analyzed, and real-time control and adjustment for the rolling production process are further carried out.

The invention discloses a method for constructing a neutral network generalized inverse adaptive controller of a three-motor driving system. Three frequency converters respectively drive three induction motors to drive a load to form the three-motor driving system, the rotating speed setting values of the three frequency converters are set by S7-300 PLC (Programmable Logic Controller), the neutral network generalized inverse of the three-motor driving system is constructed by using a static neutral network, two integrators and three transfer functions, and the neutral network generalized inverse is connected in front of the three-motor driving system to form a pseudo linear compound system. Corresponding fuzzy adaptive controllers are respectively designed for one speed subsystem and two tension subsystems to form a fuzzy adaptive closed-loop controller, and the fuzzy adaptive closed-loop controller and the neutral network generalized inverse are connected in series to form the neutral network generalized inverse adaptive controller. Control parameters can be adjusted online according to system errors, the starting time and the overshoot of the system can be greatly reduced, and the tracking accuracy and the tracking speed of the system are obviously increased.

The invention discloses a networked AC (alternating current) motor LS-SVM (least squares support vector machine) generalized inverse decoupling control method based on active-disturbance rejection. According to the method, an SVPWM (space vector pulse width modulation) controller, a three-phase voltage type PWM (pulse width modulation) inverter, a AC asynchronous motor, Clarke transformation, a rotor flux linkage observer and K / P transformation are connected to form a composite controlled object, and an LS-SVM generalized inverse system and the composite controlled object are connected in series to form a pseudo-linear composite system, and the AC asynchronous motor is decoupled into a rotating speed pseudo-linear sub-system and a rotor flux linkage pseudo-linear sub-system; active-disturbance rejection control is introduced into the pseudo-linear composite system, and networked closed-loop control is formed by communication network actuator nodes and sensor nodes. According to the technical scheme, the defects of low control accuracy, unknown AC motor model or parameters, difficulties in the inverse system construction under small sample condition, weak external disturbance robustness in a network environment, poor open-loop stability and the like in the prior art can be overcome, so that linear decoupling and high-performance control of the AC asynchronous motor can be realized in the network environment.

The invention discloses a quick sparse Radon transformation method based on iterative shrinkage. The quick sparse Radon transformation method comprises the following steps: firstly, setting an initial variable value; secondly, constructing a transformation operator L and calculating generalized inverse (LTL)-1LT of the transformation operator L; thirdly, treating a seismic channel set d to be treated by utilizing the generalized inverse (LTL)-1LT of the transformation operator L; and lastly, judging if all channel sets in a seismic data cube are treated, if not, continuing to treat the seismic channel set d to be treated by utilizing the generalized inverse (LTL)-1LT of the transformation operator L, and if so, ending. According to the quick sparse Radon transformation method, for one seismic data cube collected by adopting the same collection parameters, the generalized inverse of the transformation operator L only needs to be calculated once, then the transformation operator L and the generalized inverse (LTL)-1LT of the transformation operator L are applied to all seismic channel sets, thereby greatly reducing calculated amount; and the iterative shrinkage algorithm only includes product operation of simple matrixes and vectors and threshold operation, greatly reduces the calculated amount relative to the conventional sparse Radon transformation, and better adapts to treatment of practical seismic data.

The invention provides a method for analyzing DC power flow in a dynamictopology electric grid, belonging to the electric grid safety technical field. The method is characterized in that the method sets up an incidence matrix and a transmission line admittance matrix; according to net injection powers of electric grid nodes, the generalized inverse solution power flow equation is used. The method can be applied to connected or disconnected electric grids, and the analysis for the topological connectivity of the electric grid is unnecessary, and the selection of reference nodes in the electric grid is also unnecessary, thereby the method brings great convenience for analyzing DC power flow in the dynamictopology electric grid.

The invention relates to a gradient descent and generalized inverse-based complex-valued neural network training method. The method includes the following steps that: step 1, a single-hidden layer complex-valued neural network model is selected; step 2, the gradient descent and generalized inverse are utilized to calculate a weight matrix and a weight vector in the single-hidden layer complex-valued neural network model; step 3, the network parameters of the complex-valued neural network model are obtained according to the weight matrix and the weight vector, and mean square error is calculated, and 1 is added to the number of iterations, and the method returns to the step 2. According to the method of the invention, the input weight of a hidden layer is generated through the gradient descent, and the output weight of the hidden layer is always solved by the generalized inverse. The method of the invention has the advantages of small number of iterations, short corresponding training time, high convergence speed and high learning efficiency, and just needs few hidden layer nodes. Therefore, the method of the invention can reflect the performance of the complex-valued neural network more accurately compared with a BSCBP (Batch Split-Complex Backpropagation Algorithm) method and a CELM (Complex Extreme Learning Machine) method.

The invention discloses a super high-rise building wind load inverse analysis method based on discrete Kalman filtering. The method comprises the following steps: (1) converting wind-induced response components (displacement or velocity) of limited test floors of a structure into modal wind-induced responses based on actually measured modal shapes of first orders; (2) estimating unknown modal wind-induced response components by using discrete Kalman filtering; (3) identifying the modal wind-induced load of the structure through the estimated modal wind-induced responses (displacement, velocity and acceleration); (4) obtaining the wind load time-history of any floor of the structure by using the generalized inverse of a modal shape matrix. The method can solve the problem that the wind-induced response measuring points of super high-rise buildings are not enough. Wind load inversion results obtained by adopting the method under the influence of structure modal parameter errors, modal truncation errors and measurement noises can still satisfy engineering demands. The research technique provides a useful tool and basis for wind-resistant design of super high-rise buildings and relevant researches.

The invention provides an implementation method for a reconfigurable aircraft control system. The system comprises a controller module, a torque control and distribution module, a rudder face reconfiguration distributor, a vector thrust reconfiguration controller, two fault recognition units and a state measurement unit. The reconfigurable control system is designed through a weighted generalized inverse method; when an execution mechanism fails, the rapid configurability of the control system can be achieved by only changing the weighted value of a control efficiency weighting matrix without changing the control law; by introducing an indirect control amount, the reversing of the control matrix is not related to the state of the execution mechanism, offline calculation can be achieved, and the calculation amount of a controller is reduced.

The invention discloses a pipe network leak detecting method in combination with resistance identification, relates to pipe network leak detecting methods and aims to solve the problems that passive leakage control methods mainly need a large number of instruments, equipment and manpower and are hardly combined with automatic monitored control systems, and large deviation of optimization results due to a small number of samples and long consuming time exist in artificial neural network methods. The pipe network leak detecting method in combination with resistance identification includes that firstly, pressure observed values of flow nodes of part of pipe sections are used as known conditions; an equation set containing pipe section resistance information is established; resistance results are expressed through generalized inverse solution of the equation set. Then, a pipeline where leakage possibly occurs is divided into a plurality of different areas; in each area, observed values of operation parameters of an edge pipe network are used as known conditions, virtual nodes are introduced to represent leakage points, and specific positions and leakage flow of the virtual nodes are determined by the aid of genetic algorithm optimization; accordingly, leakage is positioned and quantified. Then sequential manual troubleshooting and re-checking is performed. The pipe network leak detecting method in combination with resistance identification is applicable to the field of pipe network leak detection.

A system and methods for reducing memory traffic and power consumption when solving systems of linear equations. Certain embodiments provide several aspects for improved performance in solving a consistent system of linear equations and in computing a generalized inverse. One aspect involves performing row transformations on AX=B, so that the transformed A contains row vectors that are either zero or are part of an orthonormal set. Another aspect involves performing column transformations on A, so that A contains column vectors that are either zero or are part of an orthonormal set. Another aspect involves performing row eliminations differently so that a variation of an LU factorization is obtained that is in a more directly useful form.

The invention discloses a cross-spectrum generalized inverse beam forming method based on cross-spectrum optimization. Firstly, a steering matrix is constructed based on the traditional generalized inverse beam formation. Secondly, an acoustic pressure cross-spectrum matrix is optimized through a linear optimization method. Finally, through the obtained steering matrix and the optimized acoustic pressure cross-spectrum matrix and according to the traditional idea of cross-spectrum matrix beam formation, a novel cross-spectrum generalized inverse beam forming algorithm based on an optimized cross-spectrum matrix is constructed. The algorithm can make full use of the anti-noise performance of cross-spectrum beam formation based on cross-spectrum optimization while taking advantage of high resolution of generalized inverse beam formation.

Methods and systems for robust and flexible extraction of image information using color filter arrays. Methods are provided comprising receiving a sample set of data generated by transforming and sampling an optical property of an original color image in a spatial basis, wherein the transformation effected is substantially local in the spatial basis and has partially overlapping spectra. A generalized inverse of the transform augmented with regularization constraints is applied to the sample set of data to infer original image data. According to one approach the generalized inverse does not use variational minimization or assume constant color ratios. According to an alternative approach regularization can take the form of predetermined spectral constraints applied to the sample set of data to infer the original image data. According to another alternative approach regularization can promote spectral sparsity. Methods are also provided for creating an optical color filter array, for sampling an image, for reducing noise in an image, and for computing a sparse representation of an image signal. Systems for carrying out these and other methods are also provided.

The invention discloses a wireless sensor network positioning method based on the RSSI vector similarity degree and generalized inverse. Gauss curve fitting is carried out on the probability of a specific RSSI value occurring at different distances, piecewise linear interpolation is carried out on an RSSI-d (relation between intensity and distances) curve, and a positioning algorithm that a quadrangle serves as a positioning unit, internal positioning of the positioning unit and external positioning of the positioning unit are carried out, and areas where nodes are likely to exist are rapidly locked is designed; meanwhile, by compassion of the similarity degree between RSSI vectors of unknown nodes and RSSI vectors of reference nodes, the reference anchor node nearest to the unknown nodes is continuously updated and determined, and the area where the unknown nodes are located is narrowed; for the situation that the distance measurement error is random and can not be controlled due to randomness of RSSI measurement errors, the generalized inverse method is introduced as the supplement of the positioning algorithm, the whole positioning algorithm is perfected, and the actual feasibility of the algorithm is improved.

The invention discloses a construction method for a neural network generalized inverse decoupling controller of a bearing-free synchronous reluctance motor, which comprises the steps: taking two Park inverse converting type inverters, two Clark inverse converting type inverters and two direct current tracking type inverters as a wholly-formed composite controlled object after the two Park inverse converting type inverters, the two Clark inverse converting type inverters and the two direct current tracking type inverters are respectively and sequentially connected with one another in series and before the two Park inverse converting type inverters, the two Clark inverse converting type inverters and the two direct current tracking type inverters are connected with the bearing-free synchronous reluctance motor; forming a generalized imitative linear system before a constructed neural network generalized inverse is connected with the composite controlled object in series, and forming a linear closed loop controller by two position controllers and a speed controller; and jointly forming the neural network generalized inverse decoupling controller by the means that the linear closed loop controller, the neural network generalized inverse, the two Park inverse converting type inverters, the two Clark inverse converting type inverters and the two direct current tracking type inverters are respectively and sequentially connected with one another in series. The independent decoupling control between the electromagnetic torque and the radial levitation force and the independent decoupling control of the radial levitation force between two components on the vertical direction are realized according to the closed ring control and the PID (proportion integration differentiation) parameter adjustment, and the control performance of the bearing-free synchronous reluctance motor is obviously improved.

The invention belongs to the field of magnetic resonance imaging, discloses an improved reconstruction method for parallel magnetic resonance images and particularly relates to a reconstruction method suitable for K spatial data in the parallel magnetic resonance imaging process. According to the method, when a weight coefficient is fitted, estimation is carried out with a K spatial data area and a self-calibration data area near undersampled data instead of adjacent points and a self-calibration line, and thus the nonlinear relation of K spatial data can be better fitted; noise in the sampled signals can be suppressed in the singular value decomposition and truncation processing process, and it is ensured that the signal-to-noise ratio of images is high. The method is a GRAPPA improving method based on matrix generalized inverse and singular value decomposition, the noise of the K spatial data can be suppressed, the fitting precision can be improved, and meanwhile the imaging quality can still be ensured when an acceleration factor is large.

The invention discloses a low-frequency oscillation parameter identification method based on an improved Prony algorithm. The original matrix inversion operation is replaced by a neural network; a matrix to be solved is used as a weight; the weight is adjusted through a gradient descent; a low-frequency oscillation parameter of the Prony algorithm is solved; repetitive solving of generalized inverse of a complex matrix is avoided; simultaneously, cyclical iteration is adopted; calculation is simply carried out; the precision is relatively high; whether a cost function is in a given precision range or not can be checked through correction of the weight; therefore, calculation is carried out more simply and effectively; operation of a synchronous phasor measurement device is optimized; and furthermore, reliable original data and data support are provided for functions, such as wide-area monitoring of an all-system power grid, automatic measurement and control of a transformer substation, steady control and self-adaptive relay protection.

Indexes of commercial property prices face much scarcer transactions data than housing indexes, yet the advent of tradable derivatives on commercial property places a premium on both high frequency and accuracy of such indexes. The dilemma is that with scarce data a low-frequency return index (such as annual) is necessary to accumulate enough sales data in each period. This invention presents an approach to address this problem using a two-stage procedure with frequency conversion, by first estimating lower-frequency indexes staggered in time, and then applying a generalized inverse estimator to convert from lower to higher frequency return series. The two-stage procedure can improve the accuracy of high-frequency indexes in scarce data environments, and also can mitigate an errors-in-variables problem that arises at very high frequency even with plentiful data (e.g., monthly indexes). In this paper the method is demonstrated and analyzed via simulation analysis and by application to empirical commercial property repeat-sales data.

The invention discloses a construction method of a fuzzy neural network generalized inverse controller of a chassis nonlinear system. An active suspension system and an electric power steering system form the integrally-formed chassis nonlinear system based on vertical and transverse motions. A fuzzy neural network and five linear elements are adopted to form a fuzzy neural network generalized inverse of the chassis nonlinear system. The fuzzy neural network generalized inverse is arranged in front of the chassis nonlinear system, and a generalized pseudo-linear system is formed through composition. The generalized pseudo-linear system is decoupled into five linear one-step subsystems, poles of five linear one-step subsystems can be reasonably configured in a complex plane by reasonably adjusting parameters of the generalized inverse system, and accordingly open loop decoupling control of the chassis nonlinear system is achieved. The controller can independently serve as an open loop controller to be directly used without an additional closed loop controller, and the controller is low in cost and easy to achieve.

The invention discloses a horizontal position control method based on a characteristic model. The method comprises the following steps of firstly, based on motion model analysis in a horizontal plane, through generalized inverse processing, acquiring a characteristic model form in which input and output are simultaneously decoupled and giving out a parameter range; and then operating a cycle control process; based on the characteristic model and the parameter range, carrying out on-line identification and acquiring a characteristic parameter estimation value; based on the characteristic parameter estimation value, designing a controller and calculating to acquire a control law; carrying out generalized interference estimation and estimating generalized interferences of two channels in the horizontal plane; carrying out coupling and conservative distribution processing and calculating to acquire an execution mechanism command; carrying out detection, configuration and decoupling processing, and calculating actual control amounts of the two channels. The control method adopts combination of adaptive combination control and generalized interference compensation based on the characteristic parameter estimation value so that simultaneous decoupling of the input and output is realized and maintenance precision of the horizontal position under the condition that a wind field changes randomly is increased.

The invention discloses a neural network generalized inverse decoupling controller of an automobile chassis integrated system. The automobile chassis integrated system is composed of a driving front-wheel steering sub-system, a direct yawing moment control sub-system and a driving suspension frame sub-system of an automobile chassis. A static neural network and a plurality of linear elements form a neural network generalized inverse of the automobile chassis integrated system, and the neural network generalized inverse and the automobile chassis integrated system are connected in series to form a generalized pseudo-linear system. The generalized pseudo-linear system is decoupled to form three pseudo-linear sub-systems with single input and single output. A linear closed-loop controller is used for carrying out PID regulation on the pseudo-linear sub-systems. The linear closed-loop controller and the neural network generalized inverse form the neural network generalized inverse decoupling controller of the automobile chassis integrated system. The invention further relates to a constriction method of the neural network generalized inverse decoupling controller of the automobile chassis integrated system.

The invention discloses a method for identifying surrounding rock load on an outer surface of a three-dimensional TBM shield, and relates to the technical field of high-efficiency tunneling and safetycontrol of a deep tunnel shield type TBM. The method comprises: 1, installing a strain monitoring sensor on a preset measuring point on an inner surface of a TBM shield; 2, obtaining strain measureddata of the measuring point [epsilon]m; 3, establishing a finite element calculation model of the TBM shield; 4, obtaining a load identification parameter through partition of the shield outer surface; 5, through Newton iteration and Moore-Penrose generalized inverse solution, obtaining surrounding rock load on the outer surface of the shield; 6, performing integration on the load to obtain outersurface friction resistance of the shield. The method has high calculation precision and good visualization effect, and is suitable for identification of outer surface load of the TBM shield on site,and can provide guidance for safe construction of tunneling, early warning of a stuck machine, and accident handling.

The invention relates to an active power distribution network coordination optimization control method considering ZIP loads. The method comprises the following steps of inputting control variables in a network topology, determining object functions and constraining conditions, building an active power distribution network coordination optimization model considering the ZIP loads; and acquiring the optimal solution of the active power distribution network optimization model according to an optimization algorithm based on function transformation and generalized inverse. The method which provides a theory base for optimization control achieves simple operations. The coordination optimization control efficiency is improved. The power grid running quality and stability are further improved.

The invention discloses a five-point relative orientation method based on forward intersection constraints. The method comprises the steps: firstly, shooting two images, with different visual angles, of an object to be measured, wherein the two images respectively comprise five points; secondly, constructing a coplanarity equation of the five pairs of points; thirdly, constructing a five-point relative orientation function based on the forward intersection constraints; fourthly, constructing an iterative equation of relative orientation elements, deriving and solving an unconstrained optimization objective function for the five-point relative orientation problem by constructing a homologous image point coplanar condition function containing the forward intersection constraints and orthogonality constraints, and solving the five relative orientation elements through the least-squares generalized inverse algorithm. Compared with an existing five-point algorithm, it can be guaranteed that the five pairs of homologous rays respectively intersect without removing error solutions. In addition, the method is high in solving precision and good in robustness and has practical value.

The invention provides a robust controller of an automotive chassis integrated system and a construction method. The controller is composed of an internal model controller and a support vector machine generalized inverse system, wherein the internal model controller is composed of a side slip angle internal model controller body, a yaw velocity internal model controller body and a vehicle roll angle internal model controller body, the support vector machine generalized inverse system is in series connection with the automotive chassis integrated system to form a generalized pseudo-linear system, the support vector machine generalized inverse system is composed of a support vector machine and four linear links, the generalized pseudo-linear system comprises a side slip angle linear subsystem, a yaw velocity linear subsystem and a vehicle roll angle linear subsystem, and the automotive chassis integrated system is composed of an active front steering subsystem, a direct yaw moment control subsystem and an active suspension subsystem. According to the robust controller, the defects of control methods of existing automotive chassis integrated systems are eliminated, and the decoupling control among the side direction, the longitudinal direction and the vertical direction of the automotive chassis system can be achieved.

The present invention relates to an experimental apparatus for predicting the multi-point vibration response frequency domain under the condition of the unknown load; an experimental data generation method for predicting the multi-point vibration response frequency domain under the condition of the unknown load; and a method for predicting frequency domain vibration response of the unknown measure point according to the frequency domain vibration response of the known measure point by using the experimental apparatus and the experimental data, and by using the multiple linear regression model and the least squares generalized inverse method of the linear relationship between frequency domain response data under the unrelated multi-source unknown load combined excitation. The multiple linear regression model and the least squares generalized inverse method of the linear relationship between frequency domain response data are directly used instead of knowing or identifying the transfer function, the load size, or even the load position of the system. According to the technical scheme of the present invention, mainly for the environment of the unrelated multi-source unknown load combined excitation, vibration response prediction of the unknown node is carried out by using the vibration response prediction of the known measure point, so that vibration response situation of one unknown node and a plurality of unknown nodes can be predicted.

The invention provides a ghost reflection removing method through a transmission matrix method. The ghost reflection removing method comprises the steps that single-channel seismic data received by each detector are acquired; a ghost reflection transmission matrix equation is established: Gm=d, and a model data vector m without ghost reflection is solved through generalized inverse solution of a G matrix, wherein m is the model data vector without ghost reflection, and D is an observation data vector with ghost reflection; and as for the single-channel seismic data received by each detector, ghost reflection noise in the single-channel seismic data is removed by repeating the step S2 until the seismic channel data received by all the detectors are completely processed, and finally the seismic data without ghost reflection are outputted. The problem of no source wavelet in processing can be effectively avoided so that the ghost reflection removing method is simple, the obtained result has high resolution and the band is broadened.

The invention discloses a random orthogonal expansion method for solving the uncertain heat conduction problem. The method comprises the following steps of performing quantification representation on uncertain parameters in the heat conduction problem by introducing random variables; building a random differential control equation of the heat conduction problem by combining the random variables; selecting an orthogonal polynomials substrate function according to the random variable distribution type; performing orthogonal expansion on the random temperature response; giving the collocation point number of each random variable; building a collocation point set of the whole uncertain space by using a tensor product law; calculating the temperature response in positions of all collocation points; solving each coefficient in the temperature response orthogonal expansion formula by using the generalized inverse of a matrix; and calculating the average value and the standard deviation of the random temperature response according to the orthogonal relationship of the substrate function. The method has the advantages that the heat conduction problem containing random uncertain parameters can be systematically solved; the calculation precision of a random uncertain analysis method is further improved; and the effect cannot be achieved by general commercial software.

Methods and systems for robust and flexible extraction of image information using color filter arrays. Methods are provided comprising receiving a sample set of data generated by transforming and sampling an optical property of an original color image in a spatial basis, wherein the transformation effected is substantially local in the spatial basis and has partially overlapping spectra. A generalized inverse of the transform augmented with regularization constraints is applied to the sample set of data to infer original image data. According to one approach the generalized inverse does not use variational minimization or assume constant color ratios. According to an alternative approach regularization can take the form of predetermined spectral constraints applied to the sample set of data to infer the original image data. According to another alternative approach regularization can promote spectral sparsity. Methods are also provided for creating an optical color filter array, for sampling an image, for reducing noise in an image, and for computing a sparse representation of an image signal. Systems for carrying out these and other methods are also provided.